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This paper studies the distributed control of network flows using an embedded sensor-actuator network. We focus on the problem of reducing the frequency of combined sewer overflow (CSO) events in city sewer systems. This is an important environmental problem whose cost effective solution is of great interest across the world. Our approach embeds microprocessor controlled sensors and actuators directly into the sewer network. These embedded processors communicate with each other over a multi-hop communication network whose topology follows the topology of the sewer network. We use Pontryagin's maximum principle to develop a switching control where control decisions are made in a distributed manner. We present simulation results showing that the proposed method has the potential of greatly reducing the frequency of CSO events over existing passive thresholding strategies.Mr. Wan and Dr. Lemmon are with the department

Abstract-Many problems associated with networked systems can be formulated as network utility maximization (NUM) problems. NUM problems maximize a global separable measure of network optimality subject to linear constraints on resources. Dual decomposition is a widely used distributed algorithm that solves the NUM problem. This approach, however, uses a step size that is inversely proportional to measures of network size such as maximum path length or maximum neighborhood size. As a result, the number of messages exchanged between nodes by a dual decomposition scales poorly with respect to these measures. This paper presents a distributed primal-dual algorithm for the NUM problem that uses event-triggering. Under event triggering, each agent broadcasts to its neighbors when a local "error" signal exceeds a state dependent threshold. The paper establishes such state-dependent event-triggering thresholds under which the proposed algorithm converges. The paper gives an upper bound on the largest number of successive data dropouts the network can tolerate while ensuring the algorithm's convergence. State-dependent lower bound on the broadcast period is also given. Simulation results show that the proposed algorithm reduce the number of message exchanges by up to two orders of magnitude, and is scale-free with respect to the above two measures of network size.