Topological Conditions For Stabilization Versus Information Transmission

With recent revolutions in sensor and actuator technologies, availability of powerful but inexpensive embedded computing and introduction of new multi-hop wireless network standards for industrial automation, control over wireless networks is becoming a disruptive technology. Traditional wired interconnections between the plant sensors, controllers and actuators can be replaced by wireless multi-hop mesh networks, yielding cost and space savings for the plant operator. These improvements have also enabled more efficient and robust means of communication, and the opportunity to move the computation of the control law within the network. Despite this tremendous promise, the introduction of wireless communications into the feedback loop presents several challenges for real-time feedback control. For instance, delays may be introduced if a multi-hop wireless network is used to route information between the plant sensors, actuators and controllers. Transmissions in the network must be scheduled carefully to avoid packet dropouts due to collisions between neighboring nodes. These issues can be detrimental to the goal of maintaining stability of the closed loop system if not explicitly accounted for, and substantial research has been devoted to understanding the performance limitations in such settings. These works typically adopt the convention of having one or more dedicated controllers or state estimators located in the system, and study the stability of the closed loop system assuming that the sensor estimator and/or controller-actuator communication channels are unreliable (dropping packets with a certain probability, for example). For this standard architecture, the use of dedicated controllers imposes a routing requirement along one or more fixed paths through the network, along with strict end-to-end delay constraints to ensure stability