A large number of potential applications of Sensor and Actuator Networks (SANETs) have emerged recently, for example in the areas of energy production and distribution and health care and telemedicine. SANETs integrate the tasks of sensing and actuation, the process of controlling the operation of a physical system by setting values for parameters of interest. Of particular importance in SANETs is the ability to set actuator parameters, typically depending on values observed by the sensors, so as to achieve a system-wide objective. However, SANETs with large number of nodes or covering wide geographical areas present scalability challenges that necessitate the use of summarization techniques resulting in sub-optimal actuation values. There is therefore a clear trade-off between the level of summarization and the quality of the computed actuation parameters. This paper focuses on two interdependent problems. The first is the issue of efficient aggregation and summarization of the measurements. The second is the distributed computation of optimal actuation parameters to achieve a system-wide objective. We first consider the problem under the assumption of semi-static sensed values and then extend our model to cover the general case where sensor state changes, triggering update events. We develop algorithms for efficient summarization of these events and demonstrate that they minimally impact optimal actuation. Our work is motivated by the domain of energy distribution networks and, in particular, intelligent electrical grids.
