A parameterized polyhedra approach for the explicit robust model predictive control

The paper considers the discrete-time linear time-invariant systems affected by input disturbances. The goal is to construct the robust model predictive control (RMPC) law taking into account the constraints existence from the design stage. The explicit formulation of the controller is found by exploiting the fact that the optimum of a min-max multi-parametric program is placed on the parameterized vertices of a parameterized polyhedron. As these vertices have specific validity domains, the control law has the form of a piecewise linear function of the current state. Its evaluation replaces the time-consuming on-line optimization problems.

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

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

[3]  Graham C. Goodwin,et al.  Constrained Control and Estimation , 2005 .

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

[5]  Alberto Bemporad,et al.  Evaluation of piecewise affine control via binary search tree , 2003, Autom..

[6]  Vincent Loechner,et al.  Parameterized Polyhedra and Their Vertices , 1997, International Journal of Parallel Programming.

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

[8]  David K. Smith.  Theory of Linear and Integer Programming , 1987 .

[9]  Francesco Borrelli,et al.  Constrained Optimal Control of Linear and Hybrid Systems , 2003, IEEE Transactions on Automatic Control.

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

[11]  Doran Wilde,et al.  A LIBRARY FOR DOING POLYHEDRAL OPERATIONS , 2000 .

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

[13]  H. Le Verge,et al.  A Note on Chernikova's algorithm , 1992 .

[14]  H. Raiffa,et al.  3. The Double Description Method , 1953 .

[15]  E. Kerrigan.  Robust Constraint Satisfaction: Invariant Sets and Predictive Control , 2000 .

[16]  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).

[17]  John Anthony Rossiter.  Model-Based Predictive Control , 2003 .

[18]  M. Morari,et al.  Robust model predictive control: Piecewise linear explicit solution , 2001, 2001 European Control Conference (ECC).

[19]  Alberto Bemporad,et al.  Convexity recognition of the union of polyhedra , 2001, Comput. Geom..

[20]  H. L. Verge.  A Note on Chernikova's algorithm , 1992 .