PARTIALLY OBSERVED DIFFERENTIAL-GAMES, INFINITE-DIMENSIONAL HAMILTON-JACOBI-ISAACS EQUATIONS, AND NONLINEAR H-INFINITY CONTROL

This paper presents new results for partially observed nonlinear diffe rential games. Using the concept of information state, we solve this p roblem in terms of an infinite-dimensional partial differential equati on, which turns out to be the Hamilton-Jacobi-Isaacs (KJI) equation fo r partially observed differential games. We give definitions of smooth and viscosity solutions and prove that the value function is a viscos ity solution of the Hn: equation. We prove a verification theorem, whi ch 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 al so present some new results concerning the certainty equivalence princ iple under certain standard assumptions. Our results are applied to a nonlinear output feedback H-infinity robust control problem.