Stochastic H ₂/H _∞ control with random coefficients

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.

Keywords

Stochastic H _∞ control / Stochastic H ₂/H _∞ control / Linear quadratic (LQ) optimal control / Indefinite backward stochastic Riccati equation

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