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

Abstract

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.

Keywords:

• High-order nonholonomic chained systems
• consensus control
• graph theory
• LaSalle invariance principle

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities [gant number XDJK2020C036]; the National Nature Science Foundation of China [grant number 61573034]; and the Development and Application Demonstration of Intelligent Light Pole Internet of Things System of Chongqing Science and Technology Commission [grant number cstc2017zdcy-zdyfX0054].