# Diz 71 en

# Consensus and Synchronization in Distributed Estimation and Adaptive Control[edit]

**Author**: Štefan Knotek

This thesis brings two complementary approaches for distributed control and estimation in spatially interconnected multi-agent systems. In particular, the first approach brings a distributed estimation scheme for large-scale systems. The plant is considered affected by process disturbance, and measurements are corrupted by measurement noise. The proposed approach fuses measurements of differing reliability so that all nodes reach consensus on the plant's state estimate. This architecture is flexible to addition of new nodes and, to a certain extent, robust to node or communication link failures. This follows from a protocol allowing existence of nodes that do not measure anything but contribute to the data fusion in the sensor network. Hence, in spite of limited observability by each of the nodes, data fusion over sensor network allows each node to obtain the full estimate of the plant's state. Structured Lyapunov functions are used to prove the convergence of the estimator. Resulting estimation error covariances are analyzed in detail.

The second approach introduces a fully distributed adaptive protocol for consensus and synchronization in multi-agent systems on directed communication networks. Agents are modeled as general linear time-invariant systems. The proposed protocol introduces a novel adaptation scheme allowing control coupling gains to decay to their reference values. This approach improves upon existing adaptive consensus protocols, which may result in overly large or even unbounded coupling gains. The protocol design in this paper does not rely on any centralized information; hence it is fully distributed. Nevertheless, the price to pay for this is the need to estimate those reference values. Convergence of the overall network dynamics is guaranteed for correctly estimated references; otherwise, the trajectory of the system is only uniformly ultimately bounded. Two estimation algorithms are proposed: one based on the interval-halving method and the other based on a distributed estimation of Laplacian eigenvalues.