Advanced Convergence Optimization in Consensus-Based Wireless Sensor Networks via Strategic Node Addition and Pinning Control

Abstract

Wireless Sensor Networks (WSNs) require precise time synchronization to ensure coordinated monitoring operations and data coherence across distributed multi-agent systems. Consensus-based protocols offer a robust, fully distributed solution for synchronizing clock offsets and frequencies by leveraging local information exchange. The convergence speed of such algorithms is heavily dependent on the algebraic connectivity of the network graph, structurally quantified by the second smallest eigenvalue of the graph’s Laplacian matrix. This paper investigates the reduction of convergence time in WSNs by strategically introducing a single dynamic node to an existing network topology. Three distinct criteria for determining the connections of the new node are proposed and mathematically analyzed: an exhaustive search for optimal positioning, a maximum degree constraint approach, and a Twin criterion that emulates the topology of an existing node. Numerical simulations establish that maximizing the second eigenvalue significantly accelerates synchronization. Furthermore, the integration of optimal node placement strategies provides a comprehensive framework for optimizing both resource cost and convergence speed.