Robust one‐step receding horizon control for constrained systems

Abstract

This paper proposes a robust receding horizon control scheme for discrete‐time uncertain linear systems with input and state constraints. The control scheme is based on the minimization of the worst‐case one‐step finite horizon cost with a finite terminal weighting matrix. It is shown that the proposed receding horizon control robustly asymptotically stabilizes uncertain constrained systems under some matrix inequality conditions on the terminal weighting matrices. This robust receding horizon control scheme has a larger feasible initial‐state set and a more general structure than existing robust receding horizon controls for uncertain constrained systems under the same design parameters. The proposed controller is obtained using semidefinite programming. Copyright © 1999 John Wiley & Sons, Ltd.

5. Linear Time-Varying Systems

“…In this paper, we propose a new RHC scheme 1 for input/state constrained discrete-time systems, which enhances feasibility and on-line computation on the constrained optimization problem compared with existing ones [1,3,4,7,9]. The control scheme is based on a time-varying finite horizon cost function with time-varying finite terminal weighting matrices, which can easily be implemented via linear matrix inequality (LMI) optimization.…”

“…Note that for implementation, the cost monotonicity with time-varying terminal weighting matrices should be handled carefully as shown in [7]. Next, we show that the proposed RHC scheme includes previous schemes [1,3,4,7,9].…”

“…Since the RHC can consider a finite horizon cost function for closed-loop stability, it takes advantage of handling input/state constraints, time-varying systems, etc. Finite horizon formulations with finite terminal weighting matrices have been widely investigated [1,2,3,4,5,6,7,8], since they include the infinite horizon formulation in [9].…”

“…In the literature, terminal weighting matrices have often been represented by inequality conditions that guarantee closed-loop stability [1,3,4,5,6].…”

“…For constrained-time varying systems, some results have conservative feasible initial-state sets since they assume a linear feedback RHC [9] or one-horizon cost function [4]. Although other results [1,3] consider a nonlinear feedback RHC and finite horizon, the terminal inequality condition in [3] is not practical as shown in [7] and the fixed terminal weighting matrix in [1] still has a small feasible initial-state set.…”