Optimal risk-sensitive controller for first degree stochastic polynomial systems

This paper presents the optimal risk-sensitive controller problem for first degree polynomial stochastic systems with a scaling intensity parameter, multiplying the diffusion term in the state and observations equations and exponential-quadratic cost function to be minimized. The optimal risk-sensitive controller equations are obtained based on the optimal risk-sensitive filtering and control equations for first degree polynomial systems and the separation principle. In the example, the risk-sensitive controller equations are compared to the conventional linear-quadratic controller equations for first degree polynomial systems. The simulation results reveal significant advantages in the criterion values in favor of the designed risk-sensitive controller, in particular, for large values of the scaling parameter.