Consensus in networks of dynamical systems with limited communication capacity. (November 2022) - Voortman, Quentin; Pogromsky, Alexander Yu.; Matveev, Alexey S.; Nijmeijer, Henk
Abstract: This paper provides a solution for the preservation of consensus in a network of several agents, described by discrete-time nonlinear dynamical systems. Consensus preservation is the problem of maintaining a certain distance between the states of several systems, given that the systems' initial states are close to each other. The agents are equipped with both a smart sensor, capable of measuring the state of the system and performing some computations, and a controller. The sensors and controllers are placed at locations that are remote from one another. A network of communication channels with limited transmission capacity connects the agents by allowing the sensors to send messages to the controllers of their system as well as to the controllers of other systems. The controllers use the messages that they receive to steer the agents such that the consensus is preserved. Sensors and controllers that achieve this feature are called consensus-preserving protocols. In this paper, three distinct consensus-preserving protocols are presented, each with an increasing degree of interaction between the systems. For each of these protocols, a theorem providing conditions on the minimum communication capacity sufficient to implement them is presented. The protocols are tested by simulations for a network of logistic maps and a network of Hénon maps. For both of these networks, analytical bounds on the sufficient transmission capacities in the communication channels to implement the protocols are provided. These bounds are compared to rates observed in simulations of the consensus-preserving protocols.