Nonlinear Stochastic H2/H∞ Output Feedback Control under State-Dependent Noise

This paper discusses the nonlinear stochastic H₂/H_∞ output feedback control design with state-dependent noise. Our results extend the linear stochastic H₂/H_∞ control to the nonlinear output feedback case. First, based on stochastic Nash game theory, an observer-based nonlinear stochastic H₂/H_∞ control is developed when the state variable is not completely available. Then, the nonlinear stochastic H₂/H_∞ observer-based output feedback control problem is transformed into two constrained optimization problems subject to their respective Hamilton-Jacobi inequality (HJI) from the suboptimal perspective, one for the design of H₂/H_∞ controller and the other for the design of H₂/H_∞ observer. Finally, the solvability of the mixed H₂/H_∞ observer-based output feedback control for nonlinear stochastic systems is discussed and an example with computer simulations is given to confirm the performance of the proposed method