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Minimal invasion: An optimal L∞ state constraint problem

Published online by Cambridge University Press:  11 October 2010

Christian Clason ,
Kazufumi Ito  and
Karl Kunisch
Christian Clason
Affiliation:
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria. christian.clason@uni-graz.at; karl.kunisch@uni-graz.at
Kazufumi Ito
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695-8205, USA. kito@math.ncsu.edu
Karl Kunisch
Affiliation:
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria. christian.clason@uni-graz.at; karl.kunisch@uni-graz.at
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Abstract

In this work, the least pointwise upper and/or lower bounds on the state variable on a specified subdomain of a control system under piecewise constant control action are sought. This results in a non-smooth optimization problem in function spaces. Introducing a Moreau-Yosida regularization of the state constraints, the problem can be solved using a superlinearly convergent semi-smooth Newton method. Optimality conditions are derived, convergence of the Moreau-Yosida regularization is proved, and well-posedness and superlinear convergence of the Newton method is shown. Numerical examples illustrate the features of this problem and the proposed approach.

Keywords

Optimal controloptimal L∞ state constraintsemi-smooth Newton method
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 3 , May 2011 , pp. 505 - 522
Copyright
© EDP Sciences, SMAI, 2010

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