Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems

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Date
2014
Authors
Gaitsgory, Vladimir
Manic, Ludmila
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Verlag
Abstract
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max–min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.
Description
Keywords
Systems theory, Operation research, Optimisation
Citation
Gaitsgory, V. and Manic, L., 2014. Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems. In: Optimization and Control Techniques and Applications, Springer Proceedings in Mathematics and Statistics, H. Xu, K.L. Teo and Y. Zhang (Eds), 86, 91-114.