This paper investigates the leaderless consensus control problem of high-order nonholonomic chained systems. Based on the relationship between state and consensus error, a novel Lyapunov function is defined and is proved positive definite and radially unbounded. The first control law is constructed to make the Lyapunov function non-increasing. The Lyapunov method, graph theory and LaSalle invariance principle are applied to analyse system stability, where some skillful mathematical calculations are conducted to overcome the difficulties caused by nonholonomic constraint and high-order structure, and the explicit expression and the conditions of control parameter matrix are calculated. Then, the second control law is designed by extending the results to the input saturation case. Both of the two controllers are smooth, time-invariant, static, distributed, and able to achieve global asymptotic consensus of nonholonomic chained systems over connected undirected graph. Numerical simulation examples are implemented to demonstrate the effectiveness of the proposed control schemes.

本文研究了高阶非完整链系统的无领导共识控制问题。基于状态和共识误差之间的关系，定义了一个新的李雅普诺夫函数，并证明了它是正定的和径向无界的。构造第一控制律使李雅普诺夫函数不增。应用李雅普诺夫方法、图论和拉萨尔不变性原理分析系统稳定性，通过巧妙的数学计算克服非完整约束和高阶结构带来的困难，控制参数矩阵的显式表达式和条件为计算。然后，通过将结果扩展到输入饱和情况来设计第二个控制律。两个控制器都是平滑的、时不变的、静态的、分布式，并且能够在连接的无向图上实现非完整链系统的全局渐近共识。实施数值模拟示例以证明所提出的控制方案的有效性。