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.
Abstract This paper is concerned with the mixed H2/H∞ control for stochastic systems with random coefficients, 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 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 H2/H∞ control are given utilizing a pair of coupled stochastic Pdccati equations.
关键词
随机系数
控制相
H2
充分必要条件
鲁棒性能
随机系统
最佳控制
经典理论
Stochastic H∞ control, Stochastic H2/H∞ control, Linear quadratic(LQ) optimal control, Indefinite backward stochastic Riccati equation