Delay-Sensitive Joint Optimal Control and Resource Management in Multiloop Networked Control Systems

In the operation of networked control systems (NCSs), where multiple processes share a resource-limited and time-varying cost-sensitive network, communication delay is inevitable and primarily induced by, first, intermittent sensor sampling to restrict nonurgent transmissions, and second, resource management to avoid contentions, excessive traffic, and data loss. In a heterogeneous scenario, where control systems may tolerate only specific levels of sensor-to-controller latency, delay sensitivities need to be considered in the design of control and network policies to achieve the desired performance guarantees. We propose a cross-layer optimal co-design of control, sampling, and resource management policies for an NCS consisting of multiple stochastic linear time-invariant systems which close their sensor-to-controller links over a shared network. Aligned with advanced communication technology, we assume that the network offers a range of latency-varying transmission services for given prices. The performance of the local closed-loop systems is measured by a combination of linear-quadratic Gaussian cost and a suitable communication cost, and the overall objective is to minimize a defined social cost by all three policymakers. We derive optimal control, sampling, and resource allocation policies under different cross-layer awareness models, including constant and time-varying parameters, and show that higher awareness generally leads to performance enhancement at the expense of higher computational complexity. This trade-off is shown to be a key feature to select the proper interaction structure for the codesign.