Risk-Sensitive Approach to Optimal Filtering and Control for Linear Stochastic Systems

The optimal exponential-quadratic control problem and exponential mean-square filtering problems are considered for stochastic Gaussian systems with polynomial first degree drift terms and intensity parameters multiplying diffusion terms in the state and observations equations. The closed-form optimal control and filtering algorithms are obtained using quadratic value functions as solutions to the corresponding H-J-B PDEs. The performance of the obtained risk-sensitive regulator and filter is verified in a numerical example. The simulation results reveal strong advantages in favor of the designed risk-sensitive algorithms in regard to the final criteria values.