Conservatism and Scalability for Distributed Controller Synthesis of Interconnected Systems

This Master project concerns the problem of distributed controller synthesis for a special class of interconnected systems known as "decomposable systems" in a large-scale setting. Due to computational limitations, scalability constitutes one of the major concerns of the controller synthesis of such large-scale systems. One possibility to deal with this limitation is to decompose the synthesis conditions by enforcing some structure on the Lyapunov and multiplier matrices. However, this approach in general introduces conservatism. The aim of this project is to analyze the conservatism introduced by imposing specific structures on the matrices involved and then to reduce the conservatism as much as possible by imposing less structure, however still achieving some degree of decomposition. The strongest limitation in terms of performance, in the state of the art of the controller synthesis for this kind of systems, comes from the structure imposed on the Lyapunov matrix that is needed both for the decomposition and for the achievement of the desired distributed controller structure. During this project a new method, based on the full-block S-Procedure and on the extended formulation of the Bounded Real Lemma has been designed. The extended synthesis LMIs are less conservative compared to the previous formulations thanks to the fact that the optimization variables related to the controller parameters are independent of the Lyapunov matrix