Finite time quantized average consensus with transmission stopping guarantees and no quantization error

Networked control systems, which are composed of spatially distributed sensors and actuators that communicate through wireless networks, are emerging as a fundamental infrastructure technology in 5G and IoT technologies. In order to increase flexibility and reduce deployment and maintenance costs, their operation needs to guarantee (i) efficient communication between nodes and (ii) preservation of available energy. Motivated by these requirements, we present and analyze a novel distributed average consensus algorithm, which (i) operates exclusively on quantized values (in order to guarantee efficient communication and data storage), (ii) relies on event-driven updates (in order to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage), and (iii) allows each node to cease transmissions once the exact average of the initial quantized values has been reached (in order to preserve its stored energy). We characterize the properties of the proposed algorithm and show that its execution, on any time-invariant and strongly connected digraph, allows all nodes to reach in finite time a common consensus value that is equal to the exact average (represented as the ratio of two quantized values). Then, we present upper bounds on (i) the number of transmissions and computations each node has to perform during the execution of the algorithm, and (ii) the memory and energy requirements of each node in order for the algorithm to be executed. Finally, we provide examples that demonstrate the operation, performance, and potential advantages of our proposed algorithm.