Adaptive control strategy improves synchronization of self-propelled agents

Abstract

This paper introduces an adaptive control strategy to the Vicsek model and investigates the collective behavior of self-propelled agents from the perspective of control theory. In the model, each agent adopts the classic proportional-integral (PI) control strategy to adjust its direction based on the deviation from the average direction of local neighbors. It is found that the integral term of the controller can eliminate the steady-state error, but strong integral effect will cause fluctuation of the system and prolong the convergence time. Therefore, the moderate integral control can adjust the headings of all agents to be synchronized after a short transient time. However, the proportional term incurs over-regulation of the directions, thus impeding the global convergence to be achieved. The robustness of the synchronizability with respect to different noise intensities is also investigated. Even in the strong noise environments, the control model can still maintain a high degree of directional consistency by adopting the conservative adjustment strategy. Furthermore, the diversity of control parameter is analyzed by considering the integral parameter following the normal distribution. It reveals that inconsistent adjustment magnitude is unfavorable to the synchronization of the system.