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Infinite horizon autonomous systems with unbounded cost

Infinite horizon autonomous systems with unbounded cost We discuss control systems defined on an infinite horizon, where typically all the associated costs become unbounded as the time grows indefinitely. It is proved, under certain lower semicontinuity and controllability assumptions, that a linear time function can be subtracted from the cost, resulting in a modified cost, which is bounded on the infinite time interval. The cost evaluated over one sampling interval has a simple representation in terms of the initial and final states. Applying this representation we obtain an optimality result for control systems represented by ordinary differential equations whose cost integrand contains a discounting factor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Infinite horizon autonomous systems with unbounded cost

Applied Mathematics and Optimization , Volume 13 (1) – Mar 23, 2005

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 1985 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/BF01442197
Publisher site
See Article on Publisher Site

Abstract

We discuss control systems defined on an infinite horizon, where typically all the associated costs become unbounded as the time grows indefinitely. It is proved, under certain lower semicontinuity and controllability assumptions, that a linear time function can be subtracted from the cost, resulting in a modified cost, which is bounded on the infinite time interval. The cost evaluated over one sampling interval has a simple representation in terms of the initial and final states. Applying this representation we obtain an optimality result for control systems represented by ordinary differential equations whose cost integrand contains a discounting factor.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 23, 2005

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