Invariant set constructions for feasible reference tracking

Model predictive control strategy is based on the iterative resolution of a constrained optimization problem. In thsi context, the feasibility represents a central issue. The present paper concentrates on the use of the invariant sets to guarantee the feasibility of the predictive control law for reference tracking applications. In a first stage, two basic algorithms to approximate the maximal invariant set (MPI) will be presented. The first one proposes set iterations using a contraction procedure, while the second one uses an expansive construction. In a second stage, these procedures are adapted for the computation of feasible reference tracking (FRT) sets.

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

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

[3]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[4]  J.A. De Dona,et al.  Analytical Solution of Input Constrained Reference Tracking Problems by Dynamic Programming , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[5]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .

[6]  Mikael Johansson,et al.  Piecewise linear control systems - a computational approach , 2002, Lecture notes in control and information sciences.

[7]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[8]  M. Johansson,et al.  Piecewise Linear Control Systems , 2003 .

[9]  Alberto Bemporad,et al.  An algorithm for multi-parametric quadratic programming and explicit MPC solutions , 2003, Autom..

[10]  D. Limón,et al.  MPC FOR TRACKING OF PIECE-WISE CONSTANT REFERENCES FOR CONSTRAINED LINEAR SYSTEMS , 2005 .

[11]  D. Mayne,et al.  Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[12]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[13]  D. Dumur,et al.  Compact explicit MPC with guarantee of feasibility for tracking , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[15]  Didier Dumur,et al.  A parameterized polyhedra approach for explicit constrained predictive control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[16]  S. Olaru,et al.  Computation and bounding of robust invariant sets for uncertain systems , 2008 .