Global 𝒦-exponential trackers for nonholonomic chained-form systems based on LMI

Abstract

Global 𝒦-exponential controllers are constructed for the tracking control problem of nonholonomic systems in chained form. Compared to previously published papers, a difference is that the reference targets are allowed to converge to a point exponentially. By using a novel transformation and the cascade-design method, the tracking control problem is converted into a stabilisation problem composed of two simple subsystems. Then the LMI-design approach is developed for the stabilising one of the above two subsystems. Assumptions on the reference signal is much more relaxed than our previous papers. A peculiar character of the presented methodology is that global 𝒦-exponential tracking can be successfully obtained for nonholonomic chained-form systems without the popular condition of persistent excitation or not converging to zero. Simulation results on a unicycle mobile robot and an articulated vehicle are presented to show the validity of the proposed strategy.

Keywords:

• chained-form systems
• global tracking
• cascaded systems
• LMI
• persistent excitation
• exponential convergence

Acknowledgements

The authors gratefully acknowledge that this work was supported partly by the National Natural Science Foundation of China (under grant 60805039) and partly by the Fund of Nanjing University of Posts and Telecommunications for Introduced Talents (under grant NY207028). They also thank the reviewers for their valuable comments and Prof. Tian for his helpful remarks, which improved the presentation of the article.