Stubborn H∞ state estimation for nonlinear distributed parameter systems subject to measurement outliers

• Published in: International journal of robust and nonlinear control Vol. 32; no. 1; pp. 13 - 28
• Main Authors: Sun, Jie, Shen, Bo, Qi, Jie, Liu, Yufei
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.01.2022
• Subjects: Distributed parameter systems; H-infinity control; H∞ state estimation; measurement outliers; nonlinear distributed parameter systems; Outliers (statistics); saturation; State estimation; stubborn state estimator
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5801

In this article, the H∞ state estimation problem is investigated for a class of distributed parameter systems (DPSs). In order to estimate the state of DPSs, we give a partition of spatial interval with a finite sequence and, on each subinterval, one sensor is placed to receive the measurements from the DPS. Due to the unexpected environment changes, the measurements will probably contain some outliers. To eliminate the effects of the possibly occurring outliers, we construct a stubborn state estimator where the innovation is constrained by a saturation function. By using Lyapunov functional, Wirtinger inequality and piecewise integration, some sufficient conditions are obtained under which the resulting estimation error system is exponentially stable and the H∞ performance requirement is satisfied. According to the obtained analysis results, the desired H∞ state estimator is designed in terms of the solution to a set of matrix inequalities. Finally, a numerical simulation example is given to verify the effectiveness of the proposed state estimation scheme.