This paper proposes an observer-based fractional order robust adaptive backstepping control scheme for incommensurate fractional order systems with partial measurable state. The chattering phenomenon is carefully analyzed, and then a class of chattering-free controllers are proposed. To handle the time-varying disturbance, a robust adaptive control scheme is developed via the backstepping procedure. The method to generate the required fractional order differential signals online is provided. After designing the controller, the stability of the resulting closed-loop system is analyzed systematically. To highlight the efficiency of our findings, one illustrative example is provided at last.
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The authors would like to thank the Associate Editor and the anonymous reviewers for their keen and insightful comments which greatly improved the contents and the presentation. The work described in this paper was fully supported by the National Natural Science Foundation of China (61601431, 61573332), the Anhui Provincial Natural Science Foundation (1708085QF141), the Fundamental Research Funds for the Central Universities (WK2100100028), and the General Financial Grant from the China Postdoctoral Science Foundation (2016M602032).
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
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Wei, Y., Sheng, D., Chen, Y. et al. Fractional order chattering-free robust adaptive backstepping control technique. Nonlinear Dyn 95, 2383–2394 (2019). https://doi.org/10.1007/s11071-018-4698-8
- Robust adaptive control
- Fractional order systems
- Incommensurate case
- Indirect Lyapunov method
- Chattering free