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A High-Order Fully Actuated System Approach for a Class of Nonlinear Systems

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Abstract

This paper utilizes the high-order fully actuated (HOFA) system approach to synthesize a class of nonlinear systems. First, the original nonlinear system can be rewritten in a quasi-linear form, which is more general than other nonlinear systems, such as strict-feedback systems. Based on a rank condition, the quasi-linear system can be transformed into a canonical form. Second, a simple transformation is adopted to convert the above canonical form into the HOFA model. Once an HOFA model is derived, the authors design a controller to make the closed-loop system a constant linear system with the desired eigenstructure. Finally, a numerical example illustrates the fitness and effectiveness of the proposed approach.

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References

  1. Asada H and Slotine J J E, Robot Analysis and Control, John Wiley & Sons, New York, 1986.

    Google Scholar 

  2. Lozano R and Brogliato B, Adaptive control of robot manipulators with flexible joints, IEEE Transactions on Automatic Control, 1992, 37(2): 174–181.

    Article  MathSciNet  Google Scholar 

  3. Bryson A E, Control of Spacecraft and Aircraft, Princeton University Press, Princeton, 1993.

    Google Scholar 

  4. Duan G R, High-order fully actuated system approaches: Part VIII. Optimal control with application in spacecraft attitude stabilisation, International Journal of Systems Science, 2022, 53(1): 54–73.

    Article  MathSciNet  Google Scholar 

  5. Gu D K, Zhang D W, and Liu Q Z, Parametric control to permanent magnet synchronous motor via proportional plus integral feedback, Transactions of the Institute of Measurement and Control, 2021, 43(4): 925–932.

    Article  Google Scholar 

  6. Dawson D M, Hu J, and Burg T C, Nonlinear Control of Electric Machinery, CRC Press, Boca Raton, 2019.

    Book  Google Scholar 

  7. Isidori A, Nonlinear Control Systems, 3rd Ed., Springer Verlag, London, 1995.

    Book  Google Scholar 

  8. Khalil H, Nonlinear Systems, 3rd Ed., Prentice Hall, Upper Saddle River, New Jersey, 2002.

    MATH  Google Scholar 

  9. Krstic M, Kanellakopoulos I, and Kokotović P V, Nonlinear and Adaptive Control Design, John Wiley & Sons, New York, 1995.

    MATH  Google Scholar 

  10. Slotine J J E and Li W, Applied Nonlinear Control, Prentice Hall, Upper Saddle River, New Jersey, 1991.

    MATH  Google Scholar 

  11. van der Schaft A J, L2-Gain and Passivity Techniques in Nonlinear Control, 2nd Ed., Springer-Verlag, London, 1999.

    Google Scholar 

  12. Gu D K, Wang R Y, and Liu Y D, A parametric approach of partial eigenstructure assignment for high-order linear systems via proportional plus derivative state feedback, AIMS Mathematics, 2021, 6(10): 11139–11166.

    Article  MathSciNet  Google Scholar 

  13. Çimen T, Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method, Annual Reviews in Control, 2010, 34(1): 32–51.

    Article  Google Scholar 

  14. Duan G R, Parametric control of quasi-linear systems via state feedback, Proceedings of 14th International Conference on Control, Automation and Systems, Eds. by Fareedi A A and Hassan S, IEEE, South Korea, 2014, 23–28.

    Google Scholar 

  15. Duan G R, Parametric control of quasi-linear systems via output feedback, Proceedings of 14th International Conference on Control, Automation and Systems, Eds. by Fareedi A A and Hassan S, IEEE, South Korea, 2014, 928–934.

    Google Scholar 

  16. Gu D K, Liu G P, and Duan G R, Parametric control to a type of quasi-linear second-order systems via output feedback, International Journal of Control, 2019, 92(2): 291–302.

    Article  MathSciNet  Google Scholar 

  17. Liu Y D, Zhang D W, Wang L M, et al., Parametric control to second-order quasi-linear systems based on dynamic compensator and multi-objective optimization, IEEE Access, 2019, 7: 67287–67304.

    Article  Google Scholar 

  18. Gu D K, Zhang D W, and Duan G R, Parametric control to a type of quasi-linear high-order systems via output feedback, European Journal of Control, 2019, 47: 44–52.

    Article  MathSciNet  Google Scholar 

  19. Gu D K and Zhang D W, A parametric method to design dynamic compensator for high-order quasi-linear systems, Nonlinear Dynamics, 2020, 100(2): 1379–01400.

    Article  Google Scholar 

  20. Gu D K and Zhang D W, Parametric control to a type of descriptor quasi-linear high-order systems via output feedback, European Journal of Control, 2021, 58: 223–231.

    Article  MathSciNet  Google Scholar 

  21. Gu D K, Zhang D W, and Liu Y D, Parametric method to design dynamic compensator for descriptor high-order quasi-linear systems, IET Control Theory & Applications, 2020, 14(19): 3179–3192.

    Article  MathSciNet  Google Scholar 

  22. Duan G R, High-order system approaches: I. Fully-actuated systems and parametric designs, Acta Automatica Sinica, 2020, 46(7): 1333–1345 (in Chinese).

    MATH  Google Scholar 

  23. Duan G R, High-order fully actuated system approaches: Part I. Models and basic procedure, International Journal of Systems Science, 2021, 52(2): 422–435.

    Article  MathSciNet  Google Scholar 

  24. Duan G R, High-order system approaches: II. Controllability and full-actuation, Acta Automatica Sinica, 2020, 46(8): 1571–1581 (in Chinese).

    MATH  Google Scholar 

  25. Duan G R, High-order fully actuated system approaches: Part II. Generalized strict-feedback systems, International Journal of Systems Science, 2021, 52(3): 437–454.

    Article  MathSciNet  Google Scholar 

  26. Duan G R, High-order fully actuated system approaches: Part VII. Controllability, stabilisability and parametric designs, International Journal of Systems Science, 2021, 52(14): 3091–3114.

    Article  MathSciNet  Google Scholar 

  27. Duan G R, High-order fully actuated system approaches: Part III. Robust control and high-order backstepping, International Journal of Systems Science, 2021, 52(5): 952–971.

    Article  MathSciNet  Google Scholar 

  28. Duan G R, High-order fully actuated system approaches: Part IV. Adaptive control and high-order backstepping, International Journal of Systems Science, 2021, 52(5): 972–989.

    Article  MathSciNet  Google Scholar 

  29. Duan G R, High-order fully actuated system approaches: Part V. Robust adaptive control, International Journal of Systems Science, 2021, 52(10): 2129–2143.

    Article  MathSciNet  Google Scholar 

  30. Duan G R, High-order fully-actuated system approaches: Part VI. Disturbance attenuation and decoupling, International Journal of Systems Science, 2021, 52(10): 2161–2181

    Article  MathSciNet  Google Scholar 

  31. Duan G R, High-order fully-actuated system approaches: Part IX. Generalised PID control and model reference tracking, International Journal of Systems Science, 2022, 53(3): 652–674.

    Article  MathSciNet  Google Scholar 

  32. Duan G R, High-order fully actuated system approaches: Part X. Basics of discrete-time systems, International Journal of Systems Science, 2021, DOI: https://doi.org/10.1080/00207721.2021.1975848.

  33. Duan G R, Generalized Sylvester Equations: Unified Parametric Solutions, CRC Press, Boca Raton, 2019.

    Google Scholar 

  34. Zuber I E, Stabilization of nonlinear systems by similarity transformations, Journal of Applied Mathematics and Stochastic Analysis, 1998, 11(4): 519–526.

    Article  MathSciNet  Google Scholar 

  35. Duan G R, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Automation Engineering, Northeast Electric Power University, Jilin, 132012, China

    Dake Gu & Shuo Wang

Authors
  1. Dake Gu
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  2. Shuo Wang
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Corresponding author

Correspondence to Dake Gu.

Additional information

This research was supported by the Major Program of National Natural Science Foundation of China under Grant Nos. 61690210 and 61690212, the National Natural Science Foundation of China under Grant No. 61333003, and also by the Science Center Program of the National Natural Science Foundation of China under Grant No. 62188101.

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Gu, D., Wang, S. A High-Order Fully Actuated System Approach for a Class of Nonlinear Systems. J Syst Sci Complex 35, 714–730 (2022). https://doi.org/10.1007/s11424-022-2041-4

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  • DOI: https://doi.org/10.1007/s11424-022-2041-4

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