Title: Optimal control for sweeping processes to prox-regular sets with
free-time

Trang Nguyen

Abstract:  This talk concerns the optimal control of discontinuous
differential inclusions of the normal cone type governed by a generalized
version of the Moreau sweeping process with free-time and the control
functions acting in nonconvex moving sets, perturbations, and running
cost.

This is a new class of optimal control problems to prox-regular sets with
free-time in comparison with previously considered counterparts where the
controlled sweeping sets are described by convex polyhedra and fixed time.

  Based on a constructive discrete approximation approach and advanced tools
of first-order and second-order variational analysis and generalized
differentiation, we establish the strong convergence of discrete optimal
solutions and derive a complete set of necessary optimality conditions for
discrete-time and continuous-time sweeping control systems that are
expressed entirely via the problem data.