Secure state estimation via robust optimization for nonlinear cyber-physical systems

This article proposes secure state estimation for cyber-physical systems against sensor attacks. The attack and defense strategies are established via additional historical data, and the defender aims to reduce the estimation error maximally while the attacker aims to degrade the system performance maximally. The algorithm is implemented in the Nash equilibrium framework where the defender first designs the defense strategy and then the attacker designs corresponding attack parameters to launch attacks. Then, a robust optimization problem is formulated using Wasserstein ambiguity sets, which turn out to be equivalent to a convex program. A novel secure observer is proposed, where the attack estimation is used to mitigate attacks. Moreover, the detector is to monitor system behavior and detects the existence of sensor attacks. Finally, simulation results and comparative results illustrate the effectiveness of the defense strategy. The attack and defense strategies are established via additional historical data, and the defender aims to reduce the estimation error maximally while the attacker aims to degrade the system performance maximally.Then, a robust optimization problem is formulated in the Nash equilibrium framework using Wasserstein ambiguity sets. Then, a novel secure observer is proposed, where the attack estimation is used to mitigate attacks.image