Optimal risk-sensitive control for bilinear stochastic systems

The optimal exponential-quadratic control problem is considered for stochastic Gaussian systems with polynomial bilinear 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 bilinear polynomial systems is verified in a numerical example, through comparing the exponential quadratic criteria values for the optimal risk-sensitive control and bilinear 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 epsiv.