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Nonlinear model reference adaptive control

Published online by Cambridge University Press:  17 February 2009

J. M. Skowronski
J. M. Skowronski
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia, Qld, 4067, Australia.
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Abstract

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The known linear model reference adaptive control (MRAC) technique is extended to cover nonlinear and nonlinearizable systems (several equilibria, etc) and used to stabilize the system about a model. The method proposed applies the same Liapunov Design Technique but avoids the classical error equation. Instead it operates in the product of the state spaces of plant and model, aiming at convergence to a diagonal set. Control program, Liapunov functions and adaptive law are specified. The case is illustrated on a two-degrees of freedom robotic manipulator.

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 2 , October 1986 , pp. 147 - 157
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Balestrino, A., Maria, G. De and Sciavicco, L., “An adaptive model following control for robotic manipulators,” Trans. A SME Ser. G. J. Dynamic Systems Measurement Control 105 (1985), 143–151.Google Scholar
[2]Choe, H. H. and Nikiforuk, P. N., “Inherently stable feedback control of a class of unknown plants,” Automatica 7 (1971), 607–625.Google Scholar
[3]Dubovsky, S. and Forges, D. I. Des, “The application of model referenced adaptive control to robotic manipulators,” Trans. ASME Ser. G. J. Dynamic Systems Measurement Control 101 (1979), 193–200.Google Scholar
[4]Erzberger, H., “Analysis and design of model following control,” Proc. 1968 JACC, Ann Arbor, Mich., 572–581.Google Scholar
[5]Gershwin, S. B. and Jacobson, D. H., “A controllability theory for nonlinear systems,” IEEE Trans. Automat. Control 16 (1971), 37–50.Google Scholar
[6]Landau, I. D., Adaptive control: the model reference approach (M. Dekker, N. Y., 1979).Google Scholar
[7]Leitmann, G. and Skowronski, J., “Avoidance Control,” J. Optim. Theory Appl. 23 (1977), 581–591.CrossRefGoogle Scholar
[8]Leitmann, G. and Skowronski, J., “Note on avoidance control,” Optimal Control Appl. Methods 4 (1983), 335–342.CrossRefGoogle Scholar
[9]Narendra, K. S. and Tripathi, S., “Identification and optimization in aircraft dynamics,” J. Aircraft 10 (1973), 193–199.CrossRefGoogle Scholar
[10]Skowronski, J. M., “Liapunov type playability for adaptive physical systems,” Proc. Nat. Systems Conf. 1977, PSG Coll. of Techn. India, Q11, 1–5.Google Scholar
[11]Skowronski, J. M., “Parameter and state identification in nonlinearizable uncertain systems,” Internat. J. Non-linear Mech. 19 (1984), 345–353.CrossRefGoogle Scholar
[12]Skowronski, J. M., “Adaptive identification of models stabilizing under uncertainty,” Lecture Notes in Biomathematics 40 (1981), 64–78.Google Scholar
[13]Skowronski, J. M., “Sufficient criterion for synthesable stability of general physical lumped systems,” Bull. Acad. Polon. Sci. Sér. Sci. Tech. 14 (1966), 425–428.Google Scholar