An LMI approach to robust model predictive control of nonlinear systems with state-dependent uncertainties

Abstract

The design of robust model predictive controller (RMPC) for uncertain nonlinear system is a challenging problem in the area of nonlinear control, yet. A new approach to RMPC is presented here for nonlinear systems with state-dependent uncertainties. The nonlinear system is considered as comprised of a linear part, a nonlinear term, and a bounded additive uncertainty. A state feedback control law is obtained via solving an optimization problem of an infinite horizon quadratic cost function in the framework of linear matrix inequalities (LMIs). To solve the optimization problem, the nonlinear and uncertain terms of the system are supposed to be bounded by a quadratic function that is obtained by solving a sum of squares (SOS) optimization problem. Moreover, the sufficient state feedback synthesis condition guarantees the robust stability of the system in the presence of unknown bounded uncertainties. In this context, a LMI-based optimization problem is solved to obtain the maximum region of stability which is desired to be a subset of the region of feasibility. The simulation examples are reported to indicate the applicability and effectiveness of the proposed approach with different uncertainty scenarios.