Consensus of Nonlinear Systems with Data-Rate Constraints⁎⁎This paper was elaborated in the UCoCoS project which received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 675080. A. Matveev’s work is supported by the Russian Science Foundation under grant 19-19-00403.

In this paper, consensus for a network of dynamical systems which communicate over data-rate constrained communication channels is considered. Each system in the network is equipped with a sensor and an actuator which are at locations remote from one another. In order to transmit the state of any system to any of the actuators, the sensors use data-rate constrained communication channels. The actuators then use the messages to determine control inputs such that the systems achieve a particular type of consensu. Sensor/actuator pairs that achieve that particular type of consensus are called consensus protocols. In this contribution, an efficient in terms of required data-rates consensus protocol is presented. For the protocol, a theorem proving conditions on the sufficient minimal data-rates to implement it is provided. The sufficient data-rate is proven to depend on the singular values of the linear part of the mapping of the systems in the network. Finally, an example is provided in the form of consensus for a network of harmonically forced bouncing ball systems, for which an analytical bound is provided on the sufficient outgoing channel rates.