Skip to main content
SpringerLink
Log in

Adaptive Control for Systems with Output Constraints Using an Online Optimization Method

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

In this paper, a new controller framework incorporating an L1 adaptive control and an online optimization scheme is presented. This framework provides a method for maintaining output constraints in the presence of non-linear time-varying matched uncertainties by predicting future output trajectories within a finite time horizon. The stability conditions of the system are derived, and the prediction error is characterized. The online optimization is formulated into a linear program problem for which many efficient algorithms exist. Simulation results demonstrate the effectiveness of the controller framework.

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

Similar content being viewed by others

References

  1. Horn, J.F., Calise, A.J., Prasad, J.: Flight envelope cueing on a tilt-rotor aircraft using neural network limit prediction. J. Am. Helicopter Soc. 46, 23–31 (2001)

  2. Tomlin, C., Lygeros, J., Sastry, S.: Aerodynamic envelope protection using hybrid control. In: Proceedings of the American Control Conference, 1998. vol. 3, pp. 1793–1796 (1998)

  3. Horn, J., Calise, A.J., Prasad, J.: Flight envelope limit detection and avoidance for rotorcraft. J. Am. Helicopter Soc. 47, 253–262 (2002)

    Article  Google Scholar 

  4. Qin, S., Badgwell, T.: A survey of industrial model predictive control technology. Control Eng. Pract. 11, 733–764 (2003)

    Article  Google Scholar 

  5. Morari, M., Lee, J.H.: Model predictive control: past, present and future. Comput. Chem. Eng. 23, 667–682 (1999)

    Article  Google Scholar 

  6. Zafiriou, E.: Robust model predictive control of processes with hard constraints. Comput. Chem. Eng. 14, 359–371 (1990)

    Article  Google Scholar 

  7. Rawlings, J., Muske, K.: The stability of constrained receding horizon control. IEEE Trans. Autom. Control 38, 1512–1516 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mayne, D.Q., Rawlings, J.B., Rao, C.V., Scokaert, P.O.: Constrained model predictive control: stability and optimality. Automatica 36, 789–814 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Zafiriou, E., Chiou, H.: Output constraint softening for siso model predictive control. In: Proceedings of American Control Conference, pp. 372–376 (1993)

  10. de Oliveira, N., Biegler, L.: Constraint handing and stability properties of model-predictive control. AIChE J 40, 1138–1155 (2004)

    Article  Google Scholar 

  11. Zheng, A., Morari, M.: Stability of model predictive control with mixed constraints. IEEE Trans. Autom. Control 40, 1818–1823 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. de Oliveira Kothare, S.L., Morari, M.: Contractive model predictive control for constrained nonlinear systems. IEEE Trans. Autom. Control 45, 1053–1071 (2000)

    Article  MATH  Google Scholar 

  13. Hovd, M., Braatz, R.: Handling state and output constraints in mpc using time-dependent weights. In: Proceedings of the 2001 American Control Conference, vol. 3, pp. 2418–2423 (2001)

  14. Zheng, Z.Q., Morari, M.: Robust stability of constrained model predictive control. In: Proceedings of American Control Conference, pp. 379–383 (1993)

  15. Kothare, M.V., Balakrishnan, V., Morari, M.: Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10), 1361–1379 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  16. Cuzzola, F.A., Geromel, J.C., Morari, M.: An improved approach for constrained robust model predictive control. Automatica 38(7), 1183–1189 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Chisci, L., Rossiter, J., Zappa, G.: Systems with persistent disturbances: predictive control with restricted constraints. Automatica 37, 1019–1028 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Mayne, D., Raković, S., Findeisen, R., Allgöwer, F.: Robust output feedback model predictive control of constrained linear systems. Automatica 42, 1217–1222 (2006)

    Article  MATH  Google Scholar 

  19. Mayne, D., Raković, S., Findeisen, R., Allgöwer, F.: Robust output feedback model predictive control of constrained linear systems: time varying case. Automatica 45, 2082–2087 (2009)

    Article  MATH  Google Scholar 

  20. Wan, Z., Kothare, M.V.: An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica 39, 837–846 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Wang, Y., Boyd, S.: Fast model predictive control using online optimization. IEEE Trans. Control Syst. Technol. 18, 267–278 (2010)

    Article  Google Scholar 

  22. Hovakimyan, N., Cao, C.: L1 Adaptive Control Theory: Guaranteed Robustness with Fast Adaptation. Siam, Philadelphia (2010)

    Book  Google Scholar 

  23. Cao, C., Hovakimyan, N.: Guaranteed transient performance with l1 adaptive controller for systems with unknown time-varying parameters and bounded disturbances: Part i. In: Proceedings of American Control Conference, pp. 3925–3930 (2007)

  24. Cao, C., Hovakimyan, N.: L1 adaptive controller for a class of systems with unknown nonlinearities: Part i. In: Proceedings of American Control Conference, pp. 4093–4098 (2008)

  25. Khalil, H.K., Grizzle, J.W.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2002)

    MATH  Google Scholar 

Download references

Acknowledgments

The authors thank the referees for careful reading of the manuscript and insightful comments, which helped to improved the quality of the paper. We also acknowledge the support by NASA contract and NSF Award IIS 1208499.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Connecticut, Storrs, CT, 06269, USA

    Jiaxing Che, Michael Santone & Chengyu Cao

Authors
  1. Jiaxing Che
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Santone
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chengyu Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chengyu Cao.

Additional information

Communicated by Josef Shinar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Che, J., Santone, M. & Cao, C. Adaptive Control for Systems with Output Constraints Using an Online Optimization Method. J Optim Theory Appl 165, 480–506 (2015). https://doi.org/10.1007/s10957-014-0615-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-014-0615-6

Keywords

Mathematics Subject Classification

Search

Navigation