Modeling wireless sensor and actuator networks using frame theory
Wireless sensor networks are often studied with the goal of removing information from the network as efficiently as possible. However, when the application also includes an actuator network, it is advantageous to determine actions in-network. In such settings, optimizing the sensor node behavior with respect to sensor information fidelity will not necessarily translate into optimum behavior in terms of action fidelity. Inspired by neural systems, we present a model of a sensor and actuator network based on the vector space tools of frame theory that applies to applications analogous to reflex behaviors in biological systems. Our analysis yields bounds on both absolute and average actuation error that point directly to strategies for limiting sensor communication based not only on local measurements but also on a measure of how important each sensor-actuator link is to the fidelity of the total actuation output.