Observer-based output feedback robust MPC via zonotopic set-membership state estimation for LPV systems with bounded disturbances and noises

Abstract

For linear parameter varying (LPV) systems with bounded disturbances and noises, this paper presents a synthesis approach to observer-based output feedback robust model predictive control (RMPC) via the zonotopic set-membership state estimation. In the off-line optimization problem, the state observer sub-gains with a minimal ellipsoidal robust positively invariant (RPI) set for the zonotopic estimation error set are designed. In the on-line control optimization problem, bounds of the current and future zontopic estimation error sets are outer approximated by scaling the minimal ellipsoidal RPI set. Then, an on-line constrained optimization problem that considers bounds of the predicted zonotopic estimation error sets is solved to guarantee robust stability of the closed-loop observer system. In the on-line receding horizon optimization, the zonotopic estimation error set is refreshed based on zonotopic properties, and its outer approximated ellipsoidal set is optimized via the technique of S-procedure. By properly considering the relationship between the zonotopic estimation error set and its outer approximated ellipsoidal set, recursive feasibility of the optimization problem can be ensured. The on-line optimization problem guarantees that the nominal estimation error system and nominal closed-loop observer system converge to the origin. When bounded disturbances and noises are considered, the estimation error system and closed-loop observer system respectively bounded within time-varying RPI sets and robust control invariant (RCI) sets are steered to a neighborhood of the origin such that robust stability of the controlled system is guaranteed. A simulation example is given to illustrate the proposed method.