Asymptotic behavior of the minima to a class of optimization problems for differential inclusions (Q1331103)

The problem of stability of solution sets \(S_ k(\xi_ k)\) of a differential inclusion \(\dot x \in F_ k (t,x)\), \(x(0) = \xi_ k\) \((t \in I\), \(x \in R^ n)\), obtained by perturbations of the dynamics of the limit inclusion \(\dot x \in F_ \infty (t,x)\), \(x(0) = \xi_ \infty\), is considered. Under appropriate assumptions the authors prove the convergence of \(S_ k (\xi_ k)\) to \(S_ \infty (\xi_ \infty)\) \((k \to \infty)\) in the sence of Kuratowski and in the sence of Mosco. These results as well as some theorems from \(\Gamma\)-convergence theory are applied to prove the stability of the optimal solutions of the optimization problem for differential inclusions with Bolza-type cost function.