Optimal tracking control of two-time-scale system under cyber-attacks

In this paper, an optimal tracking problem of two-time-scale systems under cyber-attacks is studied. And an optimal tracking control method based on singular perturbation theory and reinforcement learning is proposed for the two-time-scale systems. Firstly, aiming at the singular perturbation parameter problem of the system, the system is decomposed into fast and slow subsystems by studying the singular perturbation theory. Secondly, the off-policy Q-learning is used to design the controller solution algorithm for the two subsystems respectively. The merit of the proposed algorithm is that the optimal tracking control law based on predicted states of systems can be learned using only measured data without knowing system dynamics. Besides, to solve the problem of system state data loss caused by cyber-attacks, a state predictor based on recurrent neural networks (RNN) is designed by using the historical data generated in the system operation. Finally, the effectiveness of the proposed method is proved by simulation examples.