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Adaptive backstepping optimal control of a fractional-order chaotic magnetic-field electromechanical transducer

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Abstract

This paper develops an adaptive backstepping optimal control scheme for a fractional-order chaotic magnetic-field electromechanical transducer with the saturated control inputs. A dynamical analysis is used to check for abundant dynamical behaviors of the system by using phase diagrams and time histories under different excitations and fractional orders. A fuzzy wavelet neural network (FWNN) is utilized with an adaptive feedforward control input in order to estimate the unknown dynamical system. An auxiliary system is then developed to compensate the effects caused by the saturated control inputs, along with a tracking differentiator (TD) to realize the signal estimation associated with the fractional derivative. Taking FWNN, TD and auxiliary system into the framework of the fractional-order backstepping control, an adaptive feedforward controller is designed. In addition, we use a data-driven learning framework based on an actor critic network to solve the derived Hamilton–Jacobi–Bellman equation. The whole control policy, composing of an adaptive feedforward controller and an optimal feedback controller, not only guarantees the boundness of all signals and suppresses oscillations from the chaos and deadzone, but also makes the cost function to be smallest. Finally, the simulation results demonstrate the effectiveness of the presented scheme.

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Acknowledgements

This work is funded by the Key Project of National Natural Science Foundation of China (No.61933012), International Communication and Cooperation Program of National Natural Science Foundation of China(No. 61860206008), Young Scientific Talents of Education Department of Guizhou Province (No. [2018]111), Science and Technology Planning Project of Guizhou Province (No. [2018]5781), and Research Project of Introduction of Talents of Guizhou University (No. [2017]27).

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Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing Technology, Ministry of Education, Guizhou University, Guiyang, 550025, China

    Shaohua Luo

  2. UTA Research Institute, University of Texas at Arlington, Fort Worth, TX, 76118, USA

    Shaohua Luo & Frank L. Lewis

  3. School of Automation, Chongqing University, Chongqing, 400044, China

    Yongduan Song

  4. Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Kyriakos G. Vamvoudakis

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  1. Shaohua Luo
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  4. Kyriakos G. Vamvoudakis
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Correspondence to Shaohua Luo.

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Luo, S., Lewis, F.L., Song, Y. et al. Adaptive backstepping optimal control of a fractional-order chaotic magnetic-field electromechanical transducer. Nonlinear Dyn 100, 523–540 (2020). https://doi.org/10.1007/s11071-020-05518-5

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