混合网络攻击下马尔可夫跳变神经网络的安全容错同步控制

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

针对一类混合网络攻击下马尔可夫跳变神经网络安全容错同步控制问题,提出1种确保神经网络主从系统安全容错同步控制器的设计方法。利用2个独立的伯努利分布对随机发生的欺骗攻击和拒绝服务(DoS)攻击进行建模,将马尔可夫跳变神经网络和混合网络攻击置于同一框架中,考虑到执行器可能发生的失效故障情况,设计1种容错控制器;引入1种自由矩阵方法,构建李雅普诺夫(Lyapunov)函数,采用线性矩阵不等式分析方法和特殊的积分不等式放缩技术,推导出能够保证同步误H∞差系统随机均方稳定且满足规定的性能指标的充分条件;进一步使用1种有效的解耦方法对矩阵的耦合项进行分离解耦,运用Matlab中的LMI工具箱得到控制器参数,最后通过数值算例说明所提方法的可行性和有效性。结果表明:当执行器故障失效60%~80%时,以及遭受欺骗攻击概率为80%和DoS攻击概率为50%的混合网络攻击时,所提方法仍然能实现神经网络主从系统的安全性和同步性。

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 H∞specified 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%.