Partially observable nonlinear risk-sensitive control problems: dynamic programming and verification theorems

In this paper, we consider continuous-time partially observable optimal control problems with exponential-of-integral cost criteria. We derive a rigorous verification theorem when the state and control enter nonlinear in the dynamics. In addition, we show that the quadratic sensor problem is estimation-solvable with respect to a certain cost criterion. The framework relies on dynamic programming and the Hamilton-Jacobi theory.