Prescribed-Time Formation Control for Multi-Agent Systems Based on Distance Rigid Graphs

This study addresses the formation control challenge for multi-agent systems with double-integrator dynamics, focusing on prescribed-time convergence using rigidity graph theory. The proposed control scheme incorporates a temporal scaling mechanism that guarantees formation achievement in a predetermined finite duration, demonstrating robustness against variations in initial states and parameter selection. A distinctive feature of our approach is its decentralized architecture, where each agent requires only neighbor distance measurements and relative velocity data for control computation. This minimal information requirement enhances the method’s applicability in GPS-denied environments while simplifying practical implementation. Through theoretical analysis combining rigidity theory with Lyapunov stability methods, we establish that the multi-agent system converges to minimally and infinitesimally rigid formations in two-dimensional space within the prescribed time frame. Numerical experiments validate the efficacy of the proposed control strategy, confirming its theoretical properties.