An improved approach to the LQ non-Gaussian regulator problem

In this paper, an improved approach for the solution of the regulator problem for linear discrete-time dynamical systems with non-Gaussian disturbances and quadratic cost function is proposed. It is known that a sub-optimal control can be derived from the classical LQG solution by substituting the linear filtering part with a quadratic optimal filter. However, classical quadratic filters have some critical drawbacks when the system is not asymptotically stable and, as a consequence in that case, there is no guarantee on the stochastic stability of the controlled system. In order to enlarge the class of systems that can be controlled we will make use of the Feedback Quadratic Filter and a quadratically optimal controller is designed also for non asymptotically stable systems. Numerical results show the performance of these methods.