Predictive Control Using Semi-Definite Programming -- Efficient Approaches for Periodic Systems and Lur'e Systems

One of the main challenges in nonlinear model predictive control (NMPC) is the formulation of the associated optimisation problems in a computationally efficient way. In this context, the thesis at hand discusses the usefulness of semi-definite programs (SDPs), which represent a specific type of convex optimisation problems that can be solved efficiently using standard numerical solvers. In particular, the thesis presents several computationally attractive NMPC approaches both for the class of periodically time-varying systems and the class of sector-bounded Lur'e systems. Exploiting the structural properties of those system classes allows to derive SDPs which are used to calculate design parameters of the proposed NMPC schemes and/or to formulate computationally attractive online optimisation problems. The NMPC approaches derived are shown to guarantee closed-loop stability and their application to control both the attitude of a low Earth orbit satellite as well as a flexible link robotic arm demonstrates their practical relevance.