Dynamic triggering mechanisms for distributed adaptive synchronization control and its application to circuit systems

Nonlinear couplings among units (nodes) are ubiquitous in engineering systems including, e.g., radar and sonar systems, which have been ignored in most works. In this article, the problem of distributed synchronization of nonlinear networked systems with nonlinear couplings is studied. Specifically, two kinds of nodes' communication couplings including nonlinear relative and nonlinear absolute state couplings are considered. To reduce the requirements of control and communication among nodes and avoid any global network information, two edge-based fully adaptive event-triggered control protocols based on nonlinear relative and absolute state couplings are proposed by using the projection operator technique, which is followed by design of corresponding dynamic event-triggered mechanisms. The advantages of our proposed dynamic event-triggered strategies show that it can boil down to existing static ones as special examples, and the minimal inter-execution time of the proposed dynamic triggering laws is larger than that of static ones. Theoretical analysis shows that the proposed algorithm not only guarantees fully adaptive Zeno-free synchronization of networked systems without requiring any global information, but also avoids continuous communications among nodes, and considerably reduce the frequency of controller updates. Finally, the practical merits of the proposed algorithms are corroborated using a Chua's circuit network.