Abstract
For a class of single-input single-output nonlinear systems with unknown constant parameters, we present a direct model-reference adaptive control scheme, which requires only output, rather than full-state, measurement. The nonlinearities are not required to satisfy any growth conditions. The assumptions on the linear part of the nonlinear system are the same as in the standard adaptive control problem for linear systems, which now appears as a special case of the nonlinear problem solved in this paper.
The work of the first two authors was supported in part by the National Science Foundation under Grant ECS-87-15811 and in part by the Air Force Office of Scientific Research under Grant AFOSR 90-0011. The work of the third author was supported by the National Science Foundation under Grants ECS-88-05611 and ECS-90-12551.
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References
G. Campion and G. Bastin, “Indirect adaptive state feedback control of linearly parametrized nonlinear systems,” Int. J. Adapt. Control Sig. Proc., vol. 4, pp. 345–358, Sept. 1990.
I. Kanellakopoulos, P. V. Kokotović, and R. Marino, “Robustness of adaptive nonlinear control under an extended matching condition,” Prepr. IFAC Symp. Nonlinear Control Syst. Design, pp. 192–197, Capri, Italy, June 1989.
I. Kanellakopoulos, P. V. Kokotović, and R. Marino, “An extended direct scheme for robust adaptive nonlinear control,” Automatica, to appear, March 1991.
R. Marino, I. Kanellakopoulos, and P. V. Kokotović, “Adaptive tracking for feedback linearizable SISO systems,” Proc. 28th IEEE Conf. Dec. Control, pp. 1002–1007, Tampa, FL, Dec. 1989.
J.-J. E. Slotine and J. A. Coetsee, “Adaptive sliding controller synthesis for nonlinear systems,” Int. J. Control, vol. 43, pp. 1631–1651, June 1986.
D. G. Taylor, P. V. Kokotović, R. Marino, and I. Kanellakopoulos, “Adaptive regulation of nonlinear systems with unmodeled dynamics,” IEEE Trans. Aut. Control, vol. 34, pp. 405–412, April 1989.
K. Nam and A. Arapostathis, “A model-reference adaptive control scheme for pure-feedback nonlinear systems,” IEEE Trans. Aut. Control, vol. 33, pp. 803–811, Sept. 1988.
J.-B. Pomet and L. Praly, Adaptive nonlinear control: an estimation-based algorithm, in New Trends in Nonlinear Control Theory, J. Descusse, M. Fliess, A. Isidori and D. Leborgne Eds., Springer-Verlag, Berlin, 1989.
J.-B. Pomet and L. Praly, “Adaptive nonlinear regulation: equation error from the Lyapunov equation,” Proc. 28th IEEE Conf. Dec. Control, pp. 1008–1013, Tampa, FL, Dec. 1989.
S. S. Sastry and A. Isidori, “Adaptive control of linearizable systems,” IEEE Trans. Aut. Control, vol. 34, pp. 1123–1131, Nov. 1989.
A. Teel, R. Kadiyala, P. V. Kokotović, and S. S. Sastry, “Indirect techniques for adaptive input output linearization of nonlinear systems,” Int. J. Control, vol. 53, pp. 193–222, Jan. 1991.
I. Kanellakopoulos, P. V. Kokotović, and R. H. Middleton, “Observer-based adaptive control of nonlinear systems under matching conditions,” Proc. 1990 Amer. Control Conf., pp. 549–555, San Diego, CA, May 1990.
I. Kanellakopoulos, P. V. Kokotović, and R. H. Middleton, “Indirect adaptive output-feedback control of a class of nonlinear systems,” Proc. 29th IEEE Conf. Dec. Control, pp. 2714–2719, Honolulu, HI, Dec. 1990.
G. Bastin and M. R. Gevers, “Stable adaptive observers for nonlinear time-varying systems,” IEEE Trans. Aut. Control, vol. 33, pp. 650–658, July 1988.
R. Marino, “Adaptive observers for single output nonlinear systems,” IEEE Trans. Aut. Control, vol. 35, pp. 1054–1058, Sept. 1990.
R. Marino and P. Tomei, “Global adaptive observers for nonlinear systems via filtered transformations,” Submitted to IEEE Trans. Aut. Control, 1990.
A. Feuer and A. S. Morse, “Adaptive control of single-input single-output linear systems,” IEEE Trans. Aut. Control, vol. AC-23, pp. 557–569, Aug. 1978.
K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1989.
S. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1989.
P. V. Kokotović, I. Kanellakopoulos, and A. S. Morse, “Adaptive feedback linearization of nonlinear systems,” this volume, pp. 309–344.
A. Isidori, Nonlinear Control Systems, 2nd ed., Springer-Verlag, Berlin, 1989.
A. J. Krener and A. Isidori, “Linearization by output injection and nonlinear observers,” Syst. Control Lett., vol. 3, pp. 47–52, June 1983.
W. Respondek, Global aspects of linearization, equivalence to polynomial forms and decomposition of nonlinear control systems, in Algebraic and Geometric Methods in Nonlinear Control Theory, M. Fliess and M. Hazewinkel, eds., pp. 257–284, D. Reidel Publishing Co., Dordrecht, 1986.
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Kanellakopoulos, I., Kokotović, P.V., Morse, A.S. (1991). Adaptive output-feedback control of systems with output nonlinearities. In: Kokotović, P.V. (eds) Foundations of Adaptive Control. Lecture Notes in Control and Information Sciences, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0044783
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DOI: https://doi.org/10.1007/BFb0044783
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