Observer-based secure state estimation for multi-agents systems subjected to adversial sensor attacks

Cyber-Physical Systems (CPSs) represent a critical class of interconnected systems where physical processes are tightly integrated with computation and communication layers. Their growing deployment in safety-critical infrastructures, such as autonomous transportation, industrial automation, and smart energy grids, makes them highly exposed to malicious intrusions. Among the most harmful threats are adversarial sensor attacks, which can stealthily corrupt measurement data and undermine the reliability of state estimation, control performance, and safety. Traditional observer-based approaches, such as the Luenberger observer, provide accurate state estimation under nominal conditions but lack robustness against adversarial corruption. In this context, sparsity-aware estimation techniques inspired by compressed sensing and convex optimization have recently emerged as promising tools. This thesis explores these methods by revisiting Secure State Estimation (SSE) through the lens of sparse optimization and developing observer-based counterparts capable of jointly reconstructing both the system state and the attack vector. Particular attention is given to the Sparse Soft Observer (SSO) and its Deadbeat variant (D-SSO), which extend proximal-based iterative algorithms for sparse optimization into recursive observer structures for dynamic CPSs. While practically effective, the stability and convergence of SSO and D-SSO have not been proven in the literature. Building on these insights, the main contribution of this work is the analysis of the stability of observer design in the presence of adversarial sensor attacks. The proposed analysis introduces a novel error dynamics representation and leverages Lyapunov-based tools to establish formal stability guarantees. Overall, this thesis shows that sparsity-promoting observers, reinforced by the newly developed theoretical foundation, constitute a robust approach. The results pave the way for real-time implementations and distributed extensions in multiagent CPSs, highlighting the potential impact of the proposed methodology on the resilience of future cyber-physical infrastructures.