SpringerLink
Log in

Output feedback control of nonlinear cascaded systems with external disturbance and asymmetric constraints

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this article, an adaptive output feedback controller is considered for a class of nonlinear systems with integral input-to-state stable inverse dynamics, external disturbance and asymmetric output constraints. A tan-type barrier Lyapunov function (BLF) is introduced to solve asymmetric output constraints. Under the general framework, the designed scheme can be applied to systems with symmetric/asymmetric constraints or without constraint requirements. An extended state observer (ESO) is proposed to estimate external disturbance by defining the disturbance as the generalized system state. Moreover, a reduced-order ESO is designed to establish the error dynamic system. In combination with backstep** technique and linear matrix inequality, it is indicated that the adaptive output feedback controller not only guarantees the global asymptotic stability of the closed-loop system, but also does not violate asymmetric output constraints. Simulation results demonstrate 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

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

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

Similar content being viewed by others

Data Availability Statement

The datasets generated and/or analyzed during the current study are available from the corresponding author on a reasonable request.

References

  1. Sontag, E.D.: Smooth stabilization implies coprime factorization. IEEE Trans. Autom. Control 34(4), 435–443 (1989)

    Article  MathSciNet  Google Scholar 

  2. Sontag, E.D.: Comments on integral variants of ISS. Syst. Control 34(1), 93–100 (1998)

    Article  MathSciNet  Google Scholar 

  3. Angeli, D., Sontag, E.D., Wang, Y.: A characterization of integral input-to-state stability. IEEE Trans. Autom. Control 45(6), 1082–1097 (2000)

    Article  MathSciNet  Google Scholar 

  4. Yu, X., Wu, Y.Q., **e, X.J.: Reduced-order observer-based output feedback regulation for a class of nonlinear systems with iISS inverse dynamics. Int. J. Control 85(12), 1942–1951 (2012)

    Article  MathSciNet  Google Scholar 

  5. Jiang, Z.P., Mareels, I., Hill, D.J., Huang, J.: A unifying framework for global regulation via nonlinear output feedback: from ISS to iISS. IEEE Trans. Autom. Control 49(4), 549–562 (2004)

    Article  MathSciNet  Google Scholar 

  6. Wei, T., Li, X., Stojanovic, V.: Input-to-state stability of impulsive reaction-diffusion neural networks with infinite distributed delays. Nonlinear Dyn. 103(2), 1733–1755 (2021)

    Article  Google Scholar 

  7. Wu, Y.Q., Yu, J.B., Zhao, Y.: Further results on global asymptotic regulation control for a class of nonlinear systems with iISS inverse dynamics. IEEE Trans. Autom. Control 56(4), 941–946 (2011)

    Article  MathSciNet  Google Scholar 

  8. Fang, H., Zhu, G., Stojanovic, V., Nie, R., He, S., Luan, X., Liu, F.: 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 

  9. Cheng, P., Chen, M., Stojanovic, V., He, S.: Asynchronous fault detection filtering for piecewise homogenous Markov jump linear systems via a dual hidden Markov model. Mech. Syst. Signal Process. 151, 107353 (2021)

    Article  Google Scholar 

  10. Tao, H., Li, J., Chen, Y., Stojanovic, V., Yang, H.: Robust point-to-point iterative learning control with trial-varying initial conditions. IET Control Theory Appl. 14(19), 3344–3350 (2020)

    Article  MathSciNet  Google Scholar 

  11. Katsura, S., Matsumoto, Y., Ohnishi, K.: Modeling of force sensing and validation of disturbance observer for force control. IEEE Trans. Ind. Electron. 54(1), 530–538 (2007)

    Article  Google Scholar 

  12. Kim, B.K., Chung, W.K.: Advanced disturbance observer design for mechanical positioning systems. IEEE Trans. Ind. Electron. 50(6), 1207–1216 (2003)

    Article  Google Scholar 

  13. Zhong, Q.C., Kuperman, A., Stobart, R.K.: Design of UDE-based controllers from their two-degree-of-freedom nature. Int. J. Robust Nonlinear Control 21(17), 1994–2008 (2011)

    Article  MathSciNet  Google Scholar 

  14. Freidovich, L.B., Khalil, H.K.: Performance recovery of feedback-linearization-based designs. IEEE Trans. Autom. Control 53(10), 2324–2334 (2008)

    Article  MathSciNet  Google Scholar 

  15. Kim, K.S., Rew, K.H., Kim, S.: Disturbance observer for estimating higher order disturbances in time series expansion. IEEE Trans. Autom. Control 55(8), 1905–1911 (2010)

    Article  MathSciNet  Google Scholar 

  16. Hu, X.B., Chen, W.H.: Receding horizon control for aircraft arrival sequencing and scheduling. IEEE Trans. Intell. Transp. Syst. 6(2), 189–197 (2005)

    Article  Google Scholar 

  17. Sira-Ramírez, H., Linares-Flores, J., García-Rodríguez, C., Contreras-Ordaz, M.A.: On the control of the permanent magnet synchronous motor: an active disturbance rejection control approach. IEEE Trans. Control Syst. Technol. 22(5), 2056–2063 (2014)

    Article  Google Scholar 

  18. Han, J.: From PID to active disturbance rejection control. IEEE Trans. Ind. Electron. 56(3), 900–906 (2009)

    Article  Google Scholar 

  19. Huang, Y., Xue, W.: Active disturbance rejection control: methodology and theoretical analysis. ISA Trans. 53(4), 963–976 (2014)

    Article  MathSciNet  Google Scholar 

  20. Kim, E.: A fuzzy disturbance observer and its application to control. IEEE Trans. Fuzzy Syst. 10(1), 77–84 (2002)

    Article  Google Scholar 

  21. Sira-Ramírez, H., Oliver-Salazar, M.A.: On the robust control of buck-converter dc-motor combinations. IEEE Trans. Power Electron. 28(8), 3912–3922 (2013)

    Article  Google Scholar 

  22. Wu, K., Zhang, Z., Sun, C.: Disturbance-observer-based output feedback control of non-linear cascaded systems with external disturbance. IET Control Theory Appl. 12(6), 738–744 (2018)

    Article  MathSciNet  Google Scholar 

  23. Mokhtari, M.R., Braham, A.C., Cherki, B.: Extended state observer based control for coaxial-rotor UAV. ISA Trans. 61, 1–14 (2016)

    Article  Google Scholar 

  24. Guo, B.Z., Zhao, Z.: On the convergence of an extended state observer for nonlinear systems with uncertainty. Syst. Control. Lett. 60(6), 420–430 (2011)

    Article  MathSciNet  Google Scholar 

  25. Castillo, A., García, P., Sanz, R., Albertos, P.: Enhanced extended state observer-based control for systems with mismatched uncertainties and disturbances. Syst. Control. Lett. 73, 1–10 (2018)

    Google Scholar 

  26. Gao, F., Wu, Y., Huang, J., Liu, Y.: Output feedback stabilization within prescribed finite time of asymmetric time-varying constrained nonholonomic systems. Int. J. Robust Nonlinear Control 31(2), 427–446 (2021)

    Article  MathSciNet  Google Scholar 

  27. Tee, K.P., Ge, S.S., Tay, E.H.: Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4), 918–927 (2009)

    Article  MathSciNet  Google Scholar 

  28. Wang, C., Wu, Y.: Finite-time tracking control for strict-feedback nonlinear systems with full state constraints. Int. J. Control 92(6), 1426–1433 (2019)

    Article  MathSciNet  Google Scholar 

  29. Cao, Y., Wen, C., Song, Y.: A unified event-triggered control approach for uncertain pure-feedback systems with or without state constraints. IEEE Trans. Cybern. 51(3), 1262–1271 (2021)

    Article  Google Scholar 

  30. Fuentes-Aguilar, R.Q., Chairez, I.: Adaptive tracking control of state constraint systems based on differential neural networks: a barrier lyapunov function approach. IEEE Trans. Neural Netw. Learn. Syst. 31(12), 5390–5401 (2020)

    Article  MathSciNet  Google Scholar 

  31. Liu, Y.J., Tong, S.: Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica 64, 70–75 (2016)

    Article  MathSciNet  Google Scholar 

  32. Sun, W., Su, S.F., Dong, G., Bai, W.: Reduced adaptive fuzzy tracking control for high-order stochastic nonstrict feedback nonlinear system with full-state constraints. IEEE Trans. Syst. Man Cybern. Syst. 51(3), 1496–1506 (2021)

    Google Scholar 

  33. **, X., Xu, J.X.: Iterative learning control for output-constrained systems with both parametric and nonparametric uncertainties. Automatica 49(8), 2508–2516 (2013)

    Article  MathSciNet  Google Scholar 

  34. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM, Philadelphia (1994)

    Book  Google Scholar 

Download references

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant numbers [62173207] and [62073187], the Major Scientific and Technological Innovation Project in Shandong Province under Grant number [2019JZZY011111].

Author information

Authors and Affiliations

  1. School of Engineering, Qufu Normal University, Rizhao, 276826, China

    Jie Zhang, **g Yang, Zhongcai Zhang & Yuqiang Wu

Authors
  1. Jie Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. **g Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhongcai Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuqiang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuqiang Wu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.

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

Zhang, J., Yang, J., Zhang, Z. et al. Output feedback control of nonlinear cascaded systems with external disturbance and asymmetric constraints. Nonlinear Dyn 108, 3727–3743 (2022). https://doi.org/10.1007/s11071-022-07440-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-07440-4

Keywords

Search

Navigation