| Stochastic H2/H∞ Control with Random Coefficients |
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| 作者姓名： | Meijiao WANG |
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| 作者单位： | Department of Mathematical Finance and Stochastic Control,School of Mathematical Sciences,FudanUniversity;Faculty of Science,Ningbo University |
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| 摘 要： | This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefcients,which is actually a control combining the H2 optimization with the H∞robust performance as the name of H2/H∞ reveals.Based on the classical theory of linear-quadratic(LQ,for short)optimal control,the sufcient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation(BSRE,for short)associated with H∞ robustness are derived.Then the sufcient and necessary conditions for the existence of the H2/H∞ control are given utilizing a pair of coupled stochastic Riccati equations.
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| 关 键 词： | Stochastic H∞control Stochastic H2/H∞ control Linear quadratic (LQ) optimal control Indefinite backward stochastic Riccati equation |
Stochastic H
2/H
∞ control with random coefficients |
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| Meijiao WANG.Stochastic H
2/H
∞ control with random coefficients[J].Chinese Annals of Mathematics,Series B,2013,34(5):733-752. |
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| Authors: | Meijiao WANG |
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| Institution: | Department of Mathematical Finance and Stochastic Control, School of Mathematical Sciences, Fudan University, Shanghai 200433, China; Faculty of Science, Ningbo University, Ningbo 315211, Zhejiang,China |
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| Abstract: | This paper is concerned with the mixed H 2/H ∞ control for stochastic systems with random coefficients, which is actually a control combining the H 2 optimization with the H ∞ robust performance as the name of H 2/H ∞ reveals. Based on the classical theory of linear-quadratic (LQ, for short) optimal control, the sufficient and necessary conditions for the existence and uniqueness of the solution to the indefinite backward stochastic Riccati equation (BSRE, for short) associated with H ∞ robustness are derived. Then the sufficient and necessary conditions for the existence of the H 2/H ∞ control are given utilizing a pair of coupled stochastic Riccati equations. |
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| Keywords: | Stochastic H∞ control Stochastic H2/H∞ control Linear quadratic (LQ) optimal control Indefinite backward stochastic Riccati equation |
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