FDI in Cyber Physical Systems: A Distributed Zonotopic and Gaussian Kalman Filter with Bit-level Reduction

Abstract

The problem addressed is that of robust Fault Detection and Isolation (FDI) in Cyber Physical Systems (CPS) modeled by interconnected linear time-varying (LTV) dynamics in a noisy environment with both bounded disturbances and random noises. A Distributed Zonotopic and Gaussian Kalman Filter (DZG-KF) framework is proposed where each network node implements a local estimator using Set-membership (Zonotopic) and Probabilistic (Gaussian) Mergers (SPM/ZGM) to estimate its state. Each node communicates its own state information only to its neighbors in the network. In addition to the usual zonotope reduction, a bit-level reduction is introduced for the first time: its aim is to reduce the required communication channel capacity (bit rate) by approximating sets through quantization by the sender and reconstruction by the receiver. In order to deal with potential packet losses, the negotiation of data reconciliation strategies between agents is discussed. Fault detection and a first-level isolation emerge from agents local tests. Numerical simulations show the efficiency of the proposed scheme.