Secure synchronization control for a class of cyber-physical systems with unknown dynamics

This paper investigates the secure synchronization control problem for a class of cyber-physical systems ( CPSs ) with unknown system matrices and intermittent denial-of-service ( DoS ) attacks. For the attack free case, an optimal control law consisting of a feedback control and a compensated feedforward control is proposed to achieve the synchronization, and the feedback control gain matrix is learned by iteratively solving an algebraic Riccati equation ( ARE ) . For considering the attack cases, it is difficult to perform the stability analysis of the synchronization errors by using the existing Lyapunov function method due to the presence of unknown system matrices. In order to overcome this difficulty, a matrix polynomial replacement method is given and it is shown that, the proposed optimal control law can still guarantee the asymptotical convergence of synchronization errors if two inequality conditions related with the DoS attacks hold. Finally, two examples are given to illustrate the effectiveness of the proposed approaches.