Optimal risk-sensitive control for third degree polynomial systems

The optimal exponential-quadratic control problem is considered for stochastic Gaussian systems with polynomial third degree drift terms and intensity parameters multiplying diffusion terms in the state equation. The closed-form optimal control algorithm is obtained using a quadratic value function as a solution to the corresponding Hamilton-Jacobi-Bellman equation. The performance of the obtained risk-sensitive regulator for stochastic third degree polynomial systems is verified in a numerical example, through comparing the exponential-quadratic criteria values for the optimal risk-sensitive control and third degree control algorithms. The simulation results reveal strong advantages in favor of the designed risk-sensitive algorithm in regard to the final criteria values for all values of the parameter ε.