A duality scheme for convex control problems with time-delay
type: Item
instance of: scholarly article
title: A duality scheme for convex control problems with time-delay
zbMATH Open document ID: 0926.49017
author: G. I. Tsoutsinos
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-11-21T00:00:00Z
review text: The paper concerns optimal control problems with time-delay, both on the cost and on the dynamics, of the type \[ \text{ minimize } \;J(x,u):= l(x(0),x(1)) + \int_0^1 K(t,x(t),u(t),u(t-\theta)) dt \] subject to \(\dot x (t) = A_0(t)x(t) + A_1(t)x(t-\tau) + B(t)u(t)\), where the delay parameters \(\theta, \tau\) can be different and the functions \(l(\cdot,\cdot)\), \(k(t,\cdot,\cdot,\cdot)\) are convex. A Fenchel duality scheme is introduced in order to formulate a dual problem having a similar character to the primal one. The solutions of the dual problem are interpreted as Lagrange multipliers for the dynamic constraints on the primal problem. A necessary and sufficient optimality condition of a subdifferential type is established. This technique allows to improve by some aspects analogous results obtained by the elimination of the time-delay, based on the method of steps [\textit{S. C. Huang}, J. Optimization Theory Appl. 3, 316-360 (1969; Zbl 0172.12904)] or on the introduction of an infinite-dimensional state space [\textit{W. L. Chan} and \textit{S. P. Yung}, IMA J. Math. Control Inf. 4, 251-262 (1987; Zbl 0629.49008)].
reviewed by: Cristina Marcelli
Mathematics Subject Classification ID: 49K25
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 1246323
zbMATH Keywords: optimal control
zbMATH Keywords: convex duality
zbMATH Keywords: time-delays
zbMATH Keywords: optimality condition
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6125
OpenAlex ID: W1994270479
cites work: Q4159877
cites work: Duality Theory for the Linear-Convex Optimal Control Problem with Delays
cites work: Q4000274
cites work: Hereditary differential systems with constant delays. II: A class of affine systems and the adjoint problem
cites work: Optimal control problems with retardations and restricted phase coordinates
cites work: Existence and Duality Theorems for Convex Problems of Bolza
cites work: Conjugate convex functions in optimal control and the calculus of variations
cites work: Integrals which are convex functionals
cites work: Duality theorems for convex problems with time delay
cites work: Dual optimal control problems with time-delay
DOI: 10.1006/JMAA.1998.6125
description: scientific article; zbMATH DE number 1246323