Optimal Transmission Power Scheduling for Networked Control System Under DoS Attack

Designing networked control systems that are reliable and resilient against adversarial threats, is essential for ensuring the security of cyber-physical systems. This paper addresses the communication-control co-design problem for networked control systems under denial-of-service (DoS) attacks. In wireless channels, a transmission power scheduler periodically determines the power level for sensory data transmission. Yet DoS attacks render data packets unavailable by disrupting the communication channel. This paper co-designs the control and power scheduling laws in the presence of DoS attacks and aims to minimize the sum of regulation control performance and transmission power consumption. Both finite- and infinite-horizon discounted cost criteria are addressed. By delving into the information structure between the controller and the power scheduler under attack, the original co-design problem is divided into two subproblems that can be solved individually without compromising optimality. The optimal control is shown to be certainty equivalent, and the optimal transmission power scheduling is solved using a dynamic programming approach. Moreover, in the infinite-horizon scenario, we analyze the performance of the designed scheduling policy and develop an upper bound of the total costs. Finally, a numerical example is provided to demonstrate the theoretical results.