✦ LIBER ✦

Near-optimal control for multiparameter singularly perturbed stochastic systems

✍ Scribed by Muneomi Sagara; Hiroaki Mukaidani; Vasile Dragan

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 123 KB
Volume: 32
Category: Article
ISSN: 0143-2087
DOI: 10.1002/oca.934

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✦ Synopsis

Abstract

In this paper, the linear quadratic optimal stochastic control problem is investigated for multiparameter singularly perturbed stochastic systems in which N lower‐level fast subsystems are interconnected by a higher‐level slow subsystem. After establishing the asymptotic structure of the solution for the multiparameter stochastic algebraic Riccati equation (MSARE), a near‐optimal controller that is independent of small unknown parameters is obtained by neglecting these parameters. The stability of a closed‐loop stochastic system is investigated. Furthermore, it is shown that the resulting controller achieves an O(∥ν∥^2^) approximation to the optimal cost of the original optimal control problem. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example—a practical multi‐area power system—is solved. Copyright © 2010 John Wiley & Sons, Ltd.

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