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On the approximate solution of time-optimal control problems

On the approximate solution of time-optimal control problems In this paper we are concerned with the approximate solution of time-optimal control problems in a nonreflexive Banach SpaceE by sequences of similar problems in Banach spacesE n which are assumed to approximateE in a fairly general sense. The problems under consideration are such that the solution operator of the associated evolution equation is a strongly continuous holomorphic contraction semigroup and the class of controls is taken from the dual of the Phillips adjoint space with respect to the infinitesimal generator of that semigroup. The main object is to establish convergence of optimal controls, transition times and corresponding trajectories of the approximating control problems which can be done by means of some results from the theory of approximation of semigroups of operators. Finally, these abstract convergence results will be applied to time-optimal control problems arising from heat transfer and diffusion processes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On the approximate solution of time-optimal control problems

Hoppe, R.
Applied Mathematics and Optimization , Volume 9 (1) – Mar 26, 2005
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References (14)

Publisher
Springer Journals
Copyright
Copyright © 1982 by Springer-Verlag New York Inc.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/BF01460127
Publisher site
See Article on Publisher Site

Abstract

In this paper we are concerned with the approximate solution of time-optimal control problems in a nonreflexive Banach SpaceE by sequences of similar problems in Banach spacesE n which are assumed to approximateE in a fairly general sense. The problems under consideration are such that the solution operator of the associated evolution equation is a strongly continuous holomorphic contraction semigroup and the class of controls is taken from the dual of the Phillips adjoint space with respect to the infinitesimal generator of that semigroup. The main object is to establish convergence of optimal controls, transition times and corresponding trajectories of the approximating control problems which can be done by means of some results from the theory of approximation of semigroups of operators. Finally, these abstract convergence results will be applied to time-optimal control problems arising from heat transfer and diffusion processes.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Mar 26, 2005

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