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Sensitivity of optimal solutions to control problems for systems described by hemivariational inequalities

Denkowski Z., Migórski S.

Control and Cybernetics

2004

Vol. 33, no 2

211-236

In this paper the sensitivity of optimal solutions to control problems for the systems described by stationary and evolution heinivariational inequalities (HVIs) under perturbations of state relations and of cost functionals is investigated. First, basing on the theory of sequential [Gamma]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for HVIs (state relations) and some complementary [Gamma]-convergence of the cost functionals. Then these two properties are implemented in each considered case.

Control problems for systems described by hemivariational inequalities

Denkowski Z.

Control and Cybernetics

2002

Vol. 31, no 3

713-738

The paper considers some control problems for the systems described by the evolution, as well as the stationary hemivariational inequalities (HVIs for short). First, basing on surjectivity theorems for pseudo-monotone operators we formulate some existence results for the solutions of the HVIs and investigate some properties of the solution set (like sensitivity; i.e. its dependence on data and operators). Next we quote some existence theorems for optimal solutions for various classes of optimal control like distributed control (e.g. Bolza problem), identification of parameters, or optimal shape design for systems described by HVIs. Finally, we discuss some common features in getting the existence of optimal solutions as well as some "well-posedness" problems.