This paper proposes an algorithm for decomposing and possibly distributing an optimization problem that naturally emerges in distributed manipulation by shaping physical force fields through actuators distributed in space (arrays of actuators). One or several manipulated objects located in this field can “feel the force” and move simultaneously and independently. The control system has to produce commands for all actuators so that desired forces are developed at several prescribed places. This can be formulated as an optimization problem that has to be solved in every sampling period. Exploiting the structure of the optimization problem is crucial for platforms with many actuators and many manipulated objects, hence the goal of decomposing the huge optimization problem into several subproblems. Furthermore, if the platform is composed of interconnected actuator modules with computational capabilities, the decomposition can give guidance for the distribution of the computation to the modules. We propose an algorithm for decomposing/distributing the optimization problem using Alternating Direction Method of Multipliers (ADMM). The proposed algorithm is shown to converge to modest accuracy for various distributed platforms in a few iterations. We demonstrate our algorithm through numerical experiments corresponding to three physical experimental platforms for distributed manipulation using electric, magnetic, and pressure fields. Furthermore, we deploy and test it on real experimental platforms for distributed manipulation using an array of solenoids and ultrasonic transducers.

%8 February %0 Journal Article %J Control Engineering Practice %D 2023 %T Controlled synchronization of coupled pendulums by Koopman Model Predictive Control %A Do, Loi %A Korda, Milan %A Zdeněk Hurák %P 105629 %R 10.1016/j.conengprac.2023.105629 %V 139 %XWe propose a method to solve a class of control problems arising from a system of coupled pendulums. The system considered in this work is a one-dimensional array of pendulums pivoting around a single axis with adjacent pendulums coupled through torsion springs. Only a single torque motor attached to one of the two boundary pendulums actuates the system. This setup of coupled pendulums is a mechanical realization of the Frenkel–Kontorova (FK) model – a spatially discrete version of the sine-Gordon equation describing (nonlinear) waves. The main challenges of controlling this system are high order (the number of pendulums can be high), nonlinear and oscillatory dynamics, and only one actuator. The proposed class of problems can be characterized as controlled synchronization – designing a closed-loop controller that synchronizes the motion of the pendulums. Controlled synchronization is a special case of reference tracking, where all pendulums reach a common point or a trajectory. One can formulate many practically motivated problems within this class; here, we identify three problems: a vibration control of a flexible structure, swing-up control of all pendulums in the array, and low-friction sliding of an atomic-scale structure. We show that the presented problems can be dealt with by the Koopman Model Predictive Control (KMPC). The KMPC allows for controlling nonlinear systems by combining the classical linear model predictive control (MPC) with the Koopman operator approach for nonlinear dynamical systems. The main idea of the method is to construct a linear predictor of a nonlinear system in a higher-dimensional, lifted space and use the predictor within the linear MPC. The optimization problem formulation within the KMPC can then be tailored to a specific problem in the class. Simulations and experiments on a hardware platform realizing the FK model show the effectiveness of the method.

%8 10 %0 Conference Paper %B 2023 IEEE International Conference on Robotics and Automation (ICRA) %D 2023 %T Trajectory Optimization for Distributed Manipulation by Shaping a Physical Field %A Uchytil, Adam %A Jiří Zemánek %C London %P 10111-10117 %R 10.1109/ICRA48891.2023.10160720 %X Trajectory optimization is used to solve various planning tasks. In this paper we present a optimization-based method that solves a planning problem for multiple independent objects manipulated by a spatially continuous physical field. The field is generated and controlled (shaped) in real time by an array of actuators. In the paper we first formulate a trajectory optimization problem and a related initialization scheme, and then we demonstrate the proposed method using an experimental platform for distributed magnetic manipulation. The demonstrated task is that of planar reconfiguration of an ensemble of multiple objects, which significantly benefits from the inherent parallelism of the manipulation enabled by the array of actuators shaping the physical field. We show that the system can rearrange up to eight objects simultaneously while avoiding collisions. %0 Conference Paper %B 2022 IEEE 61st Conference on Decision and Control (CDC)2022 IEEE 61st Conference on Decision and Control (CDC) %D 2022 %T Experimental Platform for Boundary Control of Mechanical Frenkel-Kontorova Model %A Do, Loi %A Pucejdl, Kristof %A Hurak, Zdenek %C Cancun, Mexico %I IEEE %P 7618 - 7623 %R 10.1109/CDC51059.2022.9992448 %V 8 %XIn this paper, we present a laboratory mechatronic platform for experimental demonstration and verification of various dynamical and control system phenomena exhibited by the Frenkel-Kontorova (FK) model – a spatially discretized version of the sine-Gordon equation. The platform consists of an array of spring-coupled pendulums pivoting around a single axis with the first and the last pendulums controlled by motors and all pendulums’ angles measured electronically. We first introduce and describe the platform, providing details of its mechatronic design and software architecture. All the design files are freely shared with the research community under an open-source license through a public repository. The platform can be used as a testbed for various control algorithms, e.g., for distributed control or control of flexible structures. In the second part of the paper, we showcase the platform using two control problem formulations tailored to the FK model. We discuss the practical motivation for studying these problems, propose methods for solving them, and experimentally demonstrate their functionality. In particular, the first control formulation deals with the non-collocated stabilization of a single pendulum through one boundary of the array in the presence of a disturbance sent from the other boundary; the second control problem consists in synchronizing pendulums’ angular speeds. Other problems can certainly be formulated, solved, and demonstrated using the proposed platform, whether for research or education purposes.

%8 December %0 Conference Paper %B 3rd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems MICNON 2021 %D 2021 %T Synchronization in the Frenkel-Kontorova Model with Application to Control of Nanoscale Friction %A Do, Loi %A Zdeněk Hurák %E Yuh Yamashita %C Tokyo, Japan %N 14 %R https://doi.org/10.1016/j.ifacol.2021.10.388 %U https://www.sciencedirect.com/science/article/pii/S2405896321017948?via%3Dihub %V 54 %XThis paper tailors synchronization of multi-agent systems to motion control of the Frenkel-Kontorova (FK) model, a one-dimensional chain of harmonically coupled identical particles in a spatially periodic potential field. In particular, the goal is to drive all particles in the FK model to the desired trajectory by controlling only a single—boundary—particle. The proposed solution augments harmonic coupling in the FK model with dissipative inter-particle interactions, allowing all particles in the chain to synchronize to a particular reference trajectory. The boundary control represents a special case of pinning control. Moreover, as the FK model describes the frictional dynamics of a nanosheet sliding over a surface, we use its synchronization for controlling the nanoscale sliding friction. The key idea is to introduce a sliding reference trajectory that allows particles to move near synchrony. Synchronization effectively increases the system’s stiffness, so less energy ends up dissipated through inter-particle relative motion, thus reducing the frictional force. We validate the proposed solution through numerical simulations.

%8 September %0 Journal Article %J IEEE Transactions on Control Systems Technology %D 2021 %T Distributed Estimation on Sensor Networks With Measurement Uncertainties %A Knotek, Stefan %A Hengster-Movric, Kristian %A Sebek, Michael %I IEEE %N 5 %P 1997 - 2011 %R 10.1109/TCST.2020.3026815 %V 29 %8 9 %0 Journal Article %J Journal of Vibration and Control %D 2021 %T Decentralized control for large scale systems with inherently coupled subsystems %A Svoboda, Filip %A Hengster-Movric, Kristian %A Martin Hromčík %I SAGE Publications %R 10.1177/10775463211034953 %0 Conference Paper %B IFAC-PapersOnLine %D 2020 %T Queue discharge-based emergency vehicle traffic signal preemption %A Obrusník, Vít %A Herman, Ivo %A Zdeněk Hurák %E Rolf Findeisen %E Sandra Hirche %E Klaus Janschek %E Martin Mönnigmann %C Berlin, Germany %I Elsevier %N 2 %P 14997 - 15002 %R 10.1016/j.ifacol.2020.12.1998 %U https://www.sciencedirect.com/science/article/pii/S240589632032629X %V 53 %XIn this paper, we document a novel method for emergency vehicle preemption at an intersection controlled by traffic lights. The method relies on wireless vehicle-to-infrastructure (V2I) communication between the emergency vehicle and the traffic lights controller, availability of an accurate estimate of the number of vehicles in the queue, and a mathematical model of dynamics of discharging of the queue. Unlike some occasionally deployed methods that trigger the preemption the instant that the emergency vehicle appears at a prespecified distance from the intersection, the proposed method adapts the activation moment to the actual traffic conditions so that the preemption is as short as possible, thus reducing the impact on the other traffic. The method has been finetuned using numerical simulations in SUMO simulator and experimentally verified in real urban traffic.

%8 July %0 Journal Article %J IEEE/ASME Transactions on Mechatronics %D 2020 %T Electrorotation of Arbitrarily Shaped Micro-Objects: Modeling and Experiments %A Michálek, Tomáš %A Bolopion, Aude %A Zdeněk Hurák %A Gauthier, Michael %I IEEE %N 2 %P 828 - 836 %R 10.1109/TMECH.2019.2959828 %V 25 %8 4 %0 Conference Paper %B IFAC-PapersOnLine %D 2020 %T Onboard Model-based Prediction of Tram Braking Distance %A Do, Loi %A Herman, Ivo %A Zdeněk Hurák %E Rolf Findeisen %E Sandra Hirche %E Klaus Janschek %E Martin Mönnigmann %C Berlin, Germany %I Elsevier %N 2 %P 15047 - 15052 %R 10.1016/j.ifacol.2020.12.2006 %U https://www.sciencedirect.com/science/article/pii/S2405896320326409 %V 53 %XIn this paper, we document a design of a computational method for an onboard prediction of a breaking distance for a city rail vehicle—a tram. The method is based on an onboard simulation of tram braking dynamics. Inputs to this simulation are the data from a digital map and the estimated (current) position and speed, which are, in turn, estimated by combining a mathematical model of dynamics of a tram with the measurements from a GNSS/GPS receiver, an accelerometer and the data from a digital map. Experiments with real trams verify the functionality, but reliable identification of the key physical parameters turns out critically important. The proposed method provides the core functionality for a collision avoidance system based on vehicle-to-vehicle (V2V) communication.

%8 2020 %0 Journal Article %J International Journal of Robust and Nonlinear Control %D 2020 %T Distributed adaptive consensus protocol with decaying gains %A Knotek, Štefan %A Hengster‐Movric, Kristian %A Michael Šebek %I Wiley %N 15 %P 6166 - 6188 %R 10.1002/rnc.5056 %V 30 %8 10 %0 Journal Article %J IEEE Robotics and Automation Letters %D 2020 %T Wildfire Fighting by Unmanned Aerial System Exploiting Its Time-Varying Mass %A Saikin, Diego A %A Baca, Tomas %A Gurtner, Martin %A Saska, Martin %I IEEE %P 2674–2681 %R 10.1109/LRA.2020.2972827 %V 5 %0 Journal Article %J Physical Review E %D 2019 %T Control-oriented model of dielectrophoresis and electrorotation for arbitrarily shaped objects %A Michálek, Tomáš %A Bolopion, Aude %A Zdeněk Hurák %A Gauthier, Michaël %N 5 %P 053307 %R 10.1103/PhysRevE.99.053307 %U https://link.aps.org/doi/10.1103/PhysRevE.99.053307 %V 991 %8 May %0 Journal Article %J IEEE Transactions on Control Systems Technology %D 2019 %T Distributed Observer and Controller Design for Spatially Interconnected Systems %A Zhang, Xueji %A Hengster-Movric, Kristian %A Sebek, Michael %A Desmet, Wim %A Faria, Cassio %N 1 %P 1 - 13 %R 10.1109/TCST.2017.2769019 %V 27 %8 January %0 Conference Paper %B 8th IFAC Symposium on Mechatronic Systems MECHATRONICS 2019 %D 2019 %T Optimization-based Feedback Manipulation Through an Array of Ultrasonic Transducers %A Matouš, Josef %A Kollarčík, Adam %A Gurtner, Martin %A Michálek, Tomáš %A Zdeněk Hurák %E Lukasz Jadachowski %C Vienna, Austria %N 15 %P 483 - 488 %R 10.1016/j.ifacol.2019.11.722 %U https://doi.org/10.1016/j.ifacol.2019.11.722 %V 52 %XIn this paper we document a novel laboratory experimental platform for noncontact planar manipulation (positioning) of millimeter-scale objects using acoustic pressure. The manipulated objects are either floating on a water surface or rolling on a solid surface. The pressure field is shaped in real time through an 8-by-8 array (matrix) of ultrasonic transducers. The transducers are driven with square voltages whose phase-shifts are updated periodically every 20 milliseconds based on the difference between the desired and true (estimated from video) position. Numerical optimization is used within every period of a discrete-time feedback loop to determine the phase shifts for the voltages. The platform can be used as an affordable testbed for algorithms for non-contact manipulation through arrays of actuators as all the design and implementation details for the presented platform are shared with the public through a dedicated git repository. The platform can certainly be extended towards higher numbers of simultaneously yet independently manipulated objects and larger manipulation areas by expanding the transducer array.

%8 2019 %0 Journal Article %J IEEE Transactions on Control of Network Systems %D 2018 %T On the necessity of symmetric positional coupling for string stability %A Dan Martinec %A Herman, Ivo %A Michael Šebek %I IEEE %N 1 %P 45 - 54 %R 10.1109/TCNS.2016.2573739 %V 5 %XWe consider a distributed system with identical agents, constant-spacing policy and asymmetric bidirectional control, where the asymmetry is due to different controllers, which we describe by transfer functions. By applying the wave transfer function approach, it is shown that, if there are two integrators in the dynamics of agents, then the positional coupling must be symmetric, otherwise the system is string unstable. The main advantage of the transfer function approach is that it allows us to analyse the bidirectional control with an arbitrary complex asymmetry in the controllers, for instance, the control with symmetric positional but asymmetric velocity couplings.

%8 May %0 Journal Article %J Lab on a Chip %D 2018 %T Phase-shift feedback control for dielectrophoretic micromanipulation %A Jiří Zemánek %A Michálek, Tomáš %A Zdeněk Hurák %I The Royal Society of Chemistry’s %N 12 %P 1793 - 1801 %R 10.1039/C8LC00113H %XIn this paper, we present a novel approach to noncontact micromanipulation by controlled dielectrophoresis (DEP). To steer micro-objects in the desired way, the solutions reported in the literature use either DEP cages or amplitude modulation of the voltages applied to the electrodes. In contrast, we modulate the phases, that is, we control the phase shifts of the voltages applied to the electrodes, which simplifies the hardware implementation and extends the set of feasible forces. Furthermore, we introduce an innovative micro-electrode array layout, composed of four sectors with parallel (colinear) electrodes, which is capable of inducing an arbitrary movement in the manipulation area and is easy to fabricate using just an affordable one-layer technology. We then propose a closed-loop cascade control strategy based on real-time numerical optimization and deploy it to our experimental set-up. Numerical simulations and laboratory experiments demonstrate the manipulation capabilities such as positioning and steering of one or several microscopic objects (microspheres with a diameter of 50 μm) and even bringing two objects together and then separating them again. The results from simulations and experiments are compared and the positioning accuracy is evaluated in the whole manipulation area. The error in position is 8 μm in the worst case, which corresponds to 16% of the microsphere size or 0.7% of the manipulation range.

%8 2018 %0 Journal Article %J International Journal of Robust and Nonlinear Control %D 2018 %T H∞-output regulation of linear heterogeneous multiagent systems over switching graphs %A Adib Yaghmaie, Farnaz %A Movric, Kristian Hengster %A Lewis, Frank L. %A Su, Rong %A Sebek, Michael %N 13 %P 3852 - 3870 %R 10.1002/rnc.4108 %V 28 %8 09 %0 Thesis %D 2018 %T Distributed manipulation by controlling force fields through arrays of actuators %A Jiří Zemánek %I Czech Technical University in Prague %U https://support.dce.felk.cvut.cz/mediawiki/images/9/9f/Diz_2018_zemanek_jiri.pdf %9 Ph.D. thesis %0 Conference Paper %B 2018 26th Mediterranean Conference on Control and Automation (MED)2018 26th Mediterranean Conference on Control and Automation (MED) %D 2018 %T Distributed State Feedback Control for Aeroelastic Morphing Wing Flutter Supression %A Svoboda, Filip %A Hromcik, Martin %A Hengster-Movric, Kristian %C Zadar, Croatia %I IEEE %P 575 - 580 %R 10.1109/MED.2018.8442815 %0 Journal Article %J IEEE Transactions on Control Systems Technology %D 2017 %T Application of the Method of Maximum Likelihood to Identification of Bipedal Walking Robots %A Dolinsky, Kamil %A Celikovsky, Sergej %N 4 %P 1500 - 1507 %R 10.1109/TCST.2017.2709277 %V 26 %8 June %0 Journal Article %J Electrophoresis %D 2017 %T Dipole and multipole models of dielectrophoresis for a non-negligible particle size: Simulations and experiments %A Michálek, Tomáš %A Jiří Zemánek %I Wiley %N 11 %P 1419–1426 %R 10.1002/elps.201600466/full %U http://onlinelibrary.wiley.com/doi/10.1002/elps.201600466/full %V 38 %8 June %0 Journal Article %J IEEE Transactions on Automatic Control %D 2017 %T Scaling in bidirectional platoons with dynamic controllers and proportional asymmetry %A Herman, Ivo %A Dan Martinec %A Zdeněk Hurák %A Michael Šebek %I IEEE %N 4 %P 2034-2040 %R 10.1109/TAC.2016.2594169 %U http://arxiv.org/abs/1410.3943 %V 62 %XWe consider platoons composed of identical vehicles with an asymmetric nearest-neighbor interaction. We restrict ourselves to intervehicular coupling realized with dynamic arbitrary-order onboard controllers such that the coupling to the immediately preceding vehicle is proportional to the coupling to the immediately following vehicle. Each vehicle is modeled using a transfer function and we impose no restriction on the order of the vehicle. The only requirement on the controller and vehicle model is that the platoon is stable for any number of vehicles. The platoon is described by a transfer function in a convenient product form. We investigate how the H-infinity norm and the steady-state gain of the platoon scale with the number of vehicles. We conclude that if the open-loop transfer function of the vehicle contains two or more integrators and the second smallest eigenvalue of the graph Laplacian is uniformly bounded from below, the norm scales exponentially with the growing distance in the graph. If there is just one integrator in the open loop, we give a condition under which the norm of the transfer function is bounded by its steady-state gain - the platoon is string-stable. Moreover, we argue that in this case it is always possible to design a controller for the extreme asymmetry - the predecessor following strategy.

%8 July %0 Conference Paper %B 20th IFAC World Congress %D 2017 %T Vehicular platooning experiments using autonomous slot cars %A Lád, Martin %A Herman, Ivo %A Zdeněk Hurák %C Toulouse, France %U https://www.ifac2017.org/ %XThe paper reports on an affordable experimental platform for vehicular platooning. The experimental platoon consists of several autonomous slot cars (typical experiments take 5 to 20 slot cars), hence it fits into an indoor laboratory. Each car is equipped with an onboard controller and it can measure its own velocity, acceleration, and distances to its nearest neighbors. Furthermore, each car can communicate with other vehicles including the leader of the platoon. A convenient user interface allows to store, analyze and visualize the experimental data in Matlab. The platform can be used for demonstrating various decentralized and distributed control strategies for vehicular platoons, such as predecessor following, (a)symmetric bidirectional control or cooperative adaptive cruise control. Moreover, the phenomenon of string instability can be observed in experiments due to the fast dynamics of slot cars. The technical design details including the source codes and electronic schematics are shared with the public.

%8 July %0 Journal Article %J System and Control Letters %D 2017 %T A travelling wave approach to a multi-agent system with a path-graph topology %A Dan Martinec %A Herman, Ivo %A Michael Šebek %I Elsevier %P 90-98 %R 10.1016/j.sysconle.2016.12.001 %U https://doi.org/10.1016/j.sysconle.2016.12.001 %V 99 %X The paper presents a novel approach for the analysis and control of a multi-agent system with non-identical agents and a pathgraph topology. With the help of irrational wave transfer functions, the approach describes the interaction among the agents from the ‘local’ perspective and identify the travelling waves in the multi-agent system. The local treatment of the multi-agent system is complementary to the traditional ‘overall’ approach. It is shown that the dierent dynamics of the agents creates a virtual boundary that causes a partial reflection of the travelling waves. Undesired eects due to the reflection of the waves, such as amplification/attenuation, long transient or string instability, can be compensated by the feedback controllers introduced in this paper. A set of functions in MATLAB, which allows numerical simulation of the proposed approach, have been made available on MATLAB Central.

%8 January
%0 Journal Article
%J Automatica
%D 2017
%T Disturbance scaling in bidirectional vehicle platoons with different asymmetry in position and velocity coupling
%A Herman, Ivo
%A Knorn, Steffi
%A Ahlén, Anders
%I Elsevier
%P 13-20
%R 10.1016/j.automatica.2017.04.010
%U https://doi.org/10.1016/j.automatica.2017.04.010
%V 82
%X This paper considers a string of vehicles where the local control law uses the states of the vehicle’s immediate predecessor and follower. The coupling towards the preceding vehicle can be chosen dierent to the coupling towards the following vehicle, which is often referred to as an asymmetric bidirectional string. Further, the coupling dierences, i.e., asymmetry, can be chosen dierently for the velocity and the position coupling between neighbouring vehicles. This general approach includes the special cases of symmetric bidirectional strings and predecessor following control schemes. It is investigated how the eect of disturbance on the control errors in the string changes with the string length. It is shown, that in case of symmetric position coupling and asymmetric velocity coupling, linear scaling can be achieved. For symmetric interaction in both states, i.e., in symmetric bidirectional strings, the errors scale quadratically in the number of vehicles. When the coupling in position is asymmetric, exponential scaling may occur or the system might even become unstable. The paper thus gives a comprehensive overview of the achievable performance in linear, asymmetric, bidirectional platoons. The results reveal that symmetry in the position coupling and asymmetry in velocity coupling qualitatively improves the performance of the string. Extensive numerical results illustrating the theoretical findings are also presented.

%8 August %0 Journal Article %J Journal of Applied Physics %D 2017 %T Green's function-based control-oriented modeling of electric field for dielectrophoresis %A Gurtner, Martin %A Hengster-Movric, Kristian %A Zdeněk Hurák %N 5 %P 054903 %R 10.1063/1.4997725 %V 122 %7 2 %8 08 %0 Conference Paper %B 20th IFAC World Congress %D 2017 %T Ball in double hoop: demonstration model for numerical optimal control %A Gurtner, Martin %A Jiří Zemánek %I IFAC %N 1 %P 2379 - 2384 %R 10.1016/j.ifacol.2017.08.429 %V 50 %8 07/2017 %0 Conference Paper %B 20th IFAC World Congress %D 2017 %T Time-optimal Control for Bilinear Nonnegative-in-control Systems: Application to Magnetic Manipulation %A Jiří Zemánek %A Sergej Čelikovský %A Zdeněk Hurák %C Toulouse, France %N 1 %P 16032 - 16039 %R 10.1016/j.ifacol.2017.08.1916 %V 50 %8 07/2017 %0 Conference Paper %B 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems %D 2016 %T Distributed adaptive consensus protocol with decaying gains on directed graphs %A Knotek, Stefan %A Hengster-Movric, Kristian %A Sebek, Michael %C Tokyo, Japan %K adaptive control %K cooperative control %K multi-agent systems %U http://www.sciencedirect.com/science/article/pii/S2405896316320109 %XIn this paper we present a distributed adaptive consensus protocol, that solves the cooperative regulator problem for multi-agent systems with general linear time-invariant dynamics and directed, strongly connected communication graphs. The protocol addresses the problems of recent distributed adaptive consensus protocols with large or unbounded coupling gains. These problems are solved by introducing a novel coupling gain dynamics that allows the coupling gains to synchronize and decay to some estimated value. Unlike the static consensus protocols, which require the knowledge of the smallest real part of the non-zero Laplacian eigenvalues to design the coupling gain, the proposed adaptive consensus protocol does not require any centralized information. It can be therefore implemented on agents in a fully distributed fashion.

%8 September %0 Conference Paper %B 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys 2016) %D 2016 %T Scaling of H-infinity Norm in Symmetric Bidirectional Platoons %A Herman, Ivo %A Sebek, Michael %C Tokio, Japan %I IFAC %P 91-96 %R 10.1016/j.ifacol.2016.10.378 %U http://www.sciencedirect.com/science/article/pii/S2405896316319656 %XIn this paper scaling of H-infinity norm of selected transfer functions in bidirectional vehicle platoons is investigated. The vehicles are identical and use symmetric nearest-neighbor interactions, hence the communication topology is a pinned undirected path graph. The LTI open-loop model of individual vehicles can be of arbitrary order, but it is required to contain two integrators in order to track the movement of the leader. It is shown that for any agent model some transfer functions in the formation scale linearly, while others scale quadratically. The type of scaling depends on the steady-state gain of the transfer function.

%8 September %0 Conference Paper %B 20th International Student Conference on Electrical Engineering %D 2016 %T Fully distributed adaptive consensus protocol with bounded gains %A Knotek, Stefan %C Prague, Czech Republic %K adaptive control %K cooperative regulator problem %K distributed control %K multi-agent systems %K relative-state consensus %U http://radio.feld.cvut.cz/conf/poster/poster2016/proceedings/Section_ICS/ICS_040_Knotek.pdf %XThis paper introduces a novel distributed adaptive consensus protocol to solve the distributed consensus problem for multi-agent systems with general linear timeinvariant dynamics and undirected connected communication graphs. The presented protocol proposes a solution to the problems of recent adaptive consensus protocols with large or unbounded coupling gains by introducing a novel coupling gain dynamics, that allows the coupling gains to synchronize and decay to some estimated value. The proposed protocol does not require any centralized information, therefore it can be implemented on agents in fully distributed fashion.

%8 May %0 Journal Article %J Systems & Control Letters %D 2016 %T Transients of platoons with asymmetric and different Laplacians %A Herman, Ivo %A Dan Martinec %A J. J. P. Veerman %P 28-35 %R 10.1016/j.sysconle.2016.02.013 %U http://authors.elsevier.com/a/1SiQec8EXPhIg %V 91 %XWe consider an asymmetric control of platoons of identical vehicles with nearest-neighbor interaction. Recent results show that if the vehicle uses different asymmetries for position and velocity errors, the platoon has a short transient and low overshoots. In this paper we investigate the properties of vehicles with friction. To achieve consensus, an integral part is added to the controller, making the vehicle a third-order system. We show that the parameters can be chosen so that the platoon behaves as a wave equation with different wave velocities. Simulations suggest that our system has a better performance than other nearest-neighbor scenarios. Moreover, an optimization-based procedure is used to find the controller properties.

%8 May %0 Conference Paper %B 55th IEEE Conference on Decision and Control (CDC) %D 2016 %T Optimal distributed control with application to asymmetric vehicular platoons %A Herman, Ivo %A Michael Šebek %C Las Vegas, USA %I IEEE %P 4340-4345 %8 December %0 Journal Article %J IEEE Transactions on Automatic Control %D 2016 %T On Feedback Architectures With Zero-Vibration Signal Shapers %A Vyhlidal, Tomas %A Hromcik, Martin %A Kucera, Vladimir %A Milan Anderle %N 8 %P 2049 - 2064 %R 10.1109/TAC.2015.2492502 %V 61 %8 8/2016 %0 Journal Article %J Measurement Science and Technology %D 2016 %T Twin-beam real-time position estimation of micro-objects in 3D %A Gurtner, Martin %A Jiří Zemánek %N 12 %P 127003 %R 10.1088/0957-0233/27/12/127003 %V 27 %XVarious optical methods for measuring positions of micro-objects in 3D have been reported in the literature. Nevertheless, the majority of them are not suitable for real-time operation, which is needed, for example, for feedback position control. In this paper, we present a method for real-time estimation of the position of micro-objects in 3D; the method is based on twin-beam illumination and requires only a very simple hardware setup whose essential part is a standard image sensor without any lens. The performance of the proposed method is tested during a micro-manipulation task in which the estimated position served as feedback for the controller. The experiments show that the estimate is accurate to within ~3 μm in the lateral position and ~7 μm in the axial distance with the refresh rate of 10 Hz. Although the experiments are done using spherical objects, the presented method could be modified to handle non-spherical objects as well.

%8 12 %0 Journal Article %J Journal of the Franklin Institute %D 2016 %T Structured Lyapunov functions for synchronization of identical affine-in-control agents—Unified approach %A Hengster-Movric, Kristian %A Sebek, Michael %A Celikovsky, Sergej %N 14 %P 3457 - 3486 %R 10.1016/j.jfranklin.2016.06.028 %V 353 %8 09/2016 %0 Journal Article %J Control Engineering Practice %D 2016 %T Bridging the gap between the linear and nonlinear predictive control: Adaptations for efficient building climate control %A Pčolka, Matej %A Žáčeková, Eva %A Robinett, Rush %A Sergej Čelikovský %A Michael Šebek %P 124 - 138 %R 10.1016/j.conengprac.2016.01.007 %V 53 %8 08/2016 %0 Conference Paper %B 2016 IEEE Conference on Control Applications (CCA)2016 IEEE Conference on Control Applications (CCA) %D 2016 %T Distributed observer and controller design for state-output decomposed systems %A Zhang, Xueji %A Hengster-Movric, Kristian %A Sebek, Michael %C Buenos Aires, Argentina %I IEEE %P 450 - 455 %R 10.1109/CCA.2016.7587871 %0 Thesis %D 2016 %T Scaling in vehicle platoons %A Herman, Ivo %Y Sebek, Michael %Y Zdeněk Hurák %XThis thesis deals with analysis of scaling in autonomous vehicle platoons in which vehicles keep fixed distance to their neighbors. The vehicles are modelled as linear single-input single-output systems of arbitrary order. In order to control themselves, the vehicles use information from their nearest neighbors-their predecessor and successor. The states used for coupling are mainly position and velocity, but other states are allowed too. The errors to neighbors in these states can be weighted differently, hence the control law is asymmetric. Using the tools from distributed control, properties of platoons are analyzed. A comprehensive overview of the properties of platoons when identical asymmetry in all states is given. With the help of a newly derived product form of a transfer function in a network system, the steady-state gain, stability, string stability and particularly H-infinity norms are analyzed. The most important aspect specifying the scaling rate is the number of integrators in the open loop. For one integrator in the open loop the scaling of the H-infinity norm is quadratic for symmetric control and linear for asymmetric control. For two and more integrators the scaling is cubical for symmetric control and exponential for asymmetric. Since there is no good control for two integrators in the open loop with identical asymmetry, symmetric coupling in position and asymmetric in velocity is proposed. Such control is, at least for the cases analyzed in the thesis, superior to both completely symmetric and completely asymmetric control. It has similar convergence time as asymmetric control but it still keeps the bounded control effort as the symmetric control does.

%0 Book Section %B Control of Complex Systems - Theory and Applications %D 2016 %T Synchronizing Region Approach for Identical Linear Time-Invariant Agents %A Movric, K.H. %A Sebek, M. %E Kyriakos Vamvoudakis %E Sarangapani Jagannathan %Y Kyriakos Vamvoudakis %Y Sarangapani Jagannathan %C - %I Elsevier %P 519 - 548 %R 10.1016/B978-0-12-805246-4.00018-5 %7 1 %@ 9780128052464 %0 Conference Paper %B 5th IFAC Workshop on Estimation and Control of Networked Systems (NecSys) %D 2015 %T Stability of a Circular System with Multiple Asymmetric Laplacians %A Herman, Ivo %A Dan Martinec %A J. J. P. Veerman %A Michael Šebek %C Philadelphia, PA, USA %I IFAC %P 162-167 %R 10.1016/j.ifacol.2015.10.324 %U http://linkinghub.elsevier.com/retrieve/pii/S2405896315022156 %XWe consider an asymptotic stability of a circular system where the coupling Laplacians are dierent for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as conrmed by simulations in the paper, our results have an application also in path graphs.

%8 September %0 Conference Paper %B 5th IFAC Workshop on Estimation and Control of Networked Systems (NecSys) %D 2015 %T Travelling waves in a multi-agent system with general graph topology %A Dan Martinec %A Herman, Ivo %A Michael Šebek %C Philadelphia, PA, USA %P 82-87 %X The paper presents a novel approach for the analysis of a multi-agent system with arbitrary interaction topology and identical agents. The approach is based on an irrational transfer function, the Wave transfer function, that decomposes the interactions between the agents and identies the travelling waves in the multi-agent system. The approach based on the travelling waves describes the behaviour of the system from the local perspective, which is complementary to the traditional overall approach. The proposed approach allows us, for example, to describe the local eect of the agents that have more than two neighbours.

%8 September
%0 Journal Article
%J Electrophoresis
%D 2015
%T Feedback control for noise-aided parallel micromanipulation of several particles using dielectrophoresis
%A Jiří Zemánek
%A Michálek, Tomáš
%A Zdeněk Hurák
%N 13
%P 1451-1458
%R 10.1002/elps.201400521
%V 36
%X The paper describes a novel control strategy for simultaneous manipulation of several micro-scale particles over a planar micro-electrode array using dielectrophoresis (DEP). The approach is based on a combination of numerical nonlinear optimization, which gives a systematic computational procedure for finding the voltages applied to the individual electrodes, and exploitation of the intrinsic noise, which compensates for the loss of controllability when two identical particles are exposed to identical forces. Although interesting on its own, the proposed functionality can also be seen as a preliminary achievement in a quest for a technique for separation of two particles. The approach is tested experimentally with polystyrene beads (50 microns in diameter) immersed in deionized water on a flat microelectrode array with parallel electrodes. A digital camera and a computer vision algorithm are used to measure the positions. Two distinguishing features of the proposed control strategy are that the range of motion is not limited to inter-electrode gaps and that independent manipulation of several particles simultaneously is feasible even on a simple micro-electrode array.

%8 July %0 Journal Article %J Electrophoresis %D 2015 %T On benchmark problems, challenges and competitions in electrokinetics - A review %A Zdeněk Hurák %A Foret, František %I Wiley %N 13 %P 1429-1431 %R 10.1002/elps.201400520 %V 36 %XIn this critical review we comment on the absence of widely shared benchmark problems and relevant challenges or even attractive competitions in the field of electrokinetics. We argue that in some other scientific domains that are, similarly as electrokinetics, strongly multidisciplinary, the existence of these tools is very beneficial because it stimulates the discussion about what constitutes the bottleneck of further progress, allows easier exploitation of results provided by other scientific and engineering disciplines, and, last but not least, makes the research domain attractive and visible to a broader public, including students. The goal of this review is to provoke some discussion that might perhaps lead to compensating for these shortcomings.

%8 July %0 Conference Paper %D 2015 %T On zero-vibration signal shapers and a wave-absorbing controller for a chain of multi-agent dynamical systems %A Dan Martinec %A Martin Hromčík %A Herman, Ivo %A Vyhlídal, Tomáš %A Michael Šebek %C Linz, Austria %X The paper brings together two different approaches for control of chain of oscillatory lumped-parameter multi-agent systems. Namely, the multi-mode zero-vibration input shaper and the wave-absorbing controller are recalled and the similarities and links between them are broadly discussed. The special case of identical agents with a double-integrator character is at the focus throughout the paper. The report reveals that the two approaches are closely related in spite of the fact that they differ significantly in all aspects, from motivation through computational algorithms to target implementation. In addition, the presented numerical results, mostly based on numerical simulations at this moment, show that the two methods can be combined together, to take advantage of both an appropriate initial excitation of the system by the input shaper and of increased robustness coming from the wave-absorber feedback architecture. Such a combined control law is based on a special property of the multi-mode zero vibration input shaper - namely the convergence of its impulse response, as the number of agents increases, to a double bell-shaped function.

%8 July
%0 Journal Article
%J IEEE Transactions on Automatic Control
%D 2015
%T Nonzero bound on Fiedler eigenvalue causes exponential growth of H-infinity norm of vehicular platoon
%A Herman, Ivo
%A Dan Martinec
%A Zdeněk Hurák
%A Michael Šebek
%N 8
%P 2248 - 2253
%R 10.1109/TAC.2014.2366980
%U http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6945786
%V 60
%X We consider platoons composed of identical vehicles and controlled in a distributed way, that is, each vehicle has its own onboard controller. The regulation errors in spacing to the immediately preceeding and following vehicles are weighted differently by the onboard controller, which thus implements an asymmetric bidirectional control scheme. The weights can vary along the platoon. We prove that such platoons have a nonzero uniform bound on the second smallest eigenvalue of the graph Laplacian matrix—the Fiedler eigenvalue. Furthermore, it is shown that existence of this bound always signals undesirable scaling properties of the platoon. Namely, the H-infinity norm of the transfer function of the platoon grows exponentially with the number of vehicles regardless of the controllers used. Hence the benefits of a uniform gap in the spectrum of a Laplacian with an asymetric distributed controller are paid for by poor scaling as the number of vehicles grows.

%8 August %0 Journal Article %J Journal of the Franklin Institute %D 2015 %T Cooperative synchronization control for agents with control delays: A synchronizing region approach %A Hengster-Movric, Kristian %A Lewis, Frank L. %A Michael Šebek %A Vyhlídal, Tomáš %N 5 %P 2002 - 2028 %R 10.1016/j.jfranklin.2015.02.011 %V 352 %XThis paper investigates multi-agent system synchronization in the presence of control signal delays. Agents are assumed to be identical linear time-invariant systems, interacting on a directed graph topology, all having the same control delay. Distributed control of multi-agent systems is complicated by the fact that the communication graph topology interplays with single-agent dynamics. Here a design method based on a synchronizing region is given that decouples the design of local feedback gains from the detailed properties of graph topology. Such extension of the synchronizing region concept to agents with delays is rigorously justified. Delay-dependent synchronizing region is defined and methods are given guaranteeing its estimates. Qualitative properties of delay-dependent synchronizing regions and implications for control design are discussed. It is found that these regions are inherently bounded which restricts the graphs that allow for synchronization under delayed communication. Stronger property of exponential stability with a prescribed convergence rate is presented as a special case.

%8 05/2015 %0 Journal Article %J Automatica %D 2015 %T Distributed static output-feedback control for state synchronization in networks of identical LTI systems %A Hengster-Movric, Kristian %A Lewis, Frank L. %A Sebek, Michael %P 282 - 290 %R 10.1016/j.automatica.2014.12.015 %V 53 %XThis paper studies state synchronization of multi-agent systems with disturbances using distributed static output-feedback (OPFB) control. The bounded L2L2 gain synchronization problem using distributed static OPFB is defined and solved. The availability of only output measurements restricts the local controls design, while the communication graph topology restricts global information flow among the agents. It is shown here that these two types of restriction can be dealt with in a symmetric manner and lead to two similar conditions guaranteeing the existence of bounded L2L2 gain static OPFB. One condition is on the output measurement matrix on a local scale, and the other on the graph Laplacian matrix on a global scale. Under additional conditions a distributed two-player zero-sum game using static OPFB is also solved and leads to distributed Nash equilibrium on the communication graph. As a special case the static OPFB globally optimal control is given. A new class of digraphs satisfying the above condition on the graph Laplacian is studied. The synchronizing region for distributed static OPFB control is exposed and found to be conical, different than the infinite right-half plane synchronizing region for distributed state feedback.

%8 03/2015 %0 Journal Article %J Technicall %D 2015 %T Od kuliček k buňkám: Řízení pro distribuovanou (mikro)manipulaci %A Jiří Zemánek %N 1 %P 32-33 %U http://www.tecnicall.cz/res/pdf/tecnicall/2015_1.pdf %0 Generic %D 2015 %T Transfer functions in consensus systems with higher-order dynamics and external inputs %A Herman, Ivo %A Dan Martinec %A Michael Šebek %XThis paper considers transfer functions in consensus systems where agents have identical SISO dynamics of arbitrary order. The interconnecting structure is a directed graph. The transfer functions for various inputs and outputs are presented in simple product forms with a similar structure of the numerator and the denominator. This structure combines the network properties and the agent model in an explicit way. The link between a higher-order and a single-integrator dynamics is shown and the polynomials of the transfer function in the single-integrator system are related to the graph properties. These properties also allow to generalize a result on the minimal dimension of the controllable subspace to the directed graphs.

%0 Generic %D 2015 %T Traveling waves and scattering in control of chains %A Zdeněk Hurák %K chains %K scattering description %K traveling waves %0 Conference Paper %B American Control Conference (ACC) 2014 %D 2014 %T Harmonic instability of asymmetric bidirectional control of a vehicular platoon %A Herman, Ivo %A Dan Martinec %A Zdeněk Hurák %A Sebek, Michael %C Portland, Oregon %R 10.1109/ACC.2014.6858974 %U http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6858974 %8 June %0 Conference Paper %B 2014 European Control Conference (ECC) %D 2014 %T Refinement of a bidirectional platooning controller by wave absorption at the leader %A Dan Martinec %A Herman, Ivo %A Zdeněk Hurák %A Michael Šebek %C Strasbourg, France %P 2845 - 2850 %R 10.1109/ECC.2014.6862263 %U http://www.ecc14.eu/ %XThe paper tailors the so-called wave-based control known in the field of flexible mechanical structures to the problem of distributed control of vehicular platoons. The proposed solution is based on refinement of the popular symmetric bidirectional distributed controller which enables the platoon leader to actively absorb any incoming (backwards running) wave of positional changes in the platoon. In order to accomplish this, the platoon leader only needs to measure the distance to its immediate follower. This minor augmentation results in significant attenuation of undesirable long transients during the platoon manoeuvres like acceleration/deceleration or during the commanded change of the inter-vehicle distances. Numerical simulations show that the wave-absorbing controller works efficiently even for platoons with a very large number of vehicles and outperforms the known platoon control schemes such as predecessor following or bidirectional control algorithm.

%8 June %@ 978-3-9524269-1-3 %0 Conference Paper %B IEEE/ASME International Conference on Advanced Intelligent Mechatronics %D 2014 %T Dielectrophoretic actuation strategy for micromanipulation along complex trajectories %A Jiří Zemánek %A Jakub Drs %A Zdeněk Hurák %C Besancon, France %I IEEE RAS %R 10.1109/AIM.2014.6878040 %U https://doi.org/10.1109/AIM.2014.6878040 %8 July %0 Journal Article %J European Journal of Control %D 2014 %T Wave-absorbing vehicular platoon controller %A Dan Martinec %A Herman, Ivo %A Zdeněk Hurák %A Michael Šebek %P 237-248 %R 10.1016/j.ejcon.2014.06.001 %U http://www.sciencedirect.com/science/journal/09473580 %V 20 %XThe paper tailors the so-called wave-based control, popular in the field of flexible mechanical structures, to the field of distributed control of vehicular platoons. The proposed solution augments the symmetric bidirectional control algorithm with a wave-absorbing controller implemented on the leader, and/or on the rear-end vehicle. The wave-absorbing controller actively absorbs an incoming wave of positional changes in the platoon and thus prevents oscillations of inter-vehicle distances. The proposed controller significantly improves the performance of platoon manoeuvrers such as acceleration/deceleration or changing the distances between vehicles without making the platoon string unstable. Numerical simulations show that the wave-absorbing controller performs efficiently even for platoons with a large number of vehicles, for which other platooning algorithms are inefficient or require wireless communication between vehicles.

%8 July %0 Conference Paper %B 19th IFAC World Congress %D 2014 %T Two-sided wave-absorbing control of a heterogenous vehicular platoon %A Dan Martinec %A Herman, Ivo %A Michael Šebek %C Cape Town, South Africa %P 8091-8096 %U http://www.ifac2014.org/ %XThe paper tailors the so-called wave-absorbing control designed for a homogenous platoon of vehicles to a platoon where dynamics of vehicles dier. The proposed solution is based on the symmetric bidirectional control of the in-platoon vehicles and wave-absorbing control of the platoon ends. This type of control reduces oscillations of vehicle's velocities and signicantly decrease the settling time of the platoon by absorbing waves on the platoon ends. The necessary transfer-function-based mathematical apparatus for description of the so-called soft boundary is also presented. Although the soft boundary is a virtual boundary located between the vehicles of dierent dynamics, it signicantly alters the behaviour of the platoon. It is shown how to incorporate model of the soft boundary into the design of the wave-absorbing control such that its eect is minimized. The proposed control scheme is veried on numerous mathematical simulations.

%8 August %0 Conference Paper %B 19th IFAC World Congress %D 2014 %T Zeros of transfer functions in networked control with higher-order dynamics %A Herman, Ivo %A Dan Martinec %A Sebek, Michael %C Cape Town, South Africa %P 9177-9182 %8 August %0 Journal Article %J IEEE Transactions on Automatic Control %D 2014 %T Cooperative Optimal Control for Multi-Agent Systems on Directed Graph Topologies %A Movric, Kristian Hengster %A Lewis, Frank L. %N 3 %P 769 - 774 %R 10.1109/TAC.2013.2275670 %V 59 %8 03/2014 %0 Thesis %D 2014 %T Inertial stabilization, estimation and visual servoing for aerial surveillance %A Martin Řezáč %U https://dl.dropboxusercontent.com/u/36788590/thesis.pdf %0 Conference Paper %B CECE - International Interdisciplinary Meeting on Bioanalysis %D 2013 %T Integrated microfluidic device for droplet manipulation %A Evgenie Basova %A Jakub Drs %A Hurak, Zdenek %A Frantisek Foret %A Jiří Zemánek %C Brno, Hotel Continental %P s291-s293 %U http://www.ce-ce.org/CECE2013/Proceedings_CECE_JUNIOR_2013.pdf %8 November %0 Journal Article %J Multidimensional Systems and Signal Processing %D 2013 %T Distributed stabilisation of spatially invariant systems: positive polynomial approach %A Augusta, Petr %A Zdeněk Hurák %I Springer %N 1 %P 3-21 %R 10.1007/s11045-011-0152-5 %U http://dx.doi.org/10.1007/s11045-011-0152-5 %V 24 %XThe paper gives a computationally feasible characterisation of spatially distributed controllers stabilising a linear spatially invariant system, that is, a system described by linear partial differential equations with coefficients independent on time and location. With one spatial and one temporal variable such a system can be modelled by a 2-D transfer function. Stabilising distributed feedback controllers are then parametrised as a solution to the Diophantine equation ax + by = c for a given stable bi-variate polynomial c. The paper is built on the relationship between stability of a 2-D polynomial and positiveness of a related polynomial matrix on the unit circle. Such matrices are usually bilinear in the coefficients of the original polynomials. For low-order discrete-time systems it is shown that a linearising factorisation of the polynomial Schur-Cohn matrix exists. For higher order plants and/or controllers such factorisation is not possible as the solution set is non-convex and one has to resort to some relaxation. For continuous-time systems, an analogue factorisation of the polynomial Hermite-Fujiwara matrix is not known. However, for low-order systems and/or controller, positivity conditions on the closed-loop polynomial coefficients can be invoked. Then the computational framework of linear matrix inequalities can be used to describe the stability regions in the parameter space using a convex constraint.

%8 March %0 Journal Article %J Mechatronics %D 2013 %T HOSIDF-based feedforward friction compensation in low-velocity motion control systems %A Ucun, Levent %A Salášek, Jan %I Elsevier %N 2 %P 118–127 %R 10.1016/j.mechatronics.2013.12.005 %V 24 %XThe paper describes an application of a recently introduced methodology for modeling of a class of nonlinear systems — Higher-Order Sinusoidal Input Describing Function technique (HOSIDF) — to a motion control platform for which a precisely controlled motion at low velocity is required. One of the key challenges for these systems is to compensate for the friction, which is particularly difficult to model at low velocities. The frequency-domain HOSIDF modeling framework is used to assist in designing a feedforward compensator. Experiments with a laboratory benchmark system (gimballed camera platform) prove the technique useful.

%8 March %0 Journal Article %J The Cerebellum %D 2013 %T Disorders of Balance and Gait in Essential Tremor Are Associated with Midline Tremor and Age %A Hoskovcová, Martina %A Ulmanová, Olga %A Šprdlík, Otakar %A Sieger, Tomáš %A Nováková, Jana %A Jech, Robert %A Růžička, Evžen %N 1 %P 27-34 %R 10.1007/s12311-012-0384-4 %V 12 %8 February %0 Journal Article %J IFAC Mechatronics %D 2013 %T Structured MIMO H-infinity Design for Dual-Stage Inertial Stabilization: Case Study for HIFOO and Hinfstruct %A Martin Řezáč %A Zdeněk Hurák %N 8 %P 1084–1093 %R 10.1016/j.mechatronics.2013.08.003 %U http://dx.doi.org/10.1016/j.mechatronics.2013.08.003 %V 23 %8 December %0 Journal Article %J Industrial Electronics, IEEE Transactions on %D 2013 %T AC Drive Observability Analysis %A Pavel Václavek %A Petr Blaha %A Herman, Ivo %K Computational modeling %K Equations %K Induction machine %K Induction machines %K Mathematical model %K nonlinear system %K Observability %K Rotors %K Stators %K synchronous machine %P 3047-3059 %R 10.1109/TIE.2012.2203775 %V 60 %8 August %0 Conference Paper %B 4th IFAC NecSys Workshop %D 2013 %T PDdE-based analysis of vehicular platoons with spatio-temporal decoupling %A Herman, Ivo %A Dan Martinec %A Zdeněk Hurák %A Michael Šebek %C Koblenz, Germany %U http://www.ifac-papersonline.net/Detailed/62353.html %8 9 %0 Journal Article %J Automatica %D 2013 %T Synchronization of discrete-time multi-agent systems on graphs using Riccati design %A Hengster-Movric, Kristian %A You, Keyou %A Lewis, Frank L. %A Xie, Lihua %N 2 %P 414 - 423 %R 10.1016/j.automatica.2012.11.038 %V 49 %8 2/2013 %0 Journal Article %J IEEE Sensors Journal %D 2013 %T Electrolocation Sensors in Conducting Water Bio-Inspired by Electric Fish %A Servagent, Noël %A Jawad, Brahim K %A Bouvier, Stéphane %A Boyer, Frédéric %A Girin, Alexis %A Gomez, Francesco %A Lebastard, Vincent %A Gossiaux, Pol B %0 Journal Article %J IEEE Transactions on Control Systems Technology %D 2012 %T Image-based pointing and tracking for inertially stabilized airborne camera platform %A Zdeněk Hurák %A Martin Řezáč %N 5 %P 1146 - 1159 %R 10.1109/TCST.2011.2164541 %U http://dx.doi.org/10.1109/TCST.2011.2164541 %V 20 %XThis paper describes a novel image-based pointing-tracking feedback control scheme for an inertially stabilized double-gimbal airborne camera platform combined with a computer vision system. The key idea is to enhance the intuitive decoupled controller structure with measurements of the camera inertial angular rate around its optical axis. The resulting controller can also compensate for the apparent translation between the camera and the observed object, but then the velocity of this mutual translation must be measured or estimated. Even though the proposed controller is more robust against longer sampling periods of the computer-vision system then the decoupled controller, a sketch of a simple compensation of this delay is also given. Numerical simulations are accompanied by laboratory experiments with a real benchmark system.

%8 September %0 Conference Paper %B IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society %D 2012 %T Load torque and moment of inertia observability analysis for alternating current drive sensorless control %A Herman, Ivo %A Vaclavek, Pavel %C Montreal %R 10.1109/IECON.2012.6388917 %U http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6388917&navigation=1 %XKnowledge of the exact characteristics of a motor is necessary for a high-performance electrical drive control. It is useful to obtain not only the states of electrical and mechanical variables, but also other quantities. Two of the unknown parameters are the moment of inertia and the load torque. This paper addresses theoretical aspects of conditions, on which these quantities are simultaneously observable. Both asynchronous and synchronous drives are considered. The conditions are verified by a simulation and by real-motor data. Obtained results prove the possibility of their sensorless estimation. Some difficulties of the state estimation when controllers are saturated are shown.

%8 October %0 Conference Paper %B 2012 IEEE Multi-Conference on Systems and Control %D 2012 %T Vehicular platooning experiments with racing slot cars %A Dan Martinec %A Michael Šebek %A Zdeněk Hurák %C Dubrovnik, Croatia %I IEEE %R 10.1109/CCA.2012.6402709 %U https://doi.org/10.1109/CCA.2012.6402709 %XThe paper reports on an affordable platform for indoor experimental verification of algorithms for distributed control of platoons of vehicles. The platform is based on commercially available racing slot cars (by Carrera) equipped with an on-board 32-bit microcontroller-based control system. The assembled PCB board was provided by Freescale Semiconductor, Rožnov pod Radhoštěm, Czech Republic, within their Freescale Race Challenge 2012 competition of individual autonomous slot cars organized for student teams in Czech and Slovak republics. The documentation is freely available online. Some extra components such as an infrared range sensor and a wireless communication module have been added to the original system. The capabilities and potentials of the proposed platform are demonstrated on platooning experiments using two of the most popular platoon control schemes: predecessor following and leader following. Some technical parameters of the platform as well as design experience are shared in the report. It is hoped to encourage other teams to build a similar setup and possibly expose their new distributed control algorithms to an experimental competition.

%8 October %0 Conference Paper %B 2012 American Control Conference (ACC) %D 2012 %T Feedback linearization approach to distributed feedback manipulation %A Jiří Zemánek %A Zdeněk Hurák %C Montréal, Canada %I American Automatic Control Council (AACC) %P 991-996 %U http://a2c2.org/conferences/acc2012/ %XThis report formulates the problem of a distributed planar manipulation realized by shaping a spatially continuous force field. It also suggests a control strategy based on feedback linearization. Force fields derived from potential fields are considered. The potentials are ``shaped'' by a set of spatially discrete ``actuators`` such as electrodes in the case of dielectrophoresis, electromagnets in the case of planar magnetic manipulators, or linear piezoelectric actuators in the case of deformable flat surfaces. The actuators form arrays. Distinguished feature of such force fields is that the contribution from an individual actuator usually affects the situation in the neighboring zones too, but usually not in too remote zones. As an idealization, the spatial domain is considered unbounded, which enables examination of asymptotic behavior of the manipulation scheme.

%8 June %@ 978-1-4673-2102-0, 978-1-4577-1095-7 %0 Conference Paper %B 2012 American Control Conference (ACC) %D 2012 %T Kalman Filter under Nonlinear System Transformations %A Kamil Dolinský %A Sergej Čelikovský %C Montréal, Canada %I American Automatic Control Council (AACC) %U http://a2c2.org/conferences/acc2012/ %8 June %0 Journal Article %J Biomedical Signal Processing and Control %D 2012 %T Dynamic Causal Modeling and subspace identification methods %A Nováková, J. %A Hromčík, M. %A Jech, R. %N 4 %P 365–370 %R 10.1016/j.bspc.2011.07.002 %U http://dx.doi.org/10.1016/j.bspc.2011.07.002 %V 7 %8 July %0 Journal Article %J IEEE Transactions in Robotics %D 2012 %T Model of a sensor inspired by electric fish %A Boyer, Frédéric %A Gossiaux, Pol B, %A Jawad, Brahim K, %A Lebastard, Vincent, %A Porez, Mathieu, %P 492-505 %V 28 %8 April %0 Journal Article %J International Journal of Robust and Nonlinear Control %D 2012 %T Cooperative observers and regulators for discrete-time multiagent systems %A Hengster-Movric, Kristian %A Lewis, Frank %N 14 %P 1545 - 1562 %R 10.1002/rnc.2840 %V 23 %8 09/2013 %0 Journal Article %J Cybernetics and Physics %D 2012 %T Adaptive Nonlinear Tracking for Robotic Walking %A Kamil Dolinský %A Sergej Čelikovský %N 1 %P 28-35 %U http://lib.physcon.ru/doc?id=9e51935aa5bc %V 1 %XThis article deals with online adaptation of control strategy for nonlinear tracking of a walking like motion of bipedal robot. Adaptation of the control rule is done according to results of online parameter estimation. Parameter estimation was realized by an extended Kalman filter due to recursive nature of the estimation problem and abundant a priori information. Proposed estimation strategy yields at least three advantages. By utilization of extensive knowledge about the system in consideration a multi-variable estimation problem was reduced to estimation problem involving one parameter only. A heavy computation burden required for recomputation of reference trajectory and feed-forward controller is removed. This approach can also be used to eliminate the modeling mismatch. A practical situation when a robot has to carry a load of an unknown weight is demonstrated.

%0 Thesis %D 2012 %T Detection and Estimation of Human Movement Using Inertial Sensors: Applications in Neurology %A Šprdlík, Otakar %0 Conference Paper %B 18th World Congress of the International Federation of Automatic Control (IFAC) %D 2011 %T 2-D Polynomial Approach to Control of Leader Following Vehicular Platoons %A Michael Šebek %A Zdeněk Hurák %C Milano, Italy %I Elsevier %U http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac11-proceedings/data/html/papers/0807.pdf %XThis paper formulates the problems of stabilization and asymptotic following in infnite platoons of vehicles within the 2-D polynomial framework, that is, the dynamics of the problem are described using a fraction of two bivariate polynomials. In contrast to some previous works, the platoon here assumes a leader (and an infnite number of followers), therefore the often used bilateral z-transform should not be used here since it assumes a doubly infnite vehicular strings. The unilateral z-transform seems better suited. However, it brings about the need to take the boundary conditions into consideration; among other, the leader vehicle comes into the scene. The necessary formalism is introduced in the paper and used to provide elegant alternative proofs of some well-known facts about the platooning problem.

%8 September %0 Conference Paper %B 18th World Congress of the International Federation of Automatic Control (IFAC) %D 2011 %T Structured MIMO H-Infinity Design for Dual-Stage Inertial Stabilization: Case Study for HIFOO %A Martin Řezáč %A Zdeněk Hurák %C Milano, Italy %U http://www.ifac2011.org %XThe paper reports on a control design for an experimental platform that contains two aligned motorized gimbals stabilizing an optical payload around a single axis using measurements from an inertial angular rate sensor (MEMS gyro). Such a laboratory system represents a simplified testbed for the more practically useful line-of-sight stabilization. The paper defends the choice of the control configuration and argues that when using MIMO design procedures, enforcing some structure upon the transfer function matrix makes the controller implementation and fine-tuning easier. Such structural constraints were taken into consideration in the computational Hinf design by using the publicly available HIFOO solver based on algorithms for non-convex and non-smooth optimization. Results are contrasted with the controllers designed with classical methods and full MIMO Hinf optimization.

%8 September %0 Conference Paper %B 2011 IEEE International Conference on Control Applications (CCA) %D 2011 %T Vehicular platooning experiments with LEGO MINDSTORMS NXT %A Dan Martinec %A Zdeněk Hurák %C Denver, USA %R 10.1109/CCA.2011.6044393 %XThe paper reports on experimenting with a popular introductory robotics toolkit LEGO® MINDSTORMS® NXT that was aimed at demonstrating a few algorithms for distributed control of a long platoon of autonomous vehicles. The configuration used in this report measures the distance to the vehicle ahead and the velocity of the vehicle itself. The acquired technical experience with this platform is shared in the report, including recommendation towards improvements.

%8 September %0 Journal Article %J Journal of Neuroscience Methods %D 2011 %T Validation of a new tool for automatic assessment of tremor frequency from video recordings %A Zdenka Uhríková %A Šprdlík, Otakar %A Hoskovcová, Martina %A Arnošt Komárek %A Ulmanová, Olga %A Václav Hlaváč %A Chris D. Nugent %A Růžička, Evžen %I Elsevier %N 1 %P 110-113 %R j.jneumeth.2011.02.033 %U http://dx.doi.org/10.1016/j.jneumeth.2011.02.033 %V 198 %XWe present a validation study for TremAn—a tool for automatic detection of tremor and measurement of its frequency from video recordings. To assess the validity of TremAn we designed a study consisting of tremor assessment from video, by accelerometry and by clinical evaluation using Fahn–Tolosa–Marin scale. 26 patients with essential tremor and 5 healthy volunteers underwent the examination in four standardized positions with focus on the hand tremor. Results showed that the frequencies of tremor measured with TremAn and with accelerometry are closely related, attaining agreement with less than 0.1 Hz difference in 80% and less than 0.5 Hz in 94% of measured samples. The reproducibility of frequency measurements using TremAn was comparable to the accelerometry, with the TremAn/accelerometry ratio of measurement error standard deviations equal to 0.99 (95% confidence interval (0.84, 1.17)).

%8 May %0 Journal Article %J Biomedical Signal Processing and Control %D 2011 %T Tremor analysis by decomposition of acceleration into gravity and inertial acceleration using inertial measurement unit %A Šprdlík, Otakar %A Zdeněk Hurák %A Hoskovcová, Martina %A Ulmanová, Olga %A Růžička, Evžen %I Elsevier %K Accelerometer %K Gravitational artifact %K Inertial measurement unit %K Regression %K Tremor %K Tremor rating scale %N 3 %P 269-279 %R 10.1016/j.bspc.2010.09.004 %U http://dx.doi.org/10.1016/j.bspc.2010.09.004 %V 6 %X Decomposition of acceleration was investigated as an alternative to commonly used direct spectral analysis of measured acceleration or angular velocity for tremor quantification. An orientation estimation algorithm was devised to decompose the measured acceleration into the gravitational artifact and the inertial acceleration caused by sensor movement in an inertial reference frame. Resulting signals, beside the measured acceleration and angular velocity, were used to assess tremor amplitude and frequency by spectral peak detection. The algorithm was tested on experimental data from a clinical study including patients with essential tremor. The testing comprised of the classification of measurements to come from a patient or a healthy control and of the regression of the visual assessment of tremor amplitude. Small improvements in performance measures were achieved by using the decomposed acceleration. The regression accuracy was comparable to the accuracy achieved in other works. The influence of sensor calibration and connections of results to an analytic approach were analyzed briefly. %8 July %0 Journal Article %J Mechatronics %D 2011 %T Hybrid charge control for stick–slip piezoelectric actuators %A Martin Špiller %A Zdeněk Hurák %I Elsevier %N 1 %P 100 - 108 %R 10.1016/j.mechatronics.2010.09.002 %U http://dx.doi.org/10.1016/j.mechatronics.2010.09.002 %V 21 %XThe article describes an analog electronic circuit for driving stick–slip piezoelectric linear actuators. The task for the amplifier is to provide a high-voltage asymmetric sawtooth-like signal and feed it into a capacitive load. Generation of excessive heat must be avoided while maximizing the slew rate. In order to guarantee a steady translation, the hysteretic behaviour of the piezoelectric material must be compensated. Combination of a charge control scheme with switching is proposed as an efficient solution. Laboratory experiments confirm the superiority of this tailored solution over other existing techniques based on versatile linear voltage amplifiers.

%8 February %0 Conference Paper %D 2010 %T Underwater robot navigation around a sphere using electrolocation sense and Kalman filter %A Lebastard, Vincent %A Chevallereau, Christine %A Amrouche Ali %A Jawad, Brahim K %A Girin Alexis %A Boyer, Frédéric %A Gossiaux, Pol B %C IEEE IROS, Taipei, China %8 October %0 Conference Paper %B 25th International Symposium on Microscale BioSeparations MSB 2010 %D 2010 %T Modeling and simulation, design and fabrication, instrumentation and control for dielectrophoresis %A Jiří Zemánek %A Zdeněk Hurák %A Yves Bellouard %C Prague, Czech Republic %I Ústav analytické chemie AV ČR, v. v. i. %P 118 %U http://www.genomac.cz/msb2010 %V 1 %8 March %@ ISBN 978-80-254-6631-5 %0 Journal Article %J Bulletin of the Polish Academy of Sciences: Technical Sciences %D 2010 %T Robust control of distributed parameter mechanical systems using a multidimensional systems approach %A Cichy, B. %A Augusta, P. %A Rogers, E. %A Gałkowski, K. %A Hurák, Z. %C Warsaw %I Versita %N 1 %P 67 - 75 %R 10.2478/v10175-010-0007-5 %U http://dx.doi.org/10.2478/v10175-010-0007-5 %V 58 %8 March %0 Conference Paper %B Proceedings of 2010 49th IEEE Conference on Decision and Control (CDC) %D 2010 %T Delay compensation in a dual-rate cascade visual servomechanism %A Zdeněk Hurák %A Martin Řezáč %C Atlanta, GA, USA %I IEEE %P 1639 - 1643 %R 10.1109/CDC.2010.5717039 %U http://dx.doi.org/10.1109/CDC.2010.5717039 %8 December %@ 978-1-4244-7745-6 %0 Conference Paper %D 2010 %T Sensor model for the navigation of underwater vehicles by the electric sense %A Jawad, Brahim K, %A Gossiaux, Pol B %A Boyer, Frédéric %A Lebastard, Vincent %A Gomez, Francesco %A Servagent, Noël %A Bouvier, Stéphane %A Girin, Alexis %A Porez, Mathieu %C IEEE ROBIO, Tianjin, China %8 December %0 Conference Paper %B Proc. SPIE Automatic Target Recognition XX; Acquisition, Tracking, Pointing, and Laser Systems Technologies XXIV; and Optical Pattern Recognition XXI %D 2010 %T Control design for image tracking with an inertially stabilized airborne camera platform %A Zdeněk Hurák %A Martin Řezáč %C Orlando, Florida, USA %I SPIE %R 10.1117/12.849902 %U http://dx.doi.org/10.1117/12.849902 %V 7696 %XThe paper reports on a few control engineering issues related to design and implementation of an image-based pointing and tracking system for an inertially stabilized airborne camera platform. A medium-sized platform has been developed by the authors and a few more team members within a joint governmental project coordinated by Czech Air Force Research Institute. The resulting experimental platform is based on a common double gimbal configuration with two direct drive motors and off-the-shelf MEMS gyros. Automatic vision-based tracking system is built on top of the inertial stabilization. Choice of a suitable control configuration is discussed first, because the decoupled structure for the inner inertial rate controllers does not extend easily to the outer imagebased pointing and tracking loop. It appears that the pointing and tracking controller can benefit much from availability of measurements of an inertial rate of the camera around its optical axis. The proposed pointing and tracking controller relies on feedback linearization well known in image-based visual servoing. Simple compensation of a one sample delay introduced into the (slow) visual pointing and tracking loop by the computer vision system is proposed. It relies on a simple modification of the well-known Smith predictor scheme where the prediction takes advantage of availability of the (fast and undelayed) inertial rate measurements.

%8 April %0 Conference Paper %B Proc. SPIE Automatic Target Recognition XX; Acquisition, Tracking, Pointing, and Laser Systems Technologies XXIV; and Optical Pattern Recognition XXI %D 2010 %T Low-cost inertial estimation unit based on extended Kalman filtering %A Martin Řezáč %A Zdeněk Hurák %C Orlando, Florida, USA %I SPIE %R 10.1117/12.850030 %U http://dx.doi.org/10.1117/12.850030 %V 7696 %8 April %0 Conference Paper %B Proceedings of the 12th International Conference on New Actuators %D 2010 %T Towards planar micromanipulators based on dielectric elastomers in thickness mode %A Martin Řezáč %A Zdeněk Hurák %A Yves Bellouard %C Bremen, Germany %I WFB Wirtschaftsförderung Bremen GmbH, Division Messe Bremen %P 901-904 %U http://www.actuator.de %8 April %@ 978-3-933339-12-6 %0 Journal Article %J International Journal of Control %D 2010 %T Advanced LMI based analysis and design for Acrobot walking %A Milan Anderle %A Sergej Čelikovský %A Didier Henrion %A Jiří Zikmund %N 8 %P 1641 - 1652 %R 10.1080/00207179.2010.484468 %V 83 %8 08/2010 %0 Journal Article %J International Journal of Control %D 2010 %T Advanced LMI based analysis and design for Acrobot walking %A Milan Anderle %A Sergej Čelikovský %A Didier Henrion %A Jiří Zikmund %I Taylor & Francis %N 8 %P 1641 - 1652 %R 10.1080/00207179.2010.484468 %U http://dx.doi.org/10.1080/00207179.2010.484468 %V 83 %0 Journal Article %J IEEE Transactions on Industrial Electroncis %D 2010 %T Complete Fast Analytical Solution of the Optimal Odd Single-Phase Multilevel Problem %A Petr Kujan %A Martin Hromčík %A Michael Šebek %N 7 %P 2382 - 2397 %R 10.1109/TIE.2009.2034677 %U http://dx.doi.org/10.1109/TIE.2009.2034677 %V 57 %0 Conference Paper %B Proceedings of the 2009 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference %D 2009 %T Combined line-of-sight inertial stabilization and visual tracking: application to an airborne camera platform %A Zdeněk Hurák %A Martin Řezáč %C Shanghai, China %I IEEE %P 8458 - 8463 %R 10.1109/CDC.2009.5400793 %U http://dx.doi.org/10.1109/CDC.2009.5400793 %8 December %@ 978-1-4244-3871-6 %0 Journal Article %J Integral Transforms and Special Functions %D 2009 %T Effective solution of a linear system with Chebyshev coefficients %A Petr Kujan %A Martin Hromčík %A Michael Šebek %I Taylor & Francis %K hypergeometric functions %K linear system %K optimal PWM problem %K orthogonal Chebyshev polynomials %N 8 %P 619-628 %R 10.1080/10652460902727938 %U http://dx.doi.org/10.1080/10652460902727938 %V 20 %XThis paper presents an efficient algorithm for a special triangular linear system with Chebyshev coefficients. We present two methods of derivations, the first is based on formulae where the nth power of x is solved as the sum of Chebyshev polynomials and modified for a linear system. The second deduction is more complex and is based on the Gauss-Banachiewicz decomposition for orthogonal polynomials and the theory of hypergeometric functions which are well known in the context of orthogonal polynomials. The proposed procedure involves O(nm) operations only, where n is matrix size of the triangular linear system L and m is number of the nonzero elements of vector b. Memory requirements are O(m), and no recursion formula is needed. The linear system is closely related to the optimal pulse-wide modulation problem.

%0 Generic %D 2009 %T Noncontact parallel manipulation with micro- and mesoscale objects using dielectrophoresis %A Jiří Zemánek %C Prague, Czech Republic %I Czech Technical University in Prague %U http://www.golem-project.eu/Publications/GOLEM-Master%20Thesis-Jirka%20Zemanek.pdf %X This diploma project aimed at exploring dielectrophoresis as the means of noncontact, massively parallel and stochastic planar manipulation of meso- (and possibly also micro-) scale objects. As a result of the thesis, complete experimental setup for manipulation 50-micron polystyrene beads was designed, built and used to conduct numerous experiments. These were also supported by numerical simulations, which help find a simple yet useful control strategy. %0 Journal Article %J Mechanical Systems and Signal Processing %D 2008 %T On the control of distributed parameter systems using a multidimensional systems setting %A Cichy, Blazej %A Augusta, Petr %A Rogers, Eric %A Galkowski, Krzysztof %A Hurak, Zdenek %I Elsevier %N 7 %P 1566 - 1581 %R 10.1016/j.ymssp.2008.01.012 %U http://dx.doi.org/10.1016/j.ymssp.2008.01.012 %V 22 %8 October %0 Journal Article %J Automa %D 2008 %T Inerciálně stabilizovaná kamerová základna pro bezpilotní letoun %A Zdeněk Hurák %A Martin Hromčík %A Martin Řezáč %A Jaroslav Žoha %A Pavel Krsek %A Václav Hlaváč %A Tomáš Pajdla %A Milan Bartoš %N 10 %P 27-31 %U http://www.odbornecasopisy.cz/res/pdf/37934.pdf %V - %0 Journal Article %J International Journal of Robust and Nonlinear Control %D 2007 %T Minimization of l2 norm of the error signal in posicast input command shaping: a polynomial approach. %A Zdeněk Hurák %A Martin Hromčík %A Martin Špiller %I Wiley-Interscience %N 8 %P 706-719 %R 10.1002/rnc.1128 %U http://dx.doi.org/10.1002/rnc.1128 %V 17 %8 May %0 Journal Article %J International Journal of Robust and Nonlinear Control %D 2007 %T Numerical algorithms for polynomial plus/minus factorization %A Martin Hromčík %A Michael Šebek %I John Wiley & Sons, Ltd. %N 8 %P 786–802 %R 10.1002/rnc.1132 %U http://dx.doi.org/10.1002/rnc.1132 %V 17 %8 May %0 Journal Article %J SIAM Journal on Control and Optimization %D 2006 %T Minimum Distance to the Range of a Banded Lower Triangular Toeplitz Operator in l1 and Application in l1-Optimal Control %A Hurak, Zdenek %A Böttcher, Albrecht %A Sebek, Michael %I SIAM %N 1 %P 107-122 %R 10.1137/S0363012903437940 %V 45 %XThe subject of the paper is the best approximation in $\ell^1$ of a given infinite sequence by sequences in the range of a given banded lower-triangular Toeplitz operator. Necessary and sufficient conditions for the existence of a minimizing solution are established and a numerical algorithm for finding such a solution is designed and theoretically founded. It is also shown that an optimal error sequence is only finitely nonzero. The relevancy of the problem in systems theory is outlined and numerical examples are presented.

%0 Conference Paper %B Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS) %D 2004 %T MIMO l1-optimal control via block Toeplitz operators %A Zdeněk Hurák %A Böttcher, Albrecht %C Leuven %8 2004 %0 Conference Paper %B Advanced Software, Control, and Communication Systems for Astronomy %D 2004 %T Time to go H-∞? %A Erm, Toomas %A Zdeněk Hurák %A Bertrand Bauvir %E Hilton Lewis %E Gianni Raffi %C Glasgow, Scotland, United Kingdom %I SPIE %P 68 - 78 %R 10.1117/12.555606 %U http://dx.doi.org/10.1117/12.555606 %V 5496 %7 Proceedings of SPIE %8 06/2004 %0 Thesis %B Faculty of Electrical Engineering %D 2004 %T l1 optimal control - a polynomial approach %A Zdeněk Hurák %I Czech Technical University in Prague %9 Ph.D. thesis