Maximum principle for a control problem governed by an evolution equation
type: Item
instance of: scholarly article
title: Maximum principle for a control problem governed by an evolution equation
zbMATH Open document ID: 0968.49017
DOI: 10.1023/A:1004654800011
published in: Journal of Optimization Theory and Applications
publication date: 2001-05-09T00:00:00Z
review text: The control problem is that of minimizing the functional \[ \int_0^T L(t, y(t), u(t)) dt + g(y(0), y(T)) \] over the trajectories of the system \[ y'(t) + A(t)y(t)= f(t, y(t), u(t)), \quad 0 \leq t \leq T, \] \[ (y(0), y(T)) \in C, \qquad u(t) \in U(t). \] Here, \(A(t)\) is a family of unbounded operators generating an evolution system \(U(t, s)\) in a Hilbert space. The author proves Pontryagin's maximum principle for optimal controls under three different sets of assumptions involving the set \(C\) and properties of the evolution system.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49K27
zbMATH DE Number: 1523627
zbMATH Keywords: optimal control
zbMATH Keywords: distributed parameter systems
zbMATH Keywords: Pontryagin maximum principle
zbMATH Keywords: Ekeland variational principle
zbMATH Keywords: unbounded controls
author: Marcello Bertoldi
reviewed by: Hector O. Fattorini
MaRDI profile type: Publication
cites work: Pontryagin Maximum Principle for Semilinear and Quasilinear Parabolic Equations with Pointwise State Constraints
cites work: Necessary Conditions for Optimal Control of Distributed Parameter Systems
cites work: Pontryagin's Principle for State-Constrained Boundary Control Problems of Semilinear Parabolic Equations
cites work: Pontryagin's Principle for State-Constrained Control Problems Governed by Parabolic Equations with Unbounded Controls
cites work: A unified theory of necessary conditions for nonlinear nonconvex control systems
cites work: Necessary conditions for infinite-dimensional control problems
cites work: Maximum Principle for a Hybrid System Via Singular Perturbations
cites work: The Maximum Principle under Minimal Hypotheses
cites work: On the variational principle
cites work: Q3994914
cites work: Sur l'unicité réctrograde dans les problèmes mixtes paraboliques.
cites work: Sur l'unicité retrograde des équations paraboliques et quelques questions voisines
cites work: A unique continuation theorem for solutions of a parabolic differential equation
full work available at URL: a:1004654800011
OpenAlex ID: W1520776842
description: scientific article; zbMATH DE number 1523627