Existence and Structure of Optimal Solutions of Infinite-Dimensional Control Problems

Existence and Structure of Optimal Solutions of Infinite-Dimensional Control Problems In this work we analyze the structure of optimal solutions for a class of infinite-dimensional control systems. We are concerned with the existence of an overtaking optimal trajectory over an infinite horizon. The existence result that we obtain extends the result of Carlson, Haurie, and Jabrane to a situation where the trajectories are not necessarily bounded. Also, we show that an optimal trajectory defined on an interval [0,τ] is contained in a small neighborhood of the optimal steady-state in the weak topology for all t ∈ [0,τ] \backslash E , where E \subset [0,τ] is a measurable set such that the Lebesgue measure of E does not exceed a constant which depends only on the neighborhood of the optimal steady-state and does not depend on τ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Existence and Structure of Optimal Solutions of Infinite-Dimensional Control Problems

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 2000 Springer-Verlag New York
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
D.O.I.
10.1007/s002450010011
Publisher site
See Article on Publisher Site

Abstract

In this work we analyze the structure of optimal solutions for a class of infinite-dimensional control systems. We are concerned with the existence of an overtaking optimal trajectory over an infinite horizon. The existence result that we obtain extends the result of Carlson, Haurie, and Jabrane to a situation where the trajectories are not necessarily bounded. Also, we show that an optimal trajectory defined on an interval [0,τ] is contained in a small neighborhood of the optimal steady-state in the weak topology for all t ∈ [0,τ] \backslash E , where E \subset [0,τ] is a measurable set such that the Lebesgue measure of E does not exceed a constant which depends only on the neighborhood of the optimal steady-state and does not depend on τ .

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Nov 1, 2000

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