  Emerging cyber-physical systems impel the development of communication
protocols to efficiently utilize resources. This paper investigates the optimal
co-design of control and scheduling in networked control systems. The objective
is to co-design the control law and the scheduling mechanism that jointly
optimize the tradeoff between regulation performance and communication resource
consumption in the long run. The concept of the value of information (VoI) is
employed to evaluate the importance of data being transmitted. The optimal
solution includes a certainty equivalent control law and a stationary
scheduling policy based on the VoI function. The closed-loop system under the
designed scheduling policy is shown to be stochastically stable. By analyzing
the property of the VoI function, we show that the optimal scheduling policy is
symmetric and is a monotone function when the system matrix is diagonal.
Moreover, by the diagonal system matrix assumption, the optimal scheduling
policy is shown to be of threshold type. Then we provide a simplified yet
equivalent form of the threshold-based optimal scheduling policy. The threshold
value searching region is also given. Finally, the numerical simulation
illustrates the theoretical result of the VoI-based scheduling.
