The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Este artigo aborda controle quadrático linear com ruído dependente de estado para sistemas estocásticos singularmente perturbados (SPSS). Primeiro, a estrutura assintótica da equação algébrica estocástica de Riccati (SARE) é estabelecida para dois casos. Segundo, é estabelecido um novo algoritmo iterativo que combina o método de Newton com o algoritmo de ponto fixo. Como resultado, a convergência quadrática e o cálculo de ordem reduzida na mesma dimensão do subsistema são alcançados. Como outra característica importante, é fornecido um controlador de realimentação de estado de alta ordem que utiliza a solução iterativa obtida e a degradação do desempenho de custo é investigada pela primeira vez para o caso estocástico. Além disso, o controlador independente de parâmetros também é fornecido caso a perturbação singular seja desconhecida. Finalmente, para demonstrar a eficiência do algoritmo proposto, é dado um exemplo numérico para o problema prático de controle de frequência de megawatts.
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Muneomi SAGARA, Hiroaki MUKAIDANI, Toru YAMAMOTO, "Near-Optimal Control for Singularly Perturbed Stochastic Systems" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 11, pp. 2874-2882, November 2009, doi: 10.1587/transfun.E92.A.2874.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.2874/_p
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@ARTICLE{e92-a_11_2874,
author={Muneomi SAGARA, Hiroaki MUKAIDANI, Toru YAMAMOTO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Near-Optimal Control for Singularly Perturbed Stochastic Systems},
year={2009},
volume={E92-A},
number={11},
pages={2874-2882},
abstract={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.},
keywords={},
doi={10.1587/transfun.E92.A.2874},
ISSN={1745-1337},
month={November},}
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TY - JOUR
TI - Near-Optimal Control for Singularly Perturbed Stochastic Systems
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2874
EP - 2882
AU - Muneomi SAGARA
AU - Hiroaki MUKAIDANI
AU - Toru YAMAMOTO
PY - 2009
DO - 10.1587/transfun.E92.A.2874
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2009
AB - 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.
ER -