Approximations of closed-loop minimax MPC

Minimax or worst-case approaches have been used frequently recently in model predictive control (MPC) to obtain control laws that are less sensitive to uncertainty. The problem with minimax MPC is that the controller can become overly conservative. An extension to minimax MPC that can resolve this problem is closed-loop minimax MPC. Unfortunately, closed-loop minimax MPC is essentially an intractable problem. In this paper, we introduce a novel approach to approximate the solution to a number of closed-loop minimax MPC problems. The result is convex optimization problems with size growing polynomially in system dimension and prediction horizon.

[1]  Manfred Morari,et al.  Robust Model Predictive Control , 1987, 1987 American Control Conference.

[2]  Z. Zheng.  Robust Control of Systems Subject to Contraints , 1995 .

[3]  Laurent El Ghaoui,et al.  Robust Solutions to Uncertain Semidefinite Programs , 1998, SIAM J. Optim..

[4]  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).

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

[6]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[7]  Wagner Caradori do Amaral,et al.  Constrained robust predictive controller for uncertain processes modeled by orthonormal series functions , 2000, Autom..

[8]  J. Rossiter,et al.  Robust predictive control using tight sets of predicted states , 2000 .

[9]  Basil Kouvaritakis,et al.  A linear programming approach to constrained robust predictive control , 2000, IEEE Trans. Autom. Control..

[10]  Luigi Chisci,et al.  Predictive control for constrained systems with polytopic uncertainty , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[11]  F. Borrelli.  Discrete time constrained optimal control , 2002 .

[12]  J. Löfberg.  Minimax approaches to robust model predictive control , 2003 .

[13]  J. H. Leet,et al.  Worst-case formulations of model predictive control for systems with bounded parameters , 1997, Autom..

[14]  J. Maciejowski,et al.  Feedback min‐max model predictive control using a single linear program: robust stability and the explicit solution , 2004 .