Optimal risk-sensitive controller for second degree stochastic polynomial systems

This paper presents the optimal risk-sensitive controller problem for second degree polynomial stochastic systems with a scaling intensity parameter, multiplying the diffusion term in the state, 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 second degree polynomial systems and the separation principle for polynomial systems. The performance of the equations of the controller risk-sensitive of second grade equations is verified in a numerical example compared to the conventional bilinear-quadratic controller equations for second degree polynomial systems. The simulation results reveal significant advantages in the criterion values in favor of the designed risk-sensitive controller, for all values of the scaling parameter.