ADAPTIVE TRACKING CONTROL FOR FRACTIONAL-ORDER NONLINEAR UNCERTAIN SYSTEMS WITH STATE CONSTRAINTS VIA COMMAND-FILTERING AND DISTURBANCE OBSERVER

Guangming Xue, Bin Qin (), Xiulan Zhang, Bahri Cherif () and Shenggang Li ()
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Guangming Xue: School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, P. R. China†School of Mathematics and Quantitative Economics, Guangxi University of Finance and Economics, Nanning 530003, P. R. China
Bin Qin: ��School of Mathematics and Quantitative Economics, Guangxi University of Finance and Economics, Nanning 530003, P. R. China
Xiulan Zhang: ��School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, P. R. China
Bahri Cherif: �Department of Mathematics, College of Sciences and Arts, Qassim University, ArRass, Saudi Arabia
Shenggang Li: School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-20

Abstract: In this paper, the state-constrained adaptive control problem for a class of uncertain fractional-order nonlinear systems with unknown external disturbances is studied. Using the fuzzy approximation and backstepping control layout, an adaptive disturbance-observer-based control method is proposed, which can effectively estimate the unknown external disturbances through the designed disturbance observers. As we know, the standard backstepping control has inherent computational complexity. Therefore, a design approach of fractional-order command filter is introduced, which takes advantage of fractional-order command filter to pre-estimate the virtual input signal and its fractional derivative. In addition, barrier Lyapunov functions are exploited to cope with the fractional states-constrained control problem. The combination of barrier Lyapunov function technique and backstepping design not only ensures excellent tracking performance, but also enhances the robustness of the system. Furthermore, based on the fractional Lyapunov approach, the relevant stability analysis is established, which demonstrates that all states of the system remain within their constrained scope, and all signals of the closed-loop system are bounded. Finally, the effectiveness of the proposed scheme is verified by numerical simulation examples of RLC circuit and horizontal platform system.

Keywords: Fractional-Order Nonlinear System; Command Filter; Disturbance Observer; Fuzzy Logic System; State Constraint (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402459

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