  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 the
wireless channel, 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, respectively. 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.
