SIAM Journal on Control and Optimization, Vol.33, No.6, 1834-1846, 1995
A Finite-Dimensional Risk-Sensitive Control Problem
A partially observed stochastic control problem with exponential running cost is considered. The dynamics are linear and the running cost is quadratic, although the control may enter nonlinearly. Explicit solutions are found to a modified Zakai equation and a backward adjoint equation. This enables the problem to be expressed in terms of observable finite-dimensional dynamics and a separation principle to be applied.