A finite-dimensional risk-sensitive control problem. (English) Zbl 0841.93081
Summary: 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.
MSC:
93E20 | Optimal stochastic control |
93C10 | Nonlinear systems in control theory |
93E11 | Filtering in stochastic control theory |