Non-uniqueness of solutions of the Hamilton–Jacobi–Bellman equation for time-average control

Non-uniqueness of solutions of the Hamilton–Jacobi–Bellman equation for time-average control In control of diffusion processes a very useful instrument is the equation for optimal strategy and cost. For the version of infinite time horizon with time averaging this equation is much more complicated than for the version of finite time horizon, and even than for the version of infinite time horizon with discounting. In particular, the equation solution may be non-unique. This problem of non-uniqueness is researched in book of A. Arapostathis et al., 2012, for special models—near-monotone. The result received in the book is extended in the article to an important general case—models with restrictions in control which guarantee ergodicity of the process. Besides we correct the proofs from the book. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automation and Remote Control Springer Journals

Non-uniqueness of solutions of the Hamilton–Jacobi–Bellman equation for time-average control

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Control, Robotics, Mechatronics; Mechanical Engineering; Computer-Aided Engineering (CAD, CAE) and Design
ISSN
0005-1179
eISSN
1608-3032
D.O.I.
10.1134/S0005117917080045
Publisher site
See Article on Publisher Site

Abstract

In control of diffusion processes a very useful instrument is the equation for optimal strategy and cost. For the version of infinite time horizon with time averaging this equation is much more complicated than for the version of finite time horizon, and even than for the version of infinite time horizon with discounting. In particular, the equation solution may be non-unique. This problem of non-uniqueness is researched in book of A. Arapostathis et al., 2012, for special models—near-monotone. The result received in the book is extended in the article to an important general case—models with restrictions in control which guarantee ergodicity of the process. Besides we correct the proofs from the book.

Journal

Automation and Remote ControlSpringer Journals

Published: Aug 19, 2017

References

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