Robust constrained model predictive control for piecewise affine systems using saturated linear feedback controller

Abstract

Piece-Wise Af_ne (PWA) systems belong to a promising class of hybrid systems. PWA systems can be considered as a natural model class for nonlinear systems since they can be used to approximate a range of nonlinearities by a set of af_ne/ linear function. This class of representation is still an active research area. This thesis presents the application of the Robust Constrained Model Predictive Control (RCMPC) design framework for discrete-time PWA systems under parametric uncertainties. In order to guarantee robust performance, the control law applies a parameter-dependent Lyapunov function which corresponds to the vertices of the polytopic uncertainties of the PWA systems. We consider saturated linear feedback control law in deriving tractable and robustly stable closed-loop PWA systems. The design approach is divided into two parts. The first part focuses on the design of a robust control law for uncertain time-varying PWA systems with delay-free. The second part emphasizes on the design of a robust control law for uncertain time-varying PWA systems with timedelays. Moreover, we consider two sub-parts of the systems, which are PWA systems with timeinvariant delays and PWA systems with time-varying delays. The design formulations are then cast as a Linear Matrix Inequalities (LMIs) optimization problem and the algorithms are solved on-line to guarantee the robust stability of the closed-loop systems. Once a feasible solution is found, the system is guaranteed to be asymptotically stable for time kappa is more than The numerical results demonstrate that the framework adopted here is suitable and effective.