Self-Learning Control for Multi-Agent Consensus

This paper addresses the consensus problem in multi-agent systems via a self-learning control scheme that directly reuses prior control information to accelerate transient coordination while maintaining robustness. I study agents with linear dynamics and external disturbances, and design a lightweight self-learning consensus control law for the distributed consensus domain, formulated as ui(t)=k1ui(t−τ)+k2si(t) with learning intensity k1 and learning interval τ. I provide a Lyapunov-based stability proof showing uniform ultimate boundedness of the consensus error under bounded disturbances. Compared to non-learning consensus laws, the proposed strategy achieves faster agreement with reduced long-term effort and retains simplicity suitable for resource-constrained multi-agent platforms, while also achieving decent performance against external disturbances. Simulations validate the improved transient speed and steady accuracy. The full-version-source code is open-sourced.