Probabilistic-Constrained Distributed Set-Membership Estimation Over Sensor Networks: A Dynamic Periodic Event-Triggered Approach

This article is concerned with the event-triggered probabilistic-constrained distributed set-membership estimation problem for a discrete-time nonlinear system over sensor networks. For saving communication resource, a novel discrete-time dynamic periodic event-triggered mechanism (ETM) is first developed for the sensor network. Under the proposed method, the sensor node calculates the ETM in a periodic manner and the threshold is adjusted dynamically. Thereafter, a distributed set-membership estimator is constructed, and a probability-based estimated ellipsoidal constraint is put forward to acquire a more flexible set-membership estimation algorithm. Simultaneously, an auxiliary-function-dependent approach is proposed to derive the criterion for the co-design of the probabilistic-constrained set-membership estimator and the event-triggered parameter such that the system states reside in the estimated ellipsoid with a pre-specified probability. The auxiliary function is constructed in a piecewise style aiming to deal with the sawtooth constraint of sampling signals. Furthermore, a recursive convex optimization algorithm with regard to the estimated ellipsoid is presented. Finally, a simulation example is employed to verify the validity of the developed method.