Abstract
In this paper, we present an adaptive observer for nonlinear systems that include unknown constant parameters and are not necessarily observable. Sufficient conditions are given for a nonlinear system to be transformed by state-space change of coordinates into an adaptive observer canonical form. Once a nonlinear system is transformed into the proposed adaptive observer canonical form, an adaptive observer can be designed under the assumption that a certain system is strictly positive real. An illustrative example is included to show the effectiveness of the proposed method.
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References
Choi, J. S. and Baek, Y. S., 2002, “A Single DOF Magnetic Levitation System Using Time Delay Control and Reduced-Order Observer,”KSME Internationa Journal, 16 (12), pp. 1643–1651.
Choi, J. J. and Kim, J. S., 2003, “Robust Control for Rotational Inverted Pendulums Using Output Feedback Sliding Mode Controller and Disturbance Observer,”KSME International Journal, 17 (10), pp. 1466–1474.
Isidori, A., 1989,Nonlinear Control Systems, Springer-Verlag, Berlin.
Jo, N. H. and Seo, J. H., 2002, “Observer Design for Nonlinear Systems That are Not Uniformly Observable,”Int. J. Control, 75 (5), pp. 369–380.
Jo, N. H. and Seo, J. H., 2000, “Input Output Linearization Approach to State Observer Design for Nonlinear Systems,”IEEE Trans. Automat. Contr, 45, pp. 2388–2393.
Krener, A. J. and Isidori, A., 1983, “Linearization by Output Injection and Nonlinear Observers,”Systems & Control Letters, 3, pp. 47–52.
Krener, A. J. and Respondek, W., 1985, “Nonlinear Observers with Linearizable Error Dynamics,”SIAM J. Control Optim, 23 (2), pp. 197–216.
LaSalle, J. P., 1968, “Stability Theory for Ordinary Differential Equations,”Journal of Differential Equations, 4, pp. 57–65.
Marino, R., 1990, “Adaptive Observers for Single Output Nonlinear Systems,”IEEE Trans. Automat. Contr, 35, pp. 1054–1058.
Meyer, K. R., 1965, “On the Existence of Lyapunov Functions for the Problem of Lur’e,”SIAM J. Control Optim, 3, pp. 373–383.
Nijmeijer, H. and van der Schaft, A. J., 1990,Nonlinear Dynamical Control Systems. Springer-Verlag.
Rudolph, J. and Zeitz, M., 1994, “A Block Triangular Nonlinear Observer Normal Form,”Systems & Control Letters, 23, pp. 1–8.
Shim, H., Son, Y. I., Back, J. and Jo, N. H., 2003, “An Adaptive Algorithm Applied to a Design of Robust Observer,”KSME International Journal, 17 (10), pp. 1443–1449.
Son, Y. I., Shim, H. and Seo, J. H., 2002, “Set-Point Control of Elastic Joint Robots Using Only Position Measurements,”KSME International Journal, 16 (8), pp. 1079–1088.
Xia, X. H. and Gao, W. B., 1989, “Nolinear Observer Design by Observer Error Linearization,”SIAM J. Control Optim, 27, pp. 199–216.
Yoshizawa, T., 1966,Stability Theory by Lyapunov’s Second Method, The Mathematical Society of Japan.
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Jo, NH., Son, YI. Adaptive observer design for nonlinear systems using generalized nonlinear observer canonical form. KSME International Journal 18, 1150–1158 (2004). https://doi.org/10.1007/BF02983289
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DOI: https://doi.org/10.1007/BF02983289