# Dp 603 en

# Non Linear Optimal Control Strategies For Geostationary Spacecraft Orbit Station Keeping Using Electrical Propulsion Only[edit]

**Author**: Roth Maximilian

This thesis concentrates on the non-linear optimisation of the station keeping problem of a low-thrust geostationary satellite and provides with the Approximate Sequence of Riccati Equation (ASRE) optimisation method a tool to decrease the total fuel consumption to a global minimum.
Creating a perturbation model for geostationary satellites with only electrical propulsion systems and describing an optimal control algorithm called Approximated Sequence of Riccati Equations with the transition method approach which guarantees convergence to its global optimum are necessary to design an accurate simulation of the station keeping problem. Therefore, these are combined with
the spacecraft dynamics and the optimisation method to calculate a global optimal fuel consumption in a fixed time horizon. As far as the author knows the description of the ASRE algorithm with transition matrix approach is the detailed, public available one. It is the first time that the umbra and penumbra are considered for the perturbation model for the used optimisation method. For the verification of the final fuel consumption, the results of common literature, like Losa [14], are used to demonstrate the functionality of the used optimisation. The findings of this thesis illustrate the complexity of the non-linear station keeping problem as well as the Approximated Sequence of Riccati
Equations optimisation method for geostationary satellites can compete with already available solutions. Furthermore, the derivation of the State-Dependent Riccati Equations to the Approximated Sequence of Riccati Equations is discussed and approaches to decrease the propellant consumption are considered like changing the mathematical factorisations or constraining the problem in another way. The expectations of the optimisation approach are absolutely fulfilled, but the final result has to go through more optimisations of the adjustable variables to achieve better results than provided by common literature.
To conclude, the used optimisation method has the power to provide a very low propellant consumption profile for geostationary station keeping, but in the future some further improvements to the free parameters of the optimisation have to be done.

**Roth Maximilian**, mailto:rothmaxi@fel.cvut.cz