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Discrete Approximations of a Controlled Sweeping Process

Giovanni Colombo(colombo***at***math.unipd.it)
René Henrion(henrion***at***wias-berlin.de)
Nguyen Dinh Hoang(hoang.nguyen***at***usm.cl)
Boris S. Mordukhovich(boris***at***math.wayne.edu)

Abstract: The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhedral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their analysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the $W^{1,2}$ topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts.

Keywords: optimal control, sweeping process, moving controlled polyhedra, dissipative differential inclusions, discrete approximations, variational analysis

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Submitted to Set-Valued and Variational Analysis: Theory and Applications

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Entry Submitted: 07/18/2014
Entry Accepted: 07/18/2014
Entry Last Modified: 07/18/2014

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