Confidence set-membership state estimation for LPV systems with inexact scheduling variables

Abstract

In this paper, a confidence set-membership state estimator is proposed for a class of polytopic linear parameter varying (LPV) systems with inexact scheduling variables. The set-bounded and Gaussian uncertainties are considered simultaneously in the process disturbances and measurement noises. The purpose of the proposed estimator is to achieve a confidence set of the state with given confidence level. Based on the polytopic LPV uncertain enclosure model, the set-bounded/Gaussian uncertainties of the state are given by using the worst case strategy. The size of the confidence set is minimized to get the optimal gain for the estimator. Meanwhile, the constrained zonotope is adopted to represent set-bounded uncertainties for more accurate results. Finally, a vehicle example is given to illustrate the effectiveness of proposed methods.

Keywords: Constrained zonotope; Kalman filter; LPV systems; Probability measure; Set-membership; State estimation.