Optimal control of nonlinear evolution inclusions
type: Item
instance of: scholarly article
title: Optimal control of nonlinear evolution inclusions
zbMATH Open document ID: 0697.49007
DOI: 10.1007/BF00940479
author: Nikolaos S. Papageorgiou
published in: Journal of Optimization Theory and Applications
publication date: 1990-01-01T00:00:00Z
review text: We study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control, that illustrates the applicability of our results.
Mathematics Subject Classification ID: 49J24
Mathematics Subject Classification ID: 35B37
zbMATH DE Number: 4142868
zbMATH Keywords: dense embedding
zbMATH Keywords: transition probability
zbMATH Keywords: support functions
zbMATH Keywords: Caratheodory integrands
zbMATH Keywords: Arzela-Ascoli theorem
zbMATH Keywords: monotone operators
zbMATH Keywords: evolution inclusions
zbMATH Keywords: relaxed system
zbMATH Keywords: nonlinear parabolic optimal control
MaRDI profile type: Publication
cites work: Q5601627
cites work: Q3925435
cites work: Geometric and analytic views in existence theorems for optimal control. II: Distributed and boundary controls
cites work: Geometric and analytic views in existence theorems for optimal control. III: Weak solutions
cites work: Existence of optimal controls for a class of systems governed by differential inclusions on a Banach space
cites work: Relaxation and existence of optimal controls of systems governed by evolution inclusions in separable Banach spaces
cites work: Q4743352
cites work: Existence theorems for general control problems of Bolza and Lagrange
cites work: Properties of Relaxed Trajectories for a Class of Nonlinear Evolution Equations on a Banach Space
cites work: Properties of the Relaxed Trajectories of Evolution Equations and Optimal Control
cites work: Survey of Measurable Selection Theorems
cites work: Q5570501
cites work: Q4094029
cites work: Convergence theorems for Banach space valued integrable multifunctions
cites work: A survey of the theory of spectral operators
cites work: Measurable multifunctions and their applications to convex integral functionals
cites work: Lower Semicontinuity of Integral Functionals with Nonconvex Integrands by Relaxation-Compactification
cites work: Regular Conditional Expectations of Correspondences
cites work: On the theory of Banach space valued multifunctions. I: Integration and conditional expectation
cites work: Q4123053
cites work: Q3851121
cites work: Uniform convergence of probability measures: Topological criteria
cites work: A general denseness result for relaxed control theory
cites work: Q4767831
description: scientific article; zbMATH DE number 4142868