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Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach

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Abstract

This paper seeks to address the problem of finite-time stabilization for a class of uncertain Hamiltonian systems via sliding mode control approach. A novel sliding function in connection with the state and energy function of the considered system is constructed, and then, a suitable controller is designed to drive the state trajectories onto the specified sliding surface before the given finite-time. Moreover, the finite-time boundedness of the closed-loop system over both reaching phase and sliding motion phase are analyzed and the corresponding conditions are obtained. Furthermore, two optimization problems are formed to enhance the performance of finite-time boundedness, which will be solved via genetic optimization algorithm. Finally, a simulation example is provided to illustrate the proposed control strategy.

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References

  1. Amato, F., Ariola, M., Dorato, P.: Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9), 1459–1463 (2001)

    Article  Google Scholar 

  2. Beckenbach, E., Bellman, R.: Inequalities. Springer, New York (1965)

    Book  Google Scholar 

  3. Cao, Z., Niu, Y., Song, J.: Finite-time sliding-mode control of Markovian jump cyber-physical systems against randomly occurring injection attacks. IEEE Trans. Autom. Control 65(3), 1264–1271 (2020)

    Article  MathSciNet  Google Scholar 

  4. Cao, Z., Niu, Y.: Finite-time stochastic boundedness of Markovian jump systems: a sliding-mode-based hybrid design method. Nonlinear Anal. Hybrid Syst. 36(100862), 1–16 (2020)

    MathSciNet  MATH  Google Scholar 

  5. Cao, Z., Niu, Y., Lam, H.-K., et al.: Sliding mode control of Markovian jump fuzzy systems: a dynamic event-triggered method. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.3009729

    Article  Google Scholar 

  6. Ding, S., Mei, K., Li, S.: A new second-order sliding mode and its application to nonlinear constrained systems. IEEE Trans. Autom. Control 64(6), 2545–2552 (2019)

    Article  MathSciNet  Google Scholar 

  7. Dorato, P.: Short time stability in linear time-varying systems. IRE Int. Convent. Rec. Part 4, 83–87 (1961)

    Google Scholar 

  8. Du, H., Lam, J., Sze, K.Y.: Non-fragile output feedback \(H_\infty \) vehicle suspension control using genetic algorithm. Eng. Appl. Artif. Intell. 16(7–8), 667–680 (2003)

    Article  Google Scholar 

  9. Fujimoto, K., Sakata, N., Maruta, I., et al.: A passivity based sliding mode controller for simple port-Hamiltonian systems. IEEE Control Syst. Lett. 5(3), 839–844 (2021)

    Article  MathSciNet  Google Scholar 

  10. Garcia, G., Tarbouriech, S., Bernussou, J.: Finite-time stabilization of linear time-varying continuous systems. IEEE Trans. Autom. Control 54(2), 364–369 (2009)

    Article  MathSciNet  Google Scholar 

  11. Haddad, W.M., Rajpurohit, T., Jin, X.: Energy-based feedback control for stochastic port-controlled Hamiltonian systems. Automatica 97(11), 134–142 (2018)

    Article  MathSciNet  Google Scholar 

  12. Li, J., Niu, Y., Song, J.: Finite-time boundedness of sliding mode control under periodic event-triggered strategy. Int. J. Robust Nonlinear Control 31(2), 623–639 (2021)

    Article  MathSciNet  Google Scholar 

  13. Mathiyalagan, K., Park, J.H., Sakthivel, R.: Finite-time boundedness and dissipativity analysis of networked cascade control systems. Nonlinear Dyn. 84, 2149–2160 (2016)

    Article  MathSciNet  Google Scholar 

  14. Ren, Y., Sun, W.: Robust adaptive control for robotic systems with input time-varying delay using Hamiltonian method. IEEE/CAA J. Automatica Sinica 5(4), 852–859 (2018)

  15. Schiffer, J., Fridman, E., Ortega, R., et al.: Stability of a class of delayed port-Hamiltonian systems with application to microgrids with distributed rotational and electronic generation. Automatica 74(12), 71–79 (2016)

    Article  MathSciNet  Google Scholar 

  16. Song, J., Niu, Y., Zou, Y.: Finite-time stabilization via sliding mode control. IEEE Trans. Autom. Control 62(3), 1478–1483 (2017)

    Article  MathSciNet  Google Scholar 

  17. Song, J., Niu, Y.: Co-design of 2-D event generator and sliding mode controller for 2-D Roesser model via genetic algorithm. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2019.2959139

    Article  Google Scholar 

  18. Song, J., Niu, Y.: Dynamic event-triggered sliding mode control: dealing with slow sampling singularly perturbed systems. IEEE Trans. Circuits Syst. II Express Briefs 67(6), 1079–1083 (2020)

    Article  Google Scholar 

  19. Su, X., Liu, X., Shi, P., et al.: Sliding mode control of discrete-time switched systems with repeated scalar nonlinearity. IEEE Trans. Autom. Control 62(9), 4604–4610 (2017)

    Article  Google Scholar 

  20. Sun, W., Lv, X.: Practical finite-time fuzzy control for Hamiltonian systems via adaptive event-triggered approach. Int. J. Fuzzy Syst. 22(1), 35–45 (2020)

    Article  MathSciNet  Google Scholar 

  21. Sun, W., Lv, X., Qiu, M.: Distributed estimation for stochastic Hamiltonian systems with fading wireless channels. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3023547

    Article  Google Scholar 

  22. Vos, E., Scherpen, J.M.A., van der Schaft, A.J.: Equal distribution of satellite constellations on circular target orbits. Automatica 50(10), 2641–2647 (2014)

    Article  MathSciNet  Google Scholar 

  23. Wang, Y., Karimi, H.R., Shen, H., et al.: Fuzzy-model-based sliding mode control of nonlinear descriptor systems. IEEE Trans. Cybern. 49(9), 3409–3419 (2019)

    Article  Google Scholar 

  24. Wang, Y., Ge, S.S., Cheng, D.: On Hamiltonian realization of timevarying nonlinear systems. Sci. China Ser. F Inf. Sci. 50(5), 671–685 (2007)

    Article  Google Scholar 

  25. Wang, Z.-M., Wei, A., Zong, G., et al.: Finite-time stabilization and \(H_\infty \) control for a class of switched nonlinear port-controlled Hamiltonian systems subject to actuator saturation. J. Franklin Inst. 357(16), 11807–11829 (2020)

    Article  MathSciNet  Google Scholar 

  26. Xu, J., Niu, Y., Lim, C.-C., et al.: Memory output-feedback integral sliding mode control for furuta pendulum systems. IEEE Trans. Circuits Syst. I Regul. Pap. 67(6), 2042–2052 (2020)

    Article  MathSciNet  Google Scholar 

  27. Yu, H., Yu, J., Wu, H.: Energy-shaping and integral control of the three-tank liquid level system. Nonlinear Dyn. 73, 2149–2156 (2013)

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported in part by the NNSF (62073139, 61903143) from China.

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Authors and Affiliations

  1. Key Laboratory of Advanced Control and Optimization for Chemical Process (East China University of Science and Technology), Ministry of Education, Shanghai, 200237, China

    Xinyu Lv, Yugang Niu & Jun Song

Authors
  1. Xinyu Lv
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  2. Yugang Niu
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  3. Jun Song
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Correspondence to Yugang Niu.

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Lv, X., Niu, Y. & Song, J. Finite-time boundedness of uncertain Hamiltonian systems via sliding mode control approach. Nonlinear Dyn 104, 497–507 (2021). https://doi.org/10.1007/s11071-021-06292-8

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  • DOI: https://doi.org/10.1007/s11071-021-06292-8

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