A Cross-Layer Optimal Co-Design of Control and Networking in Time-Sensitive Cyber-Physical Systems

In the design of cyber-physical systems (CPS) where multiple physical systems are coupled via a communication network, a key aspect is to study how network services are distributed. In this letter, we first describe a cross-layer model for CPS to explicitly capture the coupling between control and networking and the time-sensitive requirements of each physical system. Physical systems processes are coupled via a shared network that provides a diverse range of cost-prone and capacity-limited services with distinct latency characteristics. Service prices are given such that low latency services incur higher communication cost, and prices remain fixed over a constant period of time but will be adjusted by the network for the future time periods. Physical systems decide to use specific services over each time interval depending on the service prices and their own time sensitivity requirements. Considering the service availability, the network coordinates resource allocation such that physical systems are serviced the closest to their preferences. Performance of individual systems are measured by an expected quadratic cost and we formulate a social optimization problem subject to time-sensitive requirements of the physical systems and the network constraints. From the formulated social optimization problem, we derive the joint optimal time-sensitive control and service allocation policies.