Backward stochastic \(H_2 / H_{\infty}\) control: infinite horizon case
Summary: The mixed \(H_2 / H_{\infty}\) control problem is studied for systems governed by infinite horizon backward stochastic differential equations (BSDEs) with exogenous disturbance signal. A necessary and sufficient condition for the existence of a unique solution to the \(H_2 / H_{\infty}\) control problem is derived. The equivalent feedback solution is also discussed. Contrary to deterministic or stochastic forward case, the feedback solution is no longer feedback of the current state; rather, it is feedback of the entire history of the state.
scientific article; zbMATH DE number 7016406