Abstract This paper addresses the adaptive finite-time consensus tracking problem for high-order nonlinear multi-agent systems (MASs) with powers of positive odd rational numbers under prescribed performance. Since the virtual and actual control parts of the dynamics of each follower agent are power functions containing positive odd rational numbers, the method of adding a power integrator is used to overcome the controller design difficulties caused by the power functions. With the aid of a finite-time performance function (FTPF) and neural networks (NNs), a distributed adaptive finite-time consensus tracking controller with prescribed tracking performance is properly designed by the backstepping process. It is shown that the proposed control strategy can guarantee that the consensus tracking error converges to an arbitrarily small neighborhood around zero at any settling time, while all signals of the closed-loop system are semi-globally practical finite-time stable (SGPF-stable). Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method.

中文翻译：

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一类具有正奇有理数幂和规定性能的高阶非线性多智能体系统的自适应神经网络有限时间跟踪控制

摘要 本文解决了在规定性能下具有正奇​​有理数幂的高阶非线性多智能体系统 (MAS) 的自适应有限时间一致性跟踪问题。由于每个跟随者动态的虚实控制部分都是包含正奇有理数的幂函数，因此采用添加幂积分器的方法来克服幂函数带来的控制器设计困难。在有限时间性能函数（FTPF）和神经网络（NN）的帮助下，具有规定跟踪性能的分布式自适应有限时间一致性跟踪控制器通过反步过程正确设计。结果表明，所提出的控制策略可以保证一致性跟踪误差在任何稳定时间收敛到零附近的任意小邻域，而闭环系统的所有信号都是半全局实用的有限时间稳定（SGPF-stable ）。最后，给出了一个仿真例子来证明所提出方法的有效性。