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Optimal Control of Piecewise Affine Systems: A Dynamic Programming Approach

Author(s):

F.J. Christophersen, M. Baotic, M. Morari
Conference/Journal:

vol. AUT05-04
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:

(04)Technical Report
Supervisor:

M. Morari

No Files for download available.
@TechReport{ChrEtal:05:trep,
  author       = {F. J. Christophersen and M. Baoti{\'c} and
                  M. Morari},
  title	       = {{Optimal Control of Piecewise Affine Systems: A
                  Dynamic Programming Approach}},
  institution  = {Automatic Control Laboratory},
  year	       = {2005},
  number       = {AUT05-04},
  address      = {Swiss Federal Institute of Technology (ETH)},
  month	       = may,
  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, stability},
}
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