Computationally efficient algorithms for constraint handling with guaranteed stability and near optimality

Predictive control strategies allow for the systematic handling of constraint, performance and stability. However, the associated algorithms can be computational burdensome and/or difficult to unravel. The aim of this paper is to discuss and compare algorithms based on invariant sets which meet the additional requirement for computational simplicity. There may of course be a concomitant loss of optimality, but as illustrated, this can be minimal and often is a small price to pay when one considers the significant improvements in efficiency.

[1]  B. Kouvaritakis,et al.  Efficient active set optimization in triple mode MPC , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[2]  David Clarke,et al.  Generalised predictive control with input constraints , 1988 .

[3]  P. R. Bélanger,et al.  Piecewise-linear LQ control for systems with input constraints , 1994, Autom..

[4]  J. A. Rossiter,et al.  Triple mode control in MPC , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[5]  Mark Rice,et al.  A numerically robust state-space approach to stable-predictive control strategies , 1998, Autom..

[6]  B. Kouvaritakis,et al.  A computationally efficient constrained predictive control law , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[7]  Manfred Morari,et al.  Model predictive control: Theory and practice - A survey , 1989, Autom..

[8]  B. Kouvaritakis,et al.  Stable generalised predictive control: an algorithm with guaranteed stability , 1992 .

[9]  Basil Kouvaritakis,et al.  Feasibility and stability results for constrained stable generalized predictive control , 1995, Autom..

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

[11]  Jose Alvarez-Ramirez,et al.  Global stabilization of discrete-time linear systems with bounded inputs , 1996 .

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

[13]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[14]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[15]  G. Nicolao,et al.  Stabilizing receding-horizon control of nonlinear time-varying systems , 1998, IEEE Trans. Autom. Control..

[16]  B. Kouvaritakis,et al.  Removing the Need for QP in Constrained Predictive Control , 2000 .

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

[18]  James B. Rawlings,et al.  Constrained linear quadratic regulation , 1998, IEEE Trans. Autom. Control..

[19]  Edoardo Mosca,et al.  Stable redesign of predictive control , 1992, Autom..

[20]  Luigi Chisci,et al.  Robust Predictive Control with Restricted Constraints to Cope with Estimation Errors , 2000 .

[21]  B. Kouvaritakis,et al.  Linear matrix inequalities and polyhedral invariant sets in constrained robust predictive control , 2000 .

[22]  D. Mayne,et al.  Robust receding horizon control of constrained nonlinear systems , 1993, IEEE Trans. Autom. Control..

[23]  Basil Kouvaritakis,et al.  Linear Quadratic Feasible Predictive Control , 1998, Autom..

[24]  J. A. Rossiter,et al.  Robust piecewise-linear control for polytopic systems with input constraints , 1998 .