Optimal control of difference, differential, and differential-difference inclusions
type: Item
instance of: scholarly article
title: Optimal control of difference, differential, and differential-difference inclusions
zbMATH Open document ID: 0966.49018
DOI: 10.1007/BF02672708
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-11-07T00:00:00Z
review text: The paper deals with optimal control problems for differential and differential-difference inclusions with nonconvex admissible velocity sets, the cost being a function depending on initial and terminal states satisfying given constraints. Necessary optimality conditions are presented under suitable conditions. The author derives well-posed discrete approximations with appropriate convergence results, studies optimal solutions for the corresponding finite-dimensional problems and then obtains optimality conditions for the original problem in infinite dimensions by passing to the limit in approximations. The main complications come from dynamic constraints and its finite-difference approximations that lead to an increasing number of (nonsmooth and nonconvex) geometric constraints in corresponding finite-dimensional problems. The author presents basic results of generalized differentiation that allows to handle such situations and supports limiting procedures.
Mathematics Subject Classification ID: 49K24
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 1526507
zbMATH Keywords: optimal control
zbMATH Keywords: differential and differential-difference inclusions
zbMATH Keywords: finite-dimensional approximations
zbMATH Keywords: optimality conditions
author: Boris S. Mordukhovich
reviewed by: Ernst G. Al'brekht
MaRDI profile type: Publication
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