Global smooth leaderless consensus control of high-order nonholonomic chained systems

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.