Prescribed-time consensus tracking for second-order nonlinear multiagent systems (MASs) with the unknown nonlinear dynamics satisfying a time-varying Lipschitz growth rate is investigated in this article. A time-varying function is introduced as a part of the controller gains, and it plays an important role in overcoming the rapid growth of nonlinear terms and in ensuring that the consensus can be achieved in a preassigned time. An integral sliding-mode control protocol, which forces the system trajectory to move on to the defined sliding manifold at the initial moment, is proposed for solving the prescribed-time consensus tracking problem of leader-following MASs with disturbances. Furthermore, we propose a slightly different control law based on terminal sliding-mode control, and under such a controller, the trajectories of each follower reach the sliding manifold in an arbitrary assigned time T1T_{1} , and then in a specified time T2T_{2} , the position and velocity tracking errors for all followers converge to 0 at the same time instant. Based on the graph theory, state transformations, and Lyapunov theorem, we prove that the proposed solutions are feasible and, finally, three simulation examples are provided to verify the theoretical results.

中文翻译：

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满足时变 Lipschitz 增长率的非线性动力学多智能体系统的规定时间共识跟踪


本文研究了具有满足时变 Lipschitz 增长率的未知非线性动力学的二阶非线性多智能体系统 (MAS) 的规定时间一致性跟踪。引入时变函数作为控制器增益的一部分，它对于克服非线性项的快速增长以及确保在预先指定的时间内达成共识起到了重要作用。提出了一种积分滑模控制协议，该协议强制系统轨迹在初始时刻移动到定义的滑动流形，以解决带扰动的先导跟随 MAS 的规定时间一致跟踪问题。此外，我们提出了一种基于终端滑模控制的稍微不同的控制律，在这种控制器下，每个跟随器的轨迹在任意指定时间 T1T_{1} 内到达滑动流形，然后在指定时间 T2T_{ 2} ，所有跟随器的位置和速度跟踪误差同时收敛到0。基于图论、状态变换和Lyapunov定理，我们证明了所提出的解决方案的可行性，最后提供了三个仿真例子来验证理论结果。