Modeling collective motion in multi-agent systems has gained much attention in recent years. In particular, of interest are the conditions under which flocking dynamics emerges. We present a generalization of the multi-agent model of Olfati--Saber with nonlinear navigational feedback forces. As opposed to the original model, our model is, in general, not dissipative. This makes obtaining sufficient conditions for flocking challenging due to the absence of an obvious choice of a Lyapunov function. By means of an alternative argument, we show that our model possesses a global attractor when the navigational feedback forces are bounded perturbations of the linear ones. We further demonstrate that, under mild conditions, the dynamics of the group converges to a complete velocity consensus at an exponential rate. We show that the attractor of a dissipative system can contain non-equilibrium solutions. We construct explicit examples of such solutions and obtain conditions under which they cannot exist. In addition, we present a case study of the energy efficiency of our model. We show how nonlinear navigational feedback forces, which possess flexibility that linear forces lack, can be used to reduce on-board energy consumption.

翻译：近年来，多智能体系统中的群体运动建模备受关注，其中集群动力学涌现的条件尤为引人瞩目。本文提出了Olfati-Saber多智能体模型在非线性导航反馈力作用下的推广形式。与原始模型不同，本文提出的模型通常不具有耗散性。由于缺乏李雅普诺夫函数的显式选择，这使得获取集群的充分条件具有挑战性。通过替代性论证，我们证明了当导航反馈力是线性力的有界扰动时，该模型存在全局吸引子。进一步研究表明，在温和条件下，群体动力学以指数速率收敛至完全速度一致状态。我们证明耗散系统的吸引子可能包含非平衡解，并构造了此类解的显式示例，同时获得了其不存在的条件。此外，我们通过案例分析展示了模型的能效特性：具有线性力所不具备灵活性的非线性导航反馈力，可有效降低机载能量消耗。