Probability-guaranteed set-membership filtering for nonlinear 2-D systems with measurement outliers under the adaptive event-triggered mechanism

Abstract

This paper is primarily devoted to investigating the probability-guaranteed set-membership (PGSM) filtering problem for a class of nonlinear two-dimensional (2-D) systems with measurement outliers under the adaptive event-triggered mechanism (AETM). Here, the sensors are connected to the remote filter through a bandwidth-limited communication network. With the purpose of reducing the communication burden, a novel AETM is proposed to optimize the scheduling of transmitted data to the filter, where the triggering threshold is allowed to be dynamically adjusted based on the transmission error. This paper aims to develop a two-step recursive PGSM filter, ensuring that the filtering error remains within the prescribed ellipsoidal set with a specified probability. To safeguard the filtering process against performance degradation caused by measurement outliers, a saturation function is incorporated into the filter structure to restraint the impact of outlier-contaminated innovations. By utilizing the mathematical induction approach and convex optimization technique, a sufficient condition is derived to guarantee the existence of the desired PGSM filter, and the filter gains are obtained in terms of the solutions to a series of convex optimization problems with ellipsoidal constraints. In the end, an illustrative example is implemented to reveal the effectiveness of the addressed filter design scheme. The results demonstrate that, compared with the Kalman filter and set-membership (SM) filter, the proposed PGSM filter exhibits superior filtering performance and low upper bound of filtering error in the presence of unknown but bounded (UBB) noise.