Secure control of networked switched systems against directed deception attack: A Stackelberg game with nested bi-objective PSO.

This paper addresses the secure control problem of networked switched systems (NSSs) under directed deception attack (DDA). Such attacks are characterized by first determining the deception mode that causes the greatest disruption, followed by jointly optimizing the switching signal tampering rate and state injection. To capture this, a Stackelberg-based hierarchical decision model is established to characterize the interaction between DDA and the secure controller. Novel cost functions are designed to explicitly capture the coupled impact of simultaneous attacks on both the switching signal and the system state. This is achieved by jointly aggregating the costs and rewards associated with both types of attacks, rather than modeling them as separate expense-reward pairs. To simultaneously optimize the strategies of both the attacker and the controller, a nested bi-objective particle swarm optimization (NBOPSO) algorithm is developed, in which the attacker's bi-objective particle swarm optimization (BOPSO) iteratively invokes the controller's particle swarm optimization (PSO) to compute its optimal response. The existence of the equilibrium solutions and the convergence of the NBOPSO algorithm are analytically established. Based on the equilibrium strategies, sufficient conditions are further derived to guarantee the secure stability of the NSSs. Numerical simulations conducted on a mass-varying networked unmanned surface vehicle (USV) demonstrate the efficacy and advantages of the proposed approach.