Robust constrained model predictive control with a parameter-dependent lyapunov function using linear matrix inequalities

Abstract

This thesis presents robust constrained model predictive control for linear time-varying systems under parametric uncertainties. In order to guarantee robust performance, the control law applies a parameter-dependent Lyapunov function which corresponds to vertices of the polytopic uncertainty. The design approach is divided into two parts. The first part is focused on the design of a robust state feedback law that minimizes, at each sampling time, an upper bound of the worst-case objective function, subject to constraints on control inputs and process outputs. The state feedback design problem is cast as convex optimization involving linear matrix inequalities (LMIs) which can be efficiently solved. The second part emphasizes on a robust output feedback scheme that utilizes the state feedback obtained from the first part together with state estimator. The synthesis approach is to solve off-line LMI problems to guarantee the robust stability of the augmented closed-loop system. In comparison with the previous work whose design employs a single Lyapunov function, the method proposed in this thesis yields less conservative performance and further improves the algorithm. In particular, the design method is capable of handling a wider range of uncertain time-varying parameters. Finally, several applications are presented to illustrate the effectiveness of the control technique.