Secure Fault-tolerant Synchronous Control of Markov Jumping Neural Networks under Hybrid Cyber Attacks

Aiming at the problem of secure fault-tolerant synchronous control of Markov jumping neural networks under a class of hybrid cyber attacks, a design method of controller was proposed to ensure the secure fault-tolerant synchronization of neural network master-slave system. Two independent Bernoulli distributions were used to model randomly occurring deception attacks and denial of service (DoS) attacks. Markov jump neural networks and hybrid cyber attacks were placed in the same framework. Considering the possible failure of actuators, a fault-tolerant controller was designed. A free matrix method was introduced, and Lyapunov function was constructed. Linear matrix inequality analysis method and special integral inequality reduction techniques were used to derive the sufficient conditions that can ensure the random mean square stability of the synchronous error system and meet the specified H_\infty performance index. The coupling terms of the matrix were separated and decoupled by an effective decoupling method, and the controller parameters were obtained by the LMI toolbox of Matlab. Finally, a numerical example was given to illustrate the feasibility and effectiveness of the proposed method. The results show that the proposed method can still achieve the security and synchronization of neural network master-slave system when the actuator fails by 60% to 80%, and when subjected to at hybrid cyber attacks with deception attack probability of 80% and DoS attack probability of 50%.