On the Bellman Equation for Infinite Horizon Problems with Unbounded Cost Functional

On the Bellman Equation for Infinite Horizon Problems with Unbounded Cost Functional We study a class of infinite horizon control problems for nonlinear systems, which includes the Linear Quadratic (LQ) problem, using the Dynamic Programming approach. Sufficient conditions for the regularity of the value function are given. The value function is compared with sub- and supersolutions of the Bellman equation and a uniqueness theorem is proved for this equation among locally Lipschitz functions bounded below. As an application it is shown that an optimal control for the LQ problem is nearly optimal for a large class of small unbounded nonlinear and nonquadratic pertubations of the same problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

On the Bellman Equation for Infinite Horizon Problems with Unbounded Cost Functional

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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/s002459911010
Publisher site
See Article on Publisher Site

Abstract

We study a class of infinite horizon control problems for nonlinear systems, which includes the Linear Quadratic (LQ) problem, using the Dynamic Programming approach. Sufficient conditions for the regularity of the value function are given. The value function is compared with sub- and supersolutions of the Bellman equation and a uniqueness theorem is proved for this equation among locally Lipschitz functions bounded below. As an application it is shown that an optimal control for the LQ problem is nearly optimal for a large class of small unbounded nonlinear and nonquadratic pertubations of the same problem.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2025

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