Optimal Controller for Uncertain Stochastic Linear Systems With Poisson Noises

This paper presents the optimal linear-quadratic-Poisson (LQP) controller for stochastic linear systems with Poisson noises and unknown parameters. The optimal controller equations are obtained using the separation principle, whose applicability to the considered problem is substantiated. Performance of the obtained optimal LQP controller is verified in the illustrative example against the LQP controller that is optimal for linear systems with known parameters; the designed LQP controller is also compared with the conventional linear-quadratic-Gaussian (LQG) controller available for stochastic linear systems with Gaussian noises and unknown parameters. Simulation graphs demonstrating overall performance and computational accuracy of the designed LQP controller for stochastic linear systems with Poisson noises and unknown parameters are included.