Sufficiency of Local Feedback for Sensor-Actuator Network-Based Control Systems with Distance Sensitivity Properties

Timely dissemination of required state information poses a significant challenge in the design of distributed sensor/actuator network-based control systems. In this paper, distance sensitivity properties inherent in many sensor-actuator network-based control systems are exploited to establish conditions under which information within a bounded locality of each controller closely approximates optimal control based on knowledge of system-wide state information. By doing so, it is shown that optimal control in extremely large-scale distributed control systems can be achieved in O(1) time using information only within a fixed neighborhood around each controller, the size of which depends on the decay characteristics of the actuator influence matrix.