Online sparse observers for cyber-physical systems under sensor bias

Vito Cerone, Sophie M. Fosson, Diego Regruto, Francesco Ripa

The design of state observers for cyber-physical systems under sparse sensor biases, faults, or attacks has drawn substantial attention in recent years. While sparsity-based batch approaches, which collect multiple measurements and run offline, are relatively mature, online secure state estimation, for real-time state/attack recovery, is still an open problem. Although some algorithms have been proposed, convergence guarantees remain limited, even for the case of constant attacks. As a first step toward addressing this gap, we focus on constant attacks. We analyze the observability of this setting and we study several online sparse observers, derived from different methodological frameworks such as online sparse optimization and block Bregman methods. Some of the proposed observers are adaptations of existing algorithms to the secure state-estimation setting, while others constitute novel algorithmic contributions. The goal of this paper is to provide a unified overview of practically implementable, online sparse observers, discuss their convergence properties, and compare their performance through numerical experiments.