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We consider the joint design of control and scheduling under stochasticDenial-of-Service (DoS) attacks in the context of networked control systems. Asensor takes measurements of the system output and forwards its dynamic stateestimates to a remote controller over a packet-dropping link. The controllerdetermines the optimal control law for the process using the estimates itreceives. An attacker aims at degrading the control performance by increasingthe packet-dropout rate with a DoS attack towards the sensor-controllerchannel. We assume both the controller and the attacker are rational in agame-theoretic sense and establish a partially observable stochastic game toderive the optimal joint design of scheduling and control. Using dynamicprogramming we prove that the control and scheduling policies can be designedseparately without sacrificing optimality, making the problem equivalent to acomplete information game. We employ Nash Q-learning to solve the problem andprove that the solution is guaranteed to constitute an $\epsilon$-Nashequilibrium. Numerical examples are provided to illustrate the tradeoffsbetween control performance and communication cost.

A Jointly Optimal Design of Control and Scheduling in Networked Systems under Denial-of-Service Attacks