Minimal Invasion: an Optimal L∞ State Constraint Problem
نویسندگان
چکیده
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. Received January 27, 2010. Revised June 14, 2010. Published online October 11, 2010.
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