Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/77907
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Type: Journal article
Title: The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Itô differential equations
Other Titles: The linear quadratic regulator problem for a class of controlled systems modeled by singularly perturbed Ito differential equations
Author: Dragan, V.
Mukaidani, H.
Shi, P.
Citation: SIAM Journal on Control and Optimization, 2012; 50(1):448-470
Publisher: Siam Publications
Issue Date: 2012
ISSN: 0363-0129
1095-7138
Statement of
Responsibility: 
Vasile Dragan, Hiroaki Mukaidani and Peng Shi
Abstract: This paper discusses an infinite-horizon linear quadratic (LQ) optimal control problem involving state- and control-dependent noise in singularly perturbed stochastic systems. First, an asymptotic structure along with a stabilizing solution for the stochastic algebraic Riccati equation (ARE) are newly established. It is shown that the dominant part of this solution can be obtained by solving a parameter-independent system of coupled Riccati-type equations. Moreover, sufficient conditions for the existence of the stabilizing solution to the problem are given. A new sequential numerical algorithm for solving the reduced-order AREs is also described. Based on the asymptotic behavior of the ARE, a class of O(√ε) approximate controller that stabilizes the system is obtained. Unlike the existing results in singularly perturbed deterministic systems, it is noteworthy that the resulting controller achieves an O(ε) approximation to the optimal cost of the original LQ optimal control problem. As a result, the proposed control methodology can be applied to practical applications even if the value of the small parameter ε is not precisely known. © 2012 Society for Industrial and Applied Mathematics.
Keywords: singularly perturbed control systems
asymptotic behavior
stabilizing solution
Rights: Copyright © 2012 Society for Industrial and Applied Mathematics
DOI: 10.1137/100798661
Grant ID: CNCS 1721
Published version: http://dx.doi.org/10.1137/100798661
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