Adaptive output regulation for cyber-physical systems under time-delay attacks

In this paper, we present an output regulation method for unknown cyber-physical systems (CPSs) under time-delay attacks in both the sensor-to-controller (S-C) channel and the controller-to-actuator (C-A) channel. The proposed approach is designed using control inputs and tracking errors which are accessible data. Reinforcement learning is leveraged to update the control gains in real time using policy or value iterations. A thorough stability analysis is conducted and it is found that the proposed controller can sustain the convergence and asymptotic stability even when two channels are attacked. Finally, comparison results with a simulated CPS verify the effectiveness of the proposed output regulation method.