Feedback polynomial filtering and control of non-Gaussian linear time-varying systems

This paper deals with the optimal filtering and optimal output-feedback control of discrete-time, linear time-varying non-Gaussian systems. In the hypothesis that the time-varying and non-Gaussian distributions of the state and measurement noises have bounded and known moments up to a given order, this work extends previous results about polynomial filtering and optimal control to the time-varying case. The properties of the resulting filtering and control algorithms are discussed in the light of a stable recursive representation of the Kronecker powers of the system obtained through a suitable rewriting of the system with an output injection term. The resulting sub-optimal algorithm inherits the structure and the properties of the classical LQG approach but with enhanced performance.