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Control Design for One-Sided Lipschitz Nonlinear Systems with Actuator Saturation

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Proceedings of 2020 Chinese Intelligent Systems Conference (CISC 2020)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 705))

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Abstract

In this article, the saturated controller is designed for a type of nonlinear systems satisfying one-sided Lipschitz constraints. The nonlinearity in the saturation element is transformed into a series of convex hull of linear state feedback. The stability of the closed-loop system is analyzed by the method of Lyapunov function, and the parameters of the saturated controller are derived by the constraints of several linear and bilinear matrix inequalities. At last, we provide an example to demonstrate the availability of the presented method.

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References

  1. Hu, G.: Observers for one-sided Lipschitz nonlinear systems. IMA J. Math. Control Inf. 23(4), 395–401 (2006)

    Article  MathSciNet  Google Scholar 

  2. Abbaszadeh, M., Marquez, H.: Nonlinear observer design for one-sided Lipschitz systems. In: Proceedings of the American Control Conference (2009)

    Google Scholar 

  3. Xu, M., Hu, G., Zhao, Y.: Reduced-order observer design for one-sided Lipschitz nonlinear systems. IMA J. Math. Control Inf. 26(3), 299–317 (2009)

    Article  Google Scholar 

  4. Zhang, W., Su, H., Zhu, F., Yue, D.: A note on observers for discrete-time Lipschitz nonlinear systems. IEEE Trans. Circ. Syst. II Express Briefs 59(2), 123–127 (2012)

    Article  Google Scholar 

  5. Zhang, W., Su, H., Zhu, F., Bhattacharyya, S.: Improved exponential observer design for one-sided Lipschitz nonlinear systems. Int. J. Robust Nonlinear Control 26(18), 3958–3973 (2016)

    Article  MathSciNet  Google Scholar 

  6. Yang, Y., Lin, C., Chen, B., Zhao, X.: H\(_\infty \) observer design for uncertain one-sided Lipschitz nonlinear systems with time-varying delay. Appl. Math. Comput. 375(11), 1250–1266 (2020)

    MathSciNet  Google Scholar 

  7. Donchev, T., Farkhi, E.: Stability and Euler approximation of one-sided Lipschitz differential inclusions. SIAM J. Control Optim. 36(2), 780–796 (1998)

    Article  MathSciNet  Google Scholar 

  8. Sad, W., Sellami, A., Garcia, G.: Robust stabilization of one-sided Lipschitz nonlinear systems via adaptive sliding mode control. J. Vibr. Control 26(7), 399–412 (2020)

    Article  MathSciNet  Google Scholar 

  9. Song, J., He, S.: Finite-time H\(_\infty \) control for quasi-one-sided Lipschitz nonlinear systems. Neurocomputing 149, 1433–1439 (2015)

    Article  Google Scholar 

  10. Song, J., He, S.: Robust finite-time H\(_\infty \) control for one-sided Lipschitz nonlinear systems via state feedback and output feedback. Neurocomputing 352(8), 3250–3266 (2015)

    MathSciNet  MATH  Google Scholar 

  11. Gao, W., Selmic, P.: Neural network control of a class of nonlinear systems with actuator saturation. IEEE Trans. Neural Networks 17(1), 147–156 (2006)

    Article  Google Scholar 

  12. Saifia, D., Chadli, M., Labiod, S.: H\(_\infty \) control of multiple model subject to actuator saturation: application to quarter car suspension system. Analog Integr. Cir. Sig. Process. 69(1), 81–90 (2011)

    Article  Google Scholar 

  13. Maddela, C., Subudhi, B.: Delay-dependent supplementary damping controller of TCSC for interconnected power system with time-delays and actuator saturation. Electr. Pow. Syst. Res. 164, 39–46 (2018)

    Article  Google Scholar 

  14. Liu, D., Michel, A.: Dynamical Systems With Saturation Nonlinearities: Analysis and Design. Springer, Heidelberg (1994)

    Book  Google Scholar 

  15. Hu, T., Lin, Z.: Control Systems with Actuator Saturation: Analysis and Design, vol. 38, no. 2, pp. 351–359. Springer, New York (2002)

    Google Scholar 

  16. Hu, T., Lin, Z., Chen, B.: An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica 38(2), 351–359 (2002)

    Article  Google Scholar 

  17. Lu, L.: Output regulation of a class of switched linear systems with saturated continuous feedback. In: Proceedings of the 30th Chinese Control Conference (2011)

    Google Scholar 

  18. Guan, W., Yang, G.: Adaptive fault-tolerant control of linear systems with actuator saturation and \(L_2\)-disturbances. J. Control Theor. Appl. 7(2), 119–126 (2009)

    Article  MathSciNet  Google Scholar 

  19. Rehan, M., Tufail, M., Ahn, C., Chadli, M.: Stabilization of locally Lipschitz nonlinear systems under input saturation and quantisation. IET Control Theor. Appl. 11(9), 1459–1466 (2017)

    Article  Google Scholar 

  20. Shevitz, D., Paden, B.: Lyapunov stability theory of nonsmooth systems. IEEE Trans. Autom. Control 39(9), 1910–1914 (1944)

    Article  MathSciNet  Google Scholar 

  21. Hu, T., Lin, Z.: Composite quadratic Lyapunov functions for constrained control systems. IEEE Trans. Autom. Control 48(3), 440–450 (2003)

    Article  MathSciNet  Google Scholar 

  22. Hassibi, A., How, J., Boyd, S.: A path-following method for solving BMI problems in control. In: Proceedings of the 1999 American Control Conference (1999)

    Google Scholar 

  23. Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM J. Control Optim. 15 (1994)

    Google Scholar 

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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Soochow University, Suzhou, 215131, Jiangsu, China

    Lin Yang, Jun Huang & Haoran Zhang

Authors
  1. Lin Yang
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  2. Jun Huang
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  3. Haoran Zhang
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Corresponding author

Correspondence to Jun Huang .

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Editors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beihang University, Beijing, Beijing, China

    Yingmin Jia

  2. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, Beijing, China

    Weicun Zhang

  3. School of Mechanical Engineering and Automation, Beihang University, Beijing, Beijing, China

    Yongling Fu

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Yang, L., Huang, J., Zhang, H. (2021). Control Design for One-Sided Lipschitz Nonlinear Systems with Actuator Saturation. In: Jia, Y., Zhang, W., Fu, Y. (eds) Proceedings of 2020 Chinese Intelligent Systems Conference. CISC 2020. Lecture Notes in Electrical Engineering, vol 705. Springer, Singapore. https://doi.org/10.1007/978-981-15-8450-3_63

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