Note: This content is accessible to all versions of every browser. However, this browser does not seem to support current Web standards, preventing the display of our site's design details.

  

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

File Download:

Request a copy of this publication.
(Uses JavaScript)
@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},
}
Permanent link