Achieving Consensus for Multi-Agent States Under Switching Topologies via Coordinated Control

Coordinated control constitutes a core challenge in multi-agent systems, aiming to achieve global state consensus among groups through local interactions in dynamic environments. When network topologies switch over time (e.g., due to communication link failures or mobile device position changes), the system requires enhanced robustness.

The implementation typically relies on neighbor interaction rules: each agent obtains neighbor state information based on real-time topology and adjusts its own state through predefined distributed protocols (e.g., consensus protocols). A key challenge lies in how topological switching may disrupt information propagation connectivity, necessitating algorithms that satisfy: 1) joint connectivity of switching topologies (i.e., cumulative communication over sufficiently long time windows covers the entire network); 2) adaptive gains or time-varying coupling weights to handle topology changes. In code implementation, this often involves maintaining an adjacency matrix that updates dynamically, where agents periodically broadcast their states and calculate control inputs using weighted differences from neighbors' states.

Typical methodologies include Lyapunov-function-based stability analysis, switching strategies constrained by average dwell-time, and event-triggered mechanisms to reduce communication overhead. For algorithmic implementation, one might use matrix weight updates triggered by topology detection events, with convergence ensured through eigenanalysis of the graph Laplacian matrix over switching sequences. These techniques show broad application prospects in domains such as UAV formation control and smart grid frequency synchronization.