Journal
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
Volume 52, Issue 5, Pages 952-971Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207721.2020.1849863
Keywords
High-order fully-actuated models; high-order backstepping; high-order strict-feedback systems; nonlinear uncertainties; robust control
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Funding
- Major Program of National Natural Science Foundation of China [61690210, 61690212]
- National Natural Science Foundation of China [61333003]
- SelfPlanned Task of State Key Laboratory of Robotics and System (HIT) [SKLRS201716A]
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This paper introduces three types of uncertain high-order nonlinear models and discusses their relationships. A direct method based on Lyapunov stability theory for designing robust stabilising controllers and robust tracking controllers is proposed. The proposed high-order backstepping methods require fewer steps than the usual first-order backstepping method, making them more direct and simple.
In this paper, three types of uncertain high-order nonlinear models are firstly proposed, namely, a single high-order fully actuated (HOFA) model with nonlinear uncertainties, an uncertain second-order strict-feedback system (SFS) and an uncertain high-order SFS, and the relations among these types of models are also discussed. Secondly, a direct approach for the design of robust stabilising controllers and robust tracking controllers for an uncertain single HOFA model are proposed based on the Lyapunov stability theory. Using the obtained robust control design result, the second- and high-order backstepping methods for the designs of robust stabilising controllers of the introduced second- and high-order SFSs are also proposed. The proposed approaches do not need to convert the high-order systems into first-order ones, and for a specific system design, the proposed high-order backstepping methods need fewer steps than the usual first-order backstepping method, hence are generally more direct and simpler. An illustrative example demonstrates both the effect and the application procedure of the proposed HOFA robust control approaches.
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