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Near-Optimal Control for Singularly Perturbed Stochastic Systems Muneomi SAGARA Hiroaki MUKAIDANI Toru YAMAMOTO Publication IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences Vol.E92-A No.11 pp.2874-2882 Publication Date: 2009/11/01 Online ISSN: 1745-1337 DOI: 10.1587/transfun.E92.A.2874 Print ISSN: 0916-8508 Type of Manuscript: PAPER Category: Systems and Control Keyword: stochastic LQ problem, state-dependent noise, Newton's method, fixed point algorithm, Full Text: PDF(205.3KB)>>
Summary: This paper addresses linear quadratic control with state-dependent noise for singularly perturbed stochastic systems (SPSS). First, the asymptotic structure of the stochastic algebraic Riccati equation (SARE) is established for two cases. Second, a new iterative algorithm that combines Newton's method with the fixed point algorithm is established. As a result, the quadratic convergence and the reduced-order computation in the same dimension of the subsystem are attained. As another important feature, a high-order state feedback controller that uses the obtained iterative solution is given and the degradation of the cost performance is investigated for the stochastic case for the first time. Furthermore, the parameter independent controller is also given in case the singular perturbation is unknown. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example is given for the practical megawatt-frequency control problem. | ||||||||||
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