Optimization and discrete approximation of sweeping processes with controlled moving sets and perturbations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:274

Article

Cao, Tan H.¹  Colombo, Giovanni²  Mordukhovich, Boris S.³  Dao Nguyen³ 

[1] State Univ New York Korea, Dept Appl Math & Stat, Incheon, South Korea

[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

[3] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

关键词: Optimal control;    Sweeping process;    Discrete approximation;    Variational analysis;    Generalized differentiation;    Necessary optimality conditions;   

DOI  :  10.1016/j.jde.2020.10.017

来源: Elsevier

【 摘 要 】

This paper addresses a new class of optimal control problems for perturbed sweeping processes with measurable controls in additive perturbations of the dynamics and smooth controls in polyhedral moving sets. We develop a constructive discrete approximation procedure that allows us to strongly approximate any feasible trajectory of the controlled sweeping process by feasible discrete trajectories and also establish a W-1,W-2-strong convergence of optimal trajectories for discretized control problems to a given local minimizer of the original continuous-time sweeping control problem of the Bolza type. Employing advanced tools of first-order and second-order variational analysis and generalized differentiation, we derive necessary optimality conditions for discrete optimal solutions under fairly general assumptions formulated entirely in terms of the given data. The obtained results give us efficient suboptimality (almost optimality) conditions for the original sweeping control problem that are illustrated by a nontrivial numerical example. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free