About Moreau-Yosida regularization of the minimal time crisis problem.

Resumen:

We  study an optimal control problem where the cost functional to be
minimized represents the so-called time of crisis, i.e. the time spent by
a trajectory solution of a control system outside a given set K. This
functional can be expressed using the indicator of K, that is
discontinuous preventing the use of the standard Maximum Principle. We
consider a regularization scheme of the problem based on the Moreau-Yosida
approximation of the characteristic function of K. We prove the
convergence of an optimal sequence for the approximated problem to an
optimal solution of the original problem. We then investigate the
convergence of the adjoint vector given by Pontryagin’s Principle when the
regularization parameter goes to zero.  Finally, we study an example
illustrating the convergence property and we compute explicitly an optimal
feedback policy and the value function.

Posted on May 4, 2015 in Optimization and Equilibrium, Seminars