Modeling collective motion in multi-agent systems has gained significant attention. Of particular interest are sufficient conditions for flocking dynamics. We present a generalization of the multi-agent model of Olfati--Saber with nonlinear navigational feedback forces. Unlike the original model, ours is not generally dissipative and lacks an obvious Lyapunov function. We address this by proposing a method to prove the existence of an attractor without relying on LaSalle's principle. Other contributions are as follows. We prove that, under mild conditions, agents' velocities approach the center of mass velocity exponentially, with the distance between the center of mass and the virtual leader being bounded. In the dissipative case, we show existence of a broad class of nonlinear control forces for which the attractor does not contain periodic trajectories, which cannot be ruled out by LaSalle's principle. Finally, we conduct a computational investigation of the problem of reducing propulsion energy consumption by selecting appropriate navigational feedback forces.

翻译：多智能体系统中的集体运动建模已引起广泛关注。其中，集群动力学形成的充分条件尤为值得研究。本文提出了Olfati-Saber多智能体模型的非线性导航反馈力推广形式。与原始模型不同，该模型通常不具备耗散性，且缺乏明显的Lyapunov函数。我们通过提出一种不依赖于拉萨尔原理的吸引子存在性证明方法来解决这一问题。其他贡献如下：我们证明在温和条件下，智能体速度将以指数形式趋近于质心速度，且质心与虚拟领导者之间的距离保持有界。在耗散情形下，我们证明存在一大类非线性控制力，其对应吸引子不包含周期轨迹——这一性质无法通过拉萨尔原理排除。最后，我们通过计算实验研究了如何通过选择适当的导航反馈力来降低推进能耗的问题。