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 non-linear 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 agreement 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 non-linear navigational feedback forces, which possess flexibility that linear forces lack, can be used to reduce on-board energy consumption.

翻译：近年来，多智能体系统中集体运动的建模引起了广泛关注。特别受关注的是集群动力学涌现的条件。我们提出了Olfati-Saber多智能体模型的一种推广，其中加入了非线性导航反馈力。与原始模型不同，我们的模型通常不是耗散的。由于缺乏明显的李雅普诺夫函数选择，这使得获得集群的充分条件变得具有挑战性。通过另一种论证方式，我们证明当导航反馈力是线性力的有界扰动时，我们的模型具有全局吸引子。我们进一步证明，在温和条件下，群体动力学以指数速率收敛到完全速度一致。我们证明耗散系统的吸引子可能包含非平衡解。我们构造了此类解的显式例子，并获得了它们不存在所需的条件。此外，我们针对模型的能效进行了案例研究。我们展示了具有线性力所缺乏灵活性的非线性导航反馈力如何用于降低机载能耗。