Skip to main content
SpringerLink
Log in
Book cover

Variable Structure and Lyapunov Control pp 313–333Cite as

Combined adaptive and Variable Structure Control

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 193))

Abstract

A combination of adaptive algorithms and variable structure control for the regulation of a certain class of linear time-invariant plants, has been presented. New algorithms have been developed both for the case where the state vector is available for measurement, and for SISO plants using input/output measurements only. The adaptive algorithms are driven by the tracking and the prediction error. The design is based on a new form of the Lyapunov function and exponential convergence of the tracking and estimation errors in the presence of persistent excitation has been established. The results improve the performance of existing adaptive schemes for this class of system.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Andrievsky, B.R., Stotsky, A.A., Fradkov, A.L. 1988, Speed gradient scheme in control and adaptation. Avtomatika i Telemechanika 12, 3–39 (in Russian)

    Google Scholar 

  • Bukov, V.N. 1987, Adaptive flight control systems, Nauka, Moscow, pp 232 (in Russian)

    Google Scholar 

  • Erzberger, H. 1968, Analysis and design of model reference following systems by state space tecniques. Proc. JACC, 572–580

    Google Scholar 

  • Fradkov, A.L. 1979, Velocity gradient scheme and its application in adaptive control. Avtomatika i Telemechanika 9, 90–101 (in Russian)

    Google Scholar 

  • Fradkov, A.L. 1986, Integral-derivative speed gradient algorithms. Doklady Acad. Sci. USSR 268, 798–801 (in Russian)

    Google Scholar 

  • Hsu, L. 1988, Variable structure model reference adaptive control using only input and output measurements. Proc IEEE Conference on Decision and Control, Austin, USA, 2396–2401

    Google Scholar 

  • Hsu, L. 1990, Variable structure model reference adaptive control (VSS-MRAC) using only input and output measurements: general case. IEEE Transactions on Automatic Control 35, 1238–1243

    Google Scholar 

  • Ioannou, P., Kokotovic, P. 1983, Adaptive systems with reduc models, Lecture Notes Contr. Inform. Sci. 47, Springer, New York, pp 168

    Google Scholar 

  • Landau, I.D. 1979, Adaptive control systems. The model reference approach, Dekker, New York, pp 406

    Google Scholar 

  • Lozano, R., Collado, J., Mondie, S. 1990, Model reference robust adaptive control without apriory knowledge of the high frequency gain. IEEE Transactions on Automatic Control 35, 71–78

    Google Scholar 

  • Marino, R. 1990, Adaptive observers for single output nonlinear systems IEEE Transactions on Automatic Control 35, 1054–1058

    Google Scholar 

  • Middleton, R.H., Goodwin, G.C. 1988, Adaptive computed torque control for rigid link manipulators. Systems and Control Letters 2, 9–16

    Google Scholar 

  • Miroshnik, I.V., Nikiforov, V.O. 1991, Convergence rate improvement in gradient procedure. Izv. Vuzov Priborostroenie 8, 76–82 (in Russian)

    Google Scholar 

  • Narendra, K.S., Valavani, L. 1978, Stable adaptive controller design-direct control. IEEE Transactions on Automatic Control 23, 570–583

    Google Scholar 

  • Narendra, K.S., Annasvamy, A.M. 1989, Stable adaptive systems, Prentice Hall, Englewood Cliffs, NJ, pp 494

    Google Scholar 

  • Panteley, E.V., Stotsky, A.A. 1992, Trajectory tracking for constrained robot motion: Composite adaptive control design. Proc. 36th ANIPLA, Genova,Italy, 563–571

    Google Scholar 

  • Slotine, J.J.E., Coetsee, J.A. 1986, Adaptive sliding controller synthesis for non-linear systems. International Journal of Control 43, 1631–1651

    Google Scholar 

  • Slotine, J.J.E., Li, W. 1989, Composite adaptive control of robot manipulators. Automatica 25, 509–519

    Google Scholar 

  • Stotsky, A.A. 1991, Design of combined variable structure system and reference equation system algorithms. Proc. First IFAC Symp. on Design Methods of Control Systems Zurich, Switzerland, 465–469

    Google Scholar 

  • Stotsky, A.A. 1993, Lyapunov design for convergence rate improvement in adaptive control. International Journal of Control 57, 501–504

    Google Scholar 

  • Utkin, V.I. 1981, Sliding modes in optimization and control, Nauka, Moscow, pp 368 (in Russian)

    Google Scholar 

  • Yakubovich, V.A. 1962, Solution of some matrix inequalities in systems theory, Dokl. Akad. Nauk USSR 143, 1304–1307 (in Russian)

    Google Scholar 

Download references

Authors
  1. Alexander A. Stotsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alan S. I. Zinober PhD

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag London Limited

About this chapter

Cite this chapter

Stotsky, A.A. (1994). Combined adaptive and Variable Structure Control. In: Zinober, A.S.I. (eds) Variable Structure and Lyapunov Control. Lecture Notes in Control and Information Sciences, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033690

Download citation

  • DOI: https://doi.org/10.1007/BFb0033690

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19869-7

  • Online ISBN: 978-3-540-39325-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation