A nonlinear partially observed differential game with a finite-dimensional information state

Abstract

In this paper we present an example of a deterministic nonlinear partially observed differential game for which the information state is finite-dimensional. The example is of interest because in general the information state is infinite-dimensional, as is typically the case in stochastic nonlinear filtering. The solution is presented in terms of a Hamilton-Jacobi-Isaacs equation. An “adjoint” information state is also explicitly computed. The results are illustrated in the familiar case of linear systems, and a new interpretation of the coupling condition of linear H ∞ control is given.