Optimal control for nonlinear abstract evolution systems (Q1308522)

The problem considered is to minimize Lagrange type cost functional on trajectories of a nonlinear abstract evolution system given in the framework of Gelfand triple. Under more general assumptions then in the previous works the author obtains the necessary conditions for optimality in the form of the Pontryagin maximum principle. The approach is based on the Ekeland variational principle together with the spike variation technique. Applications to the control problem for quasilinear parabolic systems are presented.