Skip to main content
SpringerLink
Log in

Adaptive Control with Guaranteed Contraction Rate for Systems with Actuator Saturation

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

Abstract

The problem of adaptive control of linear discrete-time systems with actuator saturation and unknown parameters is investigated. A novel optimal control method is presented first for linear systems with known parameters and constant actuator saturation by introducing a Lyapunov function and a performance cost function that are both dependent on a contraction rate parameter. Based on the obtained guaranteed contraction-rate control method, an adaptive control algorithm is derived for systems containing unknown system parameters and time-varying actuator saturation. To show that the closed-loop system is stable and that the adaptive control algorithm is convergent, the Lyapunov function is supplemented by an additional part defined by the trace of a quadratic function of the controller gain. The effectiveness and potential of the presented method is demonstrated by a numerical example.

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

Similar content being viewed by others

References

  1. H. Gao, X. Yang, P. Shi, Multi-objective robust H∞ control of spacecraft rendezvous. IEEE Trans. Control Syst. Technol. 17(4), 794–802 (2009)

    Article  MathSciNet  Google Scholar 

  2. C. Gokcek, P.T. Kabamba, S.M. Meerkov, An LQR/LQG theory for systems with saturating actuators. IEEE Trans. Autom. Control 46(10), 1529–1542 (2001)

    Article  MathSciNet  Google Scholar 

  3. G. Guo, W. Yue, Hierarchical platoon control with heterogeneous information feedback. IET Control Theory Appl. 5(15), 1766–1781 (2011)

    Article  MathSciNet  Google Scholar 

  4. G. Guo, W. Yue, Guaranteed cost adaptive control of nonlinear platoons with actuator delay. ASME J. Dyn. Syst. Measur. Control. Accept subject to revision (2011)

  5. T. Hayakawa, W.M. Haddad, A. Leonessa, A Lyapunov-based adaptive control framework for discrete-time nonlinear systems with exogenous disturbances. Int. J. Control 77, 250–263 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. Hong, B. Yao, A globally stable high-performance adaptive robust control algorithm with input saturation for precision motion control of linear motor drive systems. IEEE/ASME Trans. Mechatron. 12(2), 198–207 (2007)

    Article  Google Scholar 

  7. T. Hu, Z. Lin, Control Systems with Actuator Saturation: Analysis and Design. Birkhäuser, Boston (2001)

    Book  MATH  Google Scholar 

  8. T. Hu, A.R. Teel, L. Zaccarian, Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions. IEEE Trans. Autom. Control 51(11), 1770–1786 (2006)

    Article  MathSciNet  Google Scholar 

  9. M. Johansson, A. Rantzer, Computation of piecewise quadratic Lyapunov function for hybrid systems. IEEE Trans. Autom. Control 43(4), 555–559 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. V. Kapila, A.G. Sparks, H. Pan, Control of systems with actuator saturation nonlinearities: an LMI approach. Int. J. Control 74, 586–599 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Z. Lin, A. Saberi, Semi-global exponential stabilization of linear systems subject to input saturation via linear feedbacks. Syst. Control Lett. 21(3), 225–239 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. E.F. Mulder, M.V. Kothare, Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions, in Proc. American Control Conferences, Chicago (IL), June 2000 (2000), pp. 3239–3243

    Google Scholar 

  13. S. Shiekholeslam, Control of a class of interconnected nonlinear dynamical systems: the platoon problem. PhD dissertation, University of California at Berkeley, 1991

  14. W. Sun, H. Gao, O. Kaynak, Finite frequency H∞ control for vehicle active suspension systems. IEEE Trans. Control Syst. Technol. 19(2), 416–422 (2011)

    Article  Google Scholar 

  15. R. Venugopal, V.G. Rao, D.S. Bernstein, Lyapunov-based backward-horizon adaptive stabilization. Int. J. Adapt. Control Signal Process. 17, 67–84 (2003)

    Article  MATH  Google Scholar 

  16. Z. Wang, D. Ho, H. Dong, H. Gao, Robust H∞ finite-horizon control for a class of stochastic nonlinear time-varying systems subject to sensor and actuator saturations. IEEE Trans. Autom. Control 55(7), 1716–1722 (2010)

    Article  MathSciNet  Google Scholar 

  17. Y. Xiao, Y.Y. Cao, Z. Lin, Robust filtering for discrete-time systems with saturation and its application to transmultiplexers. IEEE Trans. Signal Process. 52(5), 1266–1277 (2004)

    Article  MathSciNet  Google Scholar 

  18. Y. Zhao, W. Sun, H. Gao, Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay. J. Sound Vib. 329(21), 4335–4353 (2010)

    Article  Google Scholar 

  19. Z. Zuo, Y. Wang, An improved set invariance analysis and gain-scheduled control of LPV systems subject to actuator saturation. Circuits Syst. Signal Process. 26(5), 635–649 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Z. Zuo, Y. Wang, On enlarging the domain of attraction for linear systems subject to actuator saturation. Int. J. Gen. Syst. 37(2), 239–248 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Z. Zuo, D. Ho, Y. Wang, Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation. Automatica 46(3), 569–576 (2010)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China under grant number 60974013, Fok Ying Tong Education Foundation under grant 111066 and partially supported by a Grand from the Research Grant Council of Hong Kong under the project 417207.

Author information

Authors and Affiliations

  1. School of Control Science and Engineering, Dalian University of Technology, Dalian, 116023, China

    Ge Guo & Wei Yue

Authors
  1. Ge Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ge Guo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo, G., Yue, W. Adaptive Control with Guaranteed Contraction Rate for Systems with Actuator Saturation. Circuits Syst Signal Process 31, 1559–1576 (2012). https://doi.org/10.1007/s00034-011-9386-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-011-9386-6

Keywords

Search

Navigation