Robust model predictive control: Piecewise linear explicit solution

For discrete-time linear time-invariant systems with input disturbances and constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to robust optimal control problems based on min-max optimization. We show that the optimal control sequence is a piecewise linear function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the on-line computation of the resulting MPC controller is reduced to a simple linear function evaluation. In this paper the uncertainty is modeled as an additive norm-bounded input disturbance vector. The technique can be also extended to robust control of constrained systems affected by polyhedral parametric uncertainty.

[1]  T. Gál,et al.  Multiparametric Linear Programming , 1972 .

[2]  A. Fiacco,et al.  Convexity and concavity properties of the optimal value function in parametric nonlinear programming , 1983 .

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

[4]  M. Schechter.  Polyhedral functions and multiparametric linear programming , 1987 .

[5]  Franco Blanchini,et al.  Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[6]  J. Allwright,et al.  On linear programming and robust modelpredictive control using impulse-responses , 1992 .

[7]  M. Morari,et al.  Robust Stability of Constrained Model Predictive Control , 1993, 1993 American Control Conference.

[8]  Tomas Gal,et al.  Postoptimal Analyses, Parametric Programming, and Related Topics: Degeneracy, Multicriteria Decision Making, Redundancy , 1994 .

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

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

[11]  E. Pistikopoulos,et al.  A multiparametric programming approach for linear process engineering problems under uncertainty , 1997 .

[12]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[13]  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).

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

[15]  Alberto Bemporad,et al.  Control of systems integrating logic, dynamics, and constraints , 1999, Autom..

[16]  J. Maciejowski,et al.  Invariant sets for constrained nonlinear discrete-time systems with application to feasibility in model predictive control , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[17]  M. Morari,et al.  Explicit solution of LP-based model predictive control , 2000 .

[18]  Efstratios N. Pistikopoulos,et al.  An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems , 2000, Ann. Oper. Res..

[19]  M. Morari,et al.  Optimal controllers for hybrid systems: stability and piecewise linear explicit form , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[20]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[21]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[22]  M. Morari,et al.  A geometric algorithm for multi-parametric linear programming , 2003 .

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