Christoph Mark

• This thesis focuses on the development and analysis of Stochastic Model Predictive Control (SMPC) strategies for both distributed stochastic systems and centralized stochastic systems with partially known distributional information. The first part deals with the development of distributed SMPC schemes that can be synthesized and operated in a fully distributed manner, establishing rigorous theoretical guarantees such as recursive feasibility, stability and closed-loop chance constraint satisfaction. We study several control problems of practical interest, such as the output-feedback regulation problem or the state-feedback tracking problem under additive stochastic noise, and the regulation problem under multiplicative noise. In the second part of this thesis, a novel research topic known as distributionally robust MPC (DR-MPC) is explored, which enhances the applicability of SMPC to real-world problems. DR-MPC is advantageous as it solely necessitates partial knowledge in the form of samples of the uncertainty, which is usually available in practical scenarios, while SMPC mandates exact knowledge of the (unknown) distributional information. We investigate different so-called ambiguity sets to immunize the DR-MPC optimization problem against sampling inaccuracies, leading to tractable optimization problems with strong theoretical guarantees. Altogether, both parts provide rigorous theoretical guarantees with practical design procedures demonstrated by numerical examples, which are the main contributions of this thesis.