Overview
This work investigates the development and evaluation of online sparse observers designed for cyber-physical systems (CPS) operating under sparse sensor biases, faults, or attacks. It addresses the challenge of real-time state and attack recovery, particularly focusing on the case of constant attacks. The research examines observability in this specific setting and introduces multiple online sparse observers. These observers are derived from frameworks such as online sparse optimization and block Bregman methods, with some being adaptations of existing algorithms and others representing novel contributions. The study's objective is to offer a unified overview of these practically implementable online sparse observers, discuss their convergence properties, and compare their performance through numerical experiments.
Research Context
The design of state observers for cyber-physical systems confronting sparse sensor biases, faults, or attacks has attracted considerable attention. Prior work includes sparsity-based batch approaches, which involve collecting multiple measurements and operating offline. These batch methods are described as relatively mature. However, online secure state estimation, critical for real-time state and attack recovery, remains an open problem. Existing algorithms in this area have limited convergence guarantees, even in scenarios involving constant attacks. This paper aims to address this gap by focusing on the constant attack scenario as a preliminary step.
Approach
The research approach involves several key steps:
- Observability Analysis: The study begins by analyzing the observability of cyber-physical systems under constant attacks, which is foundational for designing effective observers.
- Online Sparse Observer Derivation: Drawing from different methodological frameworks, including online sparse optimization and block Bregman methods, several online sparse observers are derived. This includes both adaptations of existing algorithms to the secure state-estimation context and novel algorithmic contributions.
- Algorithm Classification: The proposed observers are presented to provide a unified overview of practically implementable online sparse observers.
- Convergence Property Discussion: The convergence properties of these various observers are discussed.
- Performance Comparison: Numerical experiments are conducted to compare the performance of the proposed online sparse observers.
Findings
The research presents and evaluates several online sparse observers tailored for cyber-physical systems under constant sensor biases, faults, or attacks. The study analyzed the observability pertinent to this setting. It explored observers derived from online sparse optimization and block Bregman methods. Some of these observers represent adaptations of existing algorithms to the domain of secure state estimation, while others are introduced as novel algorithmic contributions. The work provides a unified overview of observers that are practically implementable in an online context. It includes a discussion of their convergence properties and a comparison of their performance, which was conducted via numerical experiments.
Why This Matters
The development of online sparse observers is significant for addressing the challenge of real-time state and attack recovery in cyber-physical systems. While offline batch approaches for handling sensor biases, faults, or attacks are established, the ability to perform these estimations in real-time with guaranteed convergence is less developed. This research, by focusing on constant attacks and presenting practically implementable online observers with discussed convergence properties and performance comparisons, contributes to bridging this gap.