Robust MPC Based on Polyhedral Invariant Sets for LPV Systems

Abstract

A robust model predictive control (RMPC) using polyhedral invariant sets for linear parameter varying (LPV) systems is presented in this work. A sequence of state feedback gains associated with a sequence of nested polyhedral invariant sets is constructed off-line in order to reduce the computational burdens. At each control iteration, when the measured state lies between any two adjacent polyhedral invariant sets constructed, a state feedback gain is determined by interpolation of two pre-computed state feedback gains incorporated with scheduling parameters. Three interpolation algorithms are proposed. In the first algorithm, the real-time state feedback gain is determined by maximizing the state feedback gain with subjected to a set of constraints associated with current invariant set. In the second algorithm, the real-time state feedback gain is calculated by minimizing the violation of the constraints of the adjacent inner invariant set with subjected to a set of constraints associated with current invariant set. In the last algorithm, the real-time state feedback gain is obtaned by minimizing the upper bound of infinite horizon worst case performance cost, which is estimated by Lyapunov function at current state, with subjected to a set of constraints associated with current invariant set. The controller design is illustrated with a case study of nonlinear two-tank system. The simulation results showed that the proposed RMPC with interpolation provides a better control performance while on-line computation is still tractable as compared to previously reported algorithms.