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Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equation

Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equation In this paper we study the existence of optimal trajectories associated with a generalized solution to the Hamilton-Jacobi-Bellman equation arising in optimal control. In general, we cannot expect such solutions to be differentiable. But, in a way analogous to the use of distributions in PDE, we replace the usual derivatives with “contingent epiderivatives” and the Hamilton-Jacobi equation by two “contingent Hamilton-Jacobi inequalities.” We show that the value function of an optimal control problem verifies these “contingent inequalities.” http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equation

Applied Mathematics and Optimization , Volume 19 (1) – Mar 23, 2005

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References (20)

Publisher
Springer Journals
Copyright
Copyright © 1989 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/BF01448202
Publisher site
See Article on Publisher Site

Abstract

In this paper we study the existence of optimal trajectories associated with a generalized solution to the Hamilton-Jacobi-Bellman equation arising in optimal control. In general, we cannot expect such solutions to be differentiable. But, in a way analogous to the use of distributions in PDE, we replace the usual derivatives with “contingent epiderivatives” and the Hamilton-Jacobi equation by two “contingent Hamilton-Jacobi inequalities.” We show that the value function of an optimal control problem verifies these “contingent inequalities.”

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Mar 23, 2005

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