Partially Observed Differential Games, Infinite Dimensional HJI Equations, and Nonlinear HControl

Abstract

This paper presents new results for partially observed nonlinear differential games, which are applied to the nonlinear output feedback Hrobust control problem. Using the concept of information state, we solve these problems in terms of an infinite dimensional partial differential equation, viz., the Hamilton-Jacobi-Isaacs equation for partial observed differential games. We give definitions of smooth and viscosity solutions, and prove that the value function is a viscosity solution of the HJI equation. We prove a verification theorem, which implies that the optimal controls are separated in that they depend on the observations through the information state. This constitutes a separation principle for partially observed differential games. We also present some new results concerning the certainty equivalence principle.