Minimal invasion: An optimal L∞ state constraint problem
Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria. email@example.com; firstname.lastname@example.org
2 Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695-8205, USA. email@example.com
Revised: 14 June 2010
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.
Mathematics Subject Classification: 49J52 / 49J20 / 49K20
Key words: Optimal control / optimal L∞ state constraint / semi-smooth Newton method
© EDP Sciences, SMAI, 2010