An Information-State Approach to Risk-Sensitive Tracking Problems

In this paper we use the information-state approach to obtain solutions to risk-sensitive quadratic control problems. Speci cally we consider the case of tracking a desired trajectory. Results are presented for linear discrete-time models with Gaussian noise, and also for nite-discrete state, discrete-time hidden Markov models with continuous-range observations. These results give insight to more general information-state methods for nonlinear systems. Using such methods the tracking solution is obtained without appealing to a certainty equivalence principle. Limit results are presented which demonstrate the link to standard linear quadratic Gaussian control. Also presented is a discussion on achieving zero steady state error with risk-sensitive control policies. Simulation studies are presented to show some advantages of using the risk-sensitive approach.