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Mutual reference adaptive control of nonlinear uncertain systems

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Mechanics and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 170))

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Abstract

The popular model reference adaptive control (MRAC) technique is extended to the case of two nonlinear dynamical systems mutually tracking and/or avoiding each other in a specified sense, subject to bounded uncertainty of their parameters (MURAC). The error equation approach classical in MRAC is replaced by a different approach which may be called the product-state-space method. Signal adaptive feedback controllers and adaptive laws are proposed together with sufficient conditions for the required tracking and avoidance. Application to a mechanical system illustrates the results.

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References

  1. Landau, I.D., Adaptive Control, M. Dekker, New York, 1979.

    Google Scholar 

  2. Balestrino, A., De Maria, G. and Sciavicco, L., An adaptive model following control for robotic manipulators, Trans. ASME, J. Dyn. Syst. Meas. Control 105 (1985), 3.

    Google Scholar 

  3. Dubovsky, S. and DesForges, D.I., The application of model referenced adaptive control to robotic manipulators, Trans. ASME., J. Dyn. Syst. Meas. Control 101 (1979), 3.

    Google Scholar 

  4. Singh, S.N., Adaptive model following of nonlinear robotic systems, IEEE Trans. Autom. Control AC-30 (1985), 1.

    Google Scholar 

  5. Skowronski, J.M., Nonlinear model reference adaptive control, J. Australian Math Soc., Series B, Applied Math. 28 (1986), 147–157.

    Google Scholar 

  6. Skowronski, J.M., Liapunov type playability for adaptive physical systems, Proc. Nat. System Conf., Combaitore PSG-College of Technology, India Section Q11 (1977), 1–5.

    Google Scholar 

  7. Skowronski, J.M., Algorithms for adaptive control of two arm flexible manipulator under uncertainty, IEEE Trans. Aerospace & Elec. Systems AES 24 (1988), 5.

    Google Scholar 

  8. Skowronski, J.M., Control Theory of Robotic Systems, World Scientific Publ., New Jersey — Singapore, 1990.

    Google Scholar 

  9. Filippov, A.F., Existence of solutions of generalized differential equations, Math. Notes 10 (1971), 608–611.

    Google Scholar 

  10. Yoshizawa, T., Stability Theory by Liapunov Second Method, Publ. Math. Soc., Japan, Tokyo, 1966.

    Google Scholar 

  11. Leitmann, G. and Skowronski, J.M., Avoidance Control, J. Opt. Th. Applic. 23 (1977), #4, 581–591.

    Google Scholar 

  12. Skowronski, J.M., Control Dynamics of Robot Manipulators, Academic Press, 1986.

    Google Scholar 

  13. Skowronski, J.M., Control of Nonlinear Mechanical Systems, Plenum, New York, 1991.

    Google Scholar 

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Janislaw M. Skowronski Henryk Flashner Ramesh S. Guttalu

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© 1992 Springer-Verlag

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Skowronski, J.M. (1992). Mutual reference adaptive control of nonlinear uncertain systems. In: Skowronski, J.M., Flashner, H., Guttalu, R.S. (eds) Mechanics and Control. Lecture Notes in Control and Information Sciences, vol 170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004314

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  • DOI: https://doi.org/10.1007/BFb0004314

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54954-3

  • Online ISBN: 978-3-540-46606-2

  • eBook Packages: Springer Book Archive

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