Distributed Fuzzy Proportional-Integral State Estimation Over Sensor Networks With Pull-Type Gossip Protocols and Fading Data

This paper addresses the problem of distributed state estimation for smooth nonlinear systems over sensor networks by means of a generalized fuzzy proportional-integral observer (PIO). A sensor network is employed to collect system measurements, with a pull-type gossip protocol governing the intermittent data exchange among neighboring nodes. Under the gossip protocol, each sensor node randomly selects one neighbor to request data, facilitating distributed information updating. Furthermore, considering challenges such as long-distance communication and complex environmental conditions, signal transmission is subject to amplitude fading. To accommodate the characteristics of the gossip protocol, a generalized fuzzy PIO with a flexible structure is developed. Sufficient conditions are derived to guarantee the$H\_{\infty }$estimation performance of the proposed observer. Based on established conditions, the parameters of both the gossip protocol and the fuzzy PIO are co-designed via a particle-swarm-optimization-based iterative algorithm, with emphasis on enhancing observer robustness. Finally, an engineering-oriented simulation example is presented to illustrate the effectiveness of the proposed methodology.