LAUSR

Abstract This study focuses on reliable control problems for cyber-physical systems (CPSs), described by linear continuous time-invariant systems, under a class of time-varying state-dependent sensor and actuator attacks. According to the state-dependent property of sensor attacks, the original reliable control problem is converted into a problem to stabilise a completely unknown time-varying system with the actuator attacks. Firstly, a dynamic neural network (NN) identifier with an indicator-function term is developed to model the unknown system dynamics. Due to the indicator term, the input distribution matrix of the identifier is guaranteed to be of full column rank. It provides a technical condition for designing an effective identifier-based integral sliding-mode (I-SM) attack compensator. It is shown that, under the proposed adaptive law, the identification errors and NN weight estimation errors are uniformly ultimately bounded. Furthermore, an identifier-critic based I-SM controller, which consists of an ADP-based controller and an adaptive I-SM attack compensator, is online learned using real-time control input and compromised sensor data, such that the unknown dynamics with the actuator attacks is stable with a nearly optimal performance. Meanwhile, it is shown that, the developed control approach ensures that the states in CPSs under sensor and actuator attacks converge to a compact set around zero. Finally, the effectiveness of the proposed one is verified by two illustrative examples.