Zonotopic non-fragile set-membership fusion estimation for nonlinear systems under sensor resolution effects: Boundedness and monotonicity

Abstract

In this paper, the zonotopic non-fragile set-membership fusion estimation problem is investigated for multi-sensor nonlinear systems under sensor resolution effects. The sensor resolutions, which characterize the smallest change of signals that can be detected by sensors, are considered to reflect the engineering practice. A sequential fusion estimator, which takes the possible estimator gain variations (PEGVs) into account, is constructed to estimate the system state. Based on the mean value theorem and the first-order Taylor expansion, a novel method is first proposed to derive a zonotope containing the one-step prediction error, and such a method is proven to be beneficial in improving the prediction accuracy. Then, a PEGV-dependent zonotope is derived to enclose the estimation error after each measurement update, and the estimator parameter is designed to minimize a certain upper bound of the F-radius of the derived zonotope. Subsequently, in order to acquire bounds of the system states, a PEGV-independent zonotope is obtained at each time instant to enclose the estimation error after the measurement update. Moreover, the monotonicity of the F-radius of the PEGV-independent zonotope is analyzed with regard to, respectively, the corresponding sensor resolution and the PEGV. Finally, two numerical examples are provided to show the effectiveness of the proposed fusion estimation method.