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Variational Stability Analysis of Optimal Control Problems for Systems Governed by Nonlinear Second Order Evolution Equations

The variational stability of optimal control problems governed by second order nonlinear evolution abstract equations is studied. First we prove an existence theorem for optimal solutions. Then admitting perturbations in all the data of the control problem, we show the results on the asymptotic behavior of optimal solutions to control problems as well as on the convergence of minimal values and reachable sets. The notions of-convergence of functionals and the Kuratowski-Mosco convergence of sets are employed. Finally an example of nonlinear hyperbolic control problem demonstrates the applicability of the results.