Cross-Layer Design of Networked Control Systems

The wireless connection of spatially separated sensors, controllers and actuators poses challenging problems to the control system, due to packet drops, delays and measurements quantization, as well as to the wireless network resource allocator. This pushes for a cross-layer design of communication and estimation/control systems. Assuming a TCP-like protocol between controller and actuator, we solve the problem of optimum control around a target state for a stable system in case of both packet drops and signal quantization. Generalization for unstable systems is also given for large bandwidth transmissions. Next, we derive the limiting behavior of the system in the infinite horizon and propose a general framework for cross-layer optimization of signal quantization and network resource allocation. As an example of application, we consider a simple scalar, stable system and compare network resource allocation in the presence of i) low-cost sensors using a fix modulation and ii) long-term future sensors capable of rate adaptation. Interestingly, almost optimal control is achievable by small bandwidth transmissions using a simple BPSK, supporting the use of low-cost sensors in applications dealing with state control in stable systems.