Abstract
The possibility for applying the control method designed in [1] for stabilization of nonlinear systems consisting of a linear minimal phase block and a nonlinear static feedback block is examined. Unlike in [1], the nonlinear characteristic of the static nonlinearity is not assumed to belong to a sector, but is the output function raised to some power.
Similar content being viewed by others
References
Bobtsov, A.A. and Nikolaev, N.A., Control Design via the Fradkov Theorem for Nonlinear Systems with Functional and Parametric Uncertainties, Avtom. Telemekh., 2005, no. 1, pp. 118–129.
Bobtsov, A.A., A Robust Control Algorithm for an Uncertain System without Measurement of the Derivatives of the Adjusted Variable, Avtom. Telemekh., 2003, no. 8, pp. 82–95.
Druzhinina, M.V., Nikiforov, V.O., and Fradkov, A.L., Output Adaptive Control Methods for Nonlinear Systems, Avtom. Telemekh., 1996, no. 2, pp. 3–33.
Nikiforov, V.O., Adaptivnoe i robastnoe upravlenie s kompensatsiei vozmushchenii (Adaptive Robust Control with Perturbation Compensation), St. Petersburg: Nauka, 2003.
Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.V., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemani (Nonlinear Adaptive Control for Complex Dynamic Systems), St. Petersburg: Nauka, 2000.
Byrnes, C.I. and Isidori, A., Asymptotic Stabilization of Minimum Phase Nonlinear Systems, IEEE Trans. Automat. Control, 1991, vol. 36, no. 10, pp. 1122–1137.
Isidori, A. and Byrnes, C.I., Output Regulation of Nonlinear Systems, IEEE Trans. Automat. Control, 1990, vol. 35, no. 2, pp. 131–140.
Isidori, A., A Remark on the Problem of Semiglobal Nonlinear Output Regulation, IEEE Trans. Automat. Control, 1997, vol. 42, no. 12, pp. 1734–1738.
Isidori, A., A Tool for Semiglobal Stabilization of Uncertain Non-Minimum-Phase Nonlinear Systems via Output Feedback, IEEE Trans. Automat. Control, 2000, vol. 45, no. 10, pp. 1817–1827.
Jiang Zhong-Ping, Mareels, I., Hill, D., and Jie Huang, Universal Output Feedback Controllers for Nonlinear Systems with Unknown Control Direction, Proc. Am. Control Conf., Denver, 2003.
Khalil, H.K. and Esfandiari, F., Semiglobal Stabilization of a Class of Nonlinear Systems using Output Feedback, IEEE Trans. Automat. Control, 1993, vol. 38, no. 9, pp. 1412–1415.
Kristic, M., Kanellakopoulos, I., and Kokotovic, P.V., Nonlinear and Adaptive Control Design, New York: Wiley, 1995.
Kristic, M. and Kokotovic, P.V., Adaptive Nonlinear Output-Feedback Schemes with Marino-Tomei Controller, IEEE Trans. Automat. Control, 1995, vol. 40, no. 6, pp. 1029–1041.
Lin, Z. and Saberi, A., Robust Semiglobal Stabilization of Minimum-Phase Input-Output Linearizable Systems via Partial State and Output Feedback, IEEE Trans. Automat. Control, 1995, vol. 40, no. 6, pp. 1029–1041.
Praly, L., Asymptotic Stabilization via Output Feedback for Lower Triangular Systems with Output-Dependent Incremental Rate, IEEE Trans. Automat. Control, 2003, vol. 48, no. 6, pp. 1103–1108.
Qian, C. and Lin, W., Output Feedback Control of a Class of Nonlinear Systems: A Nonseparation Principle Paradigm, IEEE Trans. Automat. Control, 2002, vol. 47, no. 10, pp. 1710–1715.
Qian, C., Schrader, C.B., and Lin, W., Global Regulation of a Class of Uncertain Nonlinear Systems using Output Feedback, Proc. Am. Control Conf., Denver, 2003.
Fradkov, A.L., An Adaptive Stabilization System for a Linear Dynamic System, Avtom. Telemekh., 1974, no. 12, pp. 96–103.
Polyshin, I.G., Fradkov, A.L., and Khill, D.D., Passivity and Passification of Nonlinear Systems: A Review, Avtom. Telemekh., 2000, no. 3, pp. 3–37.
Barabanov, N.E., Gelig, A.Kh., Leonov, G.A., et. al., A Frequency Theorem (The Yakubovich-Kalman Lemma) in Control Theory, Avtom. Telemekh., 1996, no. 10, pp. 3–40.
Author information
Authors and Affiliations
Additional information
Original Russian Text © I.V. Amoskin, A.A. Bobtsov, N.A. Nikolaev, K.A. Sergeev, 2006, published in Avtomatika i Telemekhanika, 2006, No. 4, pp. 105–115.
This work was supported by the Russian Foundation for Basic Research, project no. 05-08-33388-a.
Rights and permissions
About this article
Cite this article
Amoskin, I.V., Botsov, A.A., Nikolaev, N.A. et al. An adaptation algorithm for stabilization of nonlinear system in the absence of sector constraints. Autom Remote Control 67, 606–614 (2006). https://doi.org/10.1134/S0005117906040084
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0005117906040084