Cluster Synchronization Control for Discrete-Time Complex Dynamical Networks: When Data Transmission Meets Constrained Bit Rate

In this article, the cluster synchronization control problem is studied for discrete-time complex dynamical networks when the data transmission is subject to constrained bit rate. A bit-rate model is presented to quantify the limited network bandwidth, and the effects from the constrained bit rate onto the control performance of the cluster synchronization are evaluated. A sufficient condition is first proposed to guarantee the ultimate boundedness of the error dynamics of the cluster synchronization, and then, a bit-rate condition is established to reveal the fundamental relationship between the bit rate and the certain performance index of the cluster synchronization. Subsequently, two optimization problems are formulated to design the desired synchronization controllers with aim to achieve two distinct synchronization performance indices. The codesign issue for the bit-rate allocation protocol and the controller gains is further discussed to reduce the conservatism by locally minimizing a certain asymptotic upper bound of the synchronization error dynamics. Finally, three illustrative simulation examples are utilized to validate the feasibility and effectiveness of the developed synchronization control scheme.

Automated summary

This article studies the cluster synchronization control problem for discrete-time complex dynamical networks under constrained bit rate. A bit-rate model is presented to quantify the limited network bandwidth and evaluate its effects on the control performance. Sufficient conditions are proposed to ensure boundedness of the error dynamics and the fundamental relationship between bit rate and performance index is established. Two optimization problems are formulated to design synchronization controllers and co-design issues are discussed to reduce conservatism. The developed synchronization control scheme is validated through simulation examples.