# Optimal Control of Piecewise Affine Systems: A Dynamic Programming Approach

Author(s):F.J. Christophersen, M. Baotic, M. Morari |
Conference/Journal:Lecture Notes in Control and Information Sciences (LNCIS), vol. 322, pp. 183--198, "Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems" Editors: Thomas Meurer, Knut Graichen, Ernst Dieter Gilles |

Abstract:We consider the constrained finite and infinite time optimal control problem for the class of discrete-time linear piecewise affine systems. When a linear performance index is used the finite and infinite time optimal solution is a piecewise affine state feedback control law. In this paper we present an algorithm to compute the optimal solution for the finite time case where the algorithm combines a dynamic programming exploration strategy with multi-parametric linear programming and basic polyhedral manipulation. We extend the ideas to the infinite time case and show the equivalence of the dynamic programming generated solution with the solution to the infinite time optimal control problem. Further Information |
Year:2005 |

Type of Publication:(01)Article | |

Supervisor:M. Morari | |

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@String{lncis = {Lecture Notes in Control and Information Sciences}} @InCollection{ChrEtal:lncis-syncod:05, author = {F. J. Christophersen and M. Baoti{\'c} and M. Morari}, title = {{Optimal Control of Piecewise Affine Systems: A Dynamic Programming Approach}}, booktitle = {Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems}, pages = {183--198}, note = {Available from {\url{http://control.ee.ethz.ch/index.cgi?page=publications&action=details&id=2132}}}, abstract = {We consider the constrained finite and infinite time optimal control problem for the class of discrete-time linear piecewise affine systems. When a linear performance index is used the finite and infinite time optimal solution is a piecewise affine state feedback control law. In this paper we present an algorithm to compute the optimal solution for the finite time case where the algorithm combines a dynamic programming exploration strategy with multi-parametric linear programming and basic polyhedral manipulation. We extend the ideas to the infinite time case and show the equivalence of the dynamic programming generated solution with the solution to the infinite time optimal control problem.}, keywords = {constrained systems, finite time, infinite time, optimal control, discrete-time, hybrid systems, piecewise affine systems, dynamic programming, multi-parametric linear program}, editor = {T. Meurer and K. Graichen and E. D. Gilles}, publisher = {Springer-Verlag}, year = {2005}, volume = {322}, series = lncis, ISSN = {0170-8643}, ISBN = {3-540-27938-5}, address = {Berlin Heidelberg, Germany}, } | |

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