Min-max feedback model predictive control with state estimation

This paper proposes a state estimation scheme for output feedback min-max model predictive control (MPC). A set-membership state estimator bounds the current states of the physical system. A standard state estimator provides state feedback for the state feedback control law in MPC optimization over the prediction horizon. The paper presents a recursive method for the set-membership state estimation and conditions for bounded stability of the closed-loop system. The approach is illustrated with an example.

[1]  D. Bertsekas,et al.  On the minimax reachability of target sets and target tubes , 1971 .

[2]  D. Mayne,et al.  Min-max feedback model predictive control for constrained linear systems , 1998, IEEE Trans. Autom. Control..

[3]  S. Joe Qin,et al.  An Overview of Nonlinear Model Predictive Control Applications , 2000 .

[4]  Jeff S. Shamma,et al.  Set-valued observers and optimal disturbance rejection , 1999, IEEE Trans. Autom. Control..

[5]  F. Schweppe.  Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .

[6]  Michael Nikolaou,et al.  Robust stability analysis of constrained l1‐norm model predictive control , 1993 .

[7]  F. Schweppe,et al.  Control of linear dynamic systems with set constrained disturbances , 1971 .

[8]  Frank Allgöwer,et al.  Min-max output feedback predictive control with guaranteed stability , 2022 .

[9]  Olaf Stursberg,et al.  LMI Approach to Robust Model Predictive Control , 2005 .

[10]  A. Garulli,et al.  Output-feedback predictive control of constrained linear systems via set-membership state estimation , 2000 .

[11]  Jay H. Lee,et al.  Model predictive control: past, present and future , 1999 .

[12]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[13]  Alberto Bemporad,et al.  Output-feedback predictive control of constrained linear systems with disturbances via set-membership state estimation , 2000 .

[14]  D. Jia,et al.  Min-max feedback model predictive control for distributed control with communication , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[15]  Alberto Bemporad,et al.  Reducing conservativeness in predictive control of constrained systems with disturbances , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).