Skip to main content
SpringerLink
Log in

Sliding Mode Preview Tracking Control of OSL Nonlinear Discrete-Time Systems

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper studied the sliding mode preview tracking control of one-sided Lipschitz nonlinear discrete-time systems. First, an augmented system including tracking error and preview information is constructed by introducing a difference operator. Then, a sliding surface is designed, and a sufficient condition of asymptotic stability is derived for the sliding mode dynamics. A convex optimization problem based on LMI is formulated to avoid solving nonlinear matrix inequalities and the classification discussion when solving the controller. Next, a sliding mode preview control law is designed such that the reachability condition of the controlled system can be satisfied, and the output of original system can track the reference signal well. Finally, two simulation examples are given to verify the effectiveness of the proposed control scheme.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data Availability Statement

The data sets generated and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. M. Abbaszadeh, H.J. Marquez, Nonlinear observer design for one-sided Lipschitz systems, in Proceedings of the 2010 American Control Conference (2010), pp. 5284–5289

  2. S. Ahmad, M. Rehan, On observer-based control of one-sided Lipschitz systems. J. Frankl. Inst. 353(4), 903–916 (2016)

    Article  MathSciNet  Google Scholar 

  3. X. Chu, M. Li, Observer-based model following sliding mode tracking control of discrete-time linear networked systems with two-channel event-triggered schemes and quantizations. Appl. Math. Comput. 355, 428–448 (2019)

    MathSciNet  MATH  Google Scholar 

  4. H. Fang, G. Zhu, V. Stojanovic, R. Nie, S. He, X. Luan, F. Liu, Adaptive optimization algorithm for nonlinear Markov jump systems with partial unknown dynamics. Int. J. Robust Nonlinear Control 31(6), 2126–2140 (2021)

    Article  MathSciNet  Google Scholar 

  5. S.S. Ge, C. Wang, Adaptive control of uncertain Chuas circuits. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(9), 1397–1402 (2000)

    Article  MathSciNet  Google Scholar 

  6. Y. Guo, S. Song, X. Li, Backstepping sliding mode control for formation flying spacecraft. IEEE Trans. Circuits Syst. Aircr. Eng. Aerosp. Technol. 90(1), 56–64 (2018)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. C. Huang, H. Huang, Observer-based robust preview tracking control for a class of non-linear systems. IET Control Theory Appl. 14(7), 991–998 (2020)

    Article  MathSciNet  Google Scholar 

  9. L. Li, F. Liao, J. Deng, \(H_\infty \) preview control of a class of uncertain discrete-time systems. Asian J. Control 19(4), 1542–1556 (2017)

    Article  MathSciNet  Google Scholar 

  10. L. Li, Y. Lu, L. Gu, Preview control for a class of linear discrete-time periodic systems. Int. J. Control (2019). https://doi.org/10.1080/00207179.2019.1618497

    Article  Google Scholar 

  11. F. Liao, C. Jia, U. Malik, X. Yu, J. Deng, The preview control of a class of linear systems and its application in the fault-tolerant control theory. Int. J. Control Autom. Syst. 50(5), 1017–1027 (2019)

    MathSciNet  MATH  Google Scholar 

  12. F. Liao, L. Li, Robust preview control for uncertain discrete-time systems based on LMI. Optim. Control Appl. Methods 38(6), 1022–1031 (2017)

    Article  MathSciNet  Google Scholar 

  13. J. Liu, Y. Gao, X. Su, M. Wack, L. Wu, Disturbance-observer-based control for air management of PEM fuel cell systems via sliding mode technique. IEEE Trans. Control Syst. Technol. 27(3), 1129–1138 (2019)

    Article  Google Scholar 

  14. S. Liu, Z. Xiang, Exponential \(H_\infty \) output tracking control for switched neutral system with time-varying delay and nonlinear perturbations. Circuits Syst. Signal Process. 32(1), 103–121 (2013)

    Article  MathSciNet  Google Scholar 

  15. B. Nail, A. Kouzou, A. Hafaifa, Robust block roots assignment in linear discrete-time sliding mode control for a class of multivariable system: gas turbine power plant application. Trans. Inst. Meas. Control 41(5), 1216–1232 (2019)

    Article  Google Scholar 

  16. K.S. Narendra, K. Parthasarathy, Identification and control of dynamical systems using neural networks. IEEE Trans. Neural Netw. 1(1), 4–27 (1990)

    Article  Google Scholar 

  17. C.M. Nguyen, P.N. Pathirana, H. Trinh, Robust observer-based control designs for discrete nonlinear systems with disturbances. Eur. J. Control 44, 65–72 (2018)

    Article  MathSciNet  Google Scholar 

  18. S.A. Nugroho, V. Hoang, M. Radosz, S. Wang, A.F. Taha, New insights on one-sided Lipschitz and quadratically inner-bounded nonlinear dynamic systems, in Proceedings of the 2020 American Control Conference (2020), pp. 4558–4563

  19. D. Pri, N. Nedi, V. Stojanovi, A nature inspired optimal control of pneumatic-driven parallel robot platform. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 231(1), 59–71 (2017)

    Article  Google Scholar 

  20. M. Rehan, S. Ahmad, K.S. Hong, Novel results on observer-based control of one-sided Lipschitz systems under input saturation. Eur. J. Control 53, 29–42 (2020)

    Article  MathSciNet  Google Scholar 

  21. M. Rehan, K.S. Hong, S.S. Ge, Stabilization and tracking control for a class of nonlinear systems. Nonlinear Anal. Real World Appl. 12(3), 1786–1796 (2011)

    Article  MathSciNet  Google Scholar 

  22. W. Saad, A. Sellami, G. Garcia, Robust integral sliding mode-\(H_\infty \) control of one-sided Lipschitz nonlinear systems. IET Control Theory Appl. 12(17), 2357–2367 (2018)

    Article  MathSciNet  Google Scholar 

  23. W. Saad, A. Sellami, G. Garcia, \(H_\infty \)-sliding mode control of one-sided Lipschitz nonlinear systems subject to input nonlinearities and polytopic uncertainties. ISA Trans. 90, 19–29 (2019)

    Article  Google Scholar 

  24. T. Sato, T. Shiegami, T. Tsuchiya, Digital sliding mode servo systems with preview feedforward compensation. Electr. Eng. Jpn. 149(1), 33–43 (2004)

    Article  Google Scholar 

  25. J. Song, S. He, Robust finite-time \(H_\infty \) control for one-sided Lipschitz nonlinear systems via state feedback and output feedback. J. Frankl. Inst. 352(8), 3250–3266 (2015)

    Article  MathSciNet  Google Scholar 

  26. V. Stojanovic, N. Nedic, D. Prsic, L. Dubonjic, V. Djordjevic, Application of cuckoo search algorithm to constrained control problem of a parallel robot platform. Int. J. Adv. Manuf. Technol. 87(9–12), 2497–2507 (2016)

    Article  Google Scholar 

  27. G. Sun, L. Wu, Z. Kuang, Z. Ma, J. Liu, Practical tracking control of linear motor via fractional-order sliding mode. Automatica 94, 221–235 (2018)

    Article  MathSciNet  Google Scholar 

  28. H. Tao, P. Wang, Y. Chen, V. Stojanovic, H. Yang, An unsupervised fault diagnosis method for rolling bearing using STFT and generative neural networks. J. Frankl. Inst. 357(11), 7286–7307 (2020)

    Article  MathSciNet  Google Scholar 

  29. M. Tomizuka, D.E. Rosenthal, On the optimal digital state vector feedback controller with integral and preview actions. J. Dyn. Syst. Meas. Control Trans. ASME 101(2), 172–178 (1979)

    Article  Google Scholar 

  30. C. Turchetti, G. Biagetti, F. Gianfelici, P. Crippa, Nonlinear system identification: an effective framework based on the Karhunen–Loeve transform. IEEE Trans. Signal Process. 57(2), 536–550 (2009)

    Article  MathSciNet  Google Scholar 

  31. B. Wu, D. Wang, E.K. Poh, Decentralized sliding-mode control for attitude synchronization in spacecraft formation. Int. J. Robust Nonlinear Control 23(11), 1183–1197 (2013)

    Article  MathSciNet  Google Scholar 

  32. Y. Yan, S. Yu, Sliding mode tracking control of autonomous underwater vehicles with the effect of quantization. Ocean Eng. 151, 322–328 (2018)

    Article  Google Scholar 

  33. Y. Yan, S. Yu, C. Sun, Quantization-based event-triggered sliding mode tracking control of mechanical systems. Inf. Sci. 523, 296–306 (2020)

    Article  MathSciNet  Google Scholar 

  34. X. Yu, F. Liao, Preview tracking control for a class of discrete-time Lipschitz non-linear time-delay systems. IMA J. Math. Control Inf. 36(3), 849–867 (2019)

    Article  MathSciNet  Google Scholar 

  35. X. Yu, F. Liao, Output tracking control with preview action for a class of continuous-time Lipschitz nonlinear systems and its applications. Int. J. Control Autom. Syst. 26(21–22), 2081–2091 (2020)

    MathSciNet  Google Scholar 

  36. X. Yu, F. Liao, J. Deng, Tracking controller design with preview action for a class of Lipschitz nonlinear systems and its applications. Circuits Syst. Signal Process. 39(6), 2922–2947 (2020)

    Article  Google Scholar 

  37. X. Zhang, S. He, V. Stojanovic, X. Luan, F. Liu, Finite-time asynchronous dissipative filtering of conic-type nonlinear Markov jump systems. Sci. China Inf. Sci. (2021). https://doi.org/10.1007/s11432-020-2913-x

    Article  MathSciNet  Google Scholar 

  38. Y. Zhao, J. Tao, N. Shi, A note on observer design for one-sided Lipschitz nonlinear systems. Syst. Control Lett. 59(1), 66–71 (2010)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China under Grants 61673100, 61703083 and Fundamental Research Funds for Central Universities under Grant N150504011.

Author information

Authors and Affiliations

  1. College of Sciences, Northeastern University, Shenyang, 110819, China

    Qingdong Sun & Junchao Ren

Authors
  1. Qingdong Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junchao Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junchao Ren.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, Q., Ren, J. Sliding Mode Preview Tracking Control of OSL Nonlinear Discrete-Time Systems. Circuits Syst Signal Process 41, 4347–4369 (2022). https://doi.org/10.1007/s00034-022-01986-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-022-01986-9

Keywords

Search

Navigation