A stochastic controller for vector linear systems with additive cauchy noises

An optimal predictive controller for linear, vector-state dynamic systems driven by Cauchy measurement and process noises is developed. For the vector-state system, the probability distribution function (pdf) of the state conditioned on the measurement history cannot be generated. However, the characteristic function of this pdf can be expressed in an analytic form. Consequently, the performance index is evaluated in the spectral domain using this characteristic function. By using an objective function that is a product of functions resembling Cauchy pdfs, the conditional performance index is obtained analytically in closed form by using Parseval's equation and integrating over the spectral vector. This forms a non-convex function of the control signal, and must be optimized numerically at each time step. A two-state example is used to expose the interesting robustness characteristics of the proposed controller.