Resilient backstepping control for a class of switched nonlinear time-delay systems under hybrid cyber-attacks

In the present investigation, the tracking control problem is being addressed for a switched time-delay nonlinear nonstrict-feedback cyber-physical systems (CPSs). Since modern infrastructure applications depend greatly on cyber technologies, these CPSs are exposed to two types of collusive network attacks, including unknown false data injection (FDI) and denial-of-service (DoS) attacks. When a DoS attack is active, state variables are unavailable. Furthermore, when an FDI attack is launched, the general state is manipulated by the attacker. Inspired by these complications, a Lyapunov-Krasovskii (LK) candidate is employed to handle time delays, a neural network (NN) switched observer is applied to approximate unavailable system states under attacks, and a Nussbaum gain approach is implemented to deal with the unknown sign of the attack function. By using the common Lyapunov function, it is proved that all closed-loop system signals and tracking errors are bounded by the proposed resilient control. Eventually, two practical and numerical examples to corroborate the capability of the proposed scheme, are presented.