UCLA

An efficient recursive state estimator and an optimal model predictive controller are developed for two-state linear systems driven by Cauchy distributed process and measurement noises. For a general vector-state system, the estimator is based on recursively propagating the characteristic function (CF) of the conditional probability density function (cpdf), where the number of terms in the sum that expresses this CF grows with each measurement update. The proposed two-state estimator reduces substantially the number of terms needed to express the CF of the cpdf by taking advantage of relationships not yet developed in the general vector-state case. Further, by using a fixed sliding window of the most recent measurements, the improved efficiency of the proposed two state estimator allows an accurate approximation for real-time computation. For control of the general vector-state system, the conditional performance index is evaluated in the spectral domain using this CF. The expectation is of an objective function that is a product of functions resembling Cauchy pdfs. Using this method, the conditional performance index for a two-state system is obtained analytically in closed form by using Parseval's identity and integrating over the spectral variables. This forms a deterministic, non-convex function of the control signal and the measurement history that must be optimized numerically at each time step. Examples are given of both the estimator and the controller, to demonstrate their performance and expose their interesting robustness characteristics.