Information-state approach to linear/risk-sensitive/quadratic/Gaussian control

In this paper we use an information-state approach to obtain the solution to the linear risk-sensitive quadratic Gaussian control problem. With these methods the solution is obtained without appealing to a certainty equivalence principle. Specifically we consider the case of tracking a desired trajectory. The result gives some insight to more general information-state methods for non-linear systems. Limit results are presented which demonstrate the link to standard linear quadratic Gaussian control. Also, a risk-sensitive filtering result is presented which shows the relationship between tracking and filtering problems. Finally, simulation studies are presented to indicate some advantages gained via a risk-sensitive control approach.