Stochastic H2/H∞ control with (x, u, v)-dependent noise: Finite horizon case

Abstract

In this paper, the finite horizon mixed H₂/H_∞ control problem is studied for the systems governed by Ito-type nonlinear stochastic differential equations with state, control and external disturbance-dependent noise. It is shown that the mixed H₂/H_∞ control under consideration is associated with the four cross-coupled Hamilton-Jacobi equations in nonlinear case. Some necessary and/or sufficient conditions for the existence of finite horizon stochastic H₂/H_∞ controllers are derived. In particular, some previous results on deterministic and stochastic H_∞ (H₂/H_∞) can be viewed as simple corollaries of our main theorems