Abstract
Consideration was given to the control by measurements of the output of nonlinear systems with unknown functional and parametric uncertainties. On the basis of the A.L. Fradkov theorem on passification of linear systems, an approach to the design of the control law that stabilizes the system output was proposed. The theoretical results were illustrated by an example and the results of computer modeling.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Fradkov, A.L., Design of Adaptive Stabilization System for Linear Dynamic Plant, Avtom. Telemekh., 1974, no. 12, pp. 96–103.
Fradkov, A.L., Quadratic Lyapunov Functions in the Problem of Adaptive Stabilization of the Linear Dynamic Plant, Sib. Mat. Zh., 1976, no. 2, pp. 436–446.
Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.L., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimisistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg: Nauka, 2000.
Kokotovic, P. and Murat, A., Constructive Nonlinear Control: A Historical Perspective, Automatica, 2001, vol. 37, no. 5, pp. 637–662.
Fradkov, A. and Hill, D., Exponential Feedback Passivity and Stabilizability of Nonlinear Systems, Automatica, 1998, vol. 34, no. 6, pp. 697–703.
Polushin, I.G., Fradkov, A.L., and Hill, D.D., Passivity and Passification of the Nonlinear Systems. Review, Avtom. Telemekh., 2000, no. 3, pp. 3–37.
Fradkov, A.L., Adaptivnoe upravlenie v slozhnykh sistemakh (Adaptive Control in Complex Systems), Moscow: Nauka, 1990.
Bobtsov, A.A. and Romasheva, D.A., Adaptive Control Law for Uncertain System with Static Nonlinearity, 11th Mediterranean Conf. Control Automat. MED’03, Rhodes, Greece, 2003.
Bobtsov, A.A., Robust Output Control of the Linear System with Uncertain Coefficients, Avtom. Telemekh., 2002, no. 11, pp. 108–117.
Arcak, M. and Kokotovic, P., Feasibility Conditions for Circle Criterion Design, Syst. Control Lett., 2001, vol. 42, no. 5, pp. 405–412.
Arcak, M., Larsen, M., and Kokotovic, P., Circle and Popov Criteria as Tools for Nonlinear Feedback Design, 15th Triennial World IFAC Congress, Barcelona, Spain, 2002.
Arcak, M., Larsen, M., and Kokotovic, P., Circle and Popov Criteria as Tools for Nonlinear Feedback Design, Automatica, 2003, vol. 39, no. 4, pp. 643–650.
Qian, S. and Lin, W., Output Feedback Control of a Class of Nonlinear Systems: a Nonseparation Principle Paradigm, IEEE Trans. Automat. Contr., 2002, vol. 47, no. 10, pp. 1710–1715.
Tsinias, J., A Theorem on Global Stabilization of Nonlinear Systems by Linear Feedback, Syst. Control Lett., 1991, vol. 17, pp. 357–362.
Fradkov, A.L. Adaptive Stabilization of the Minimum-phase Plants with Vector Input without Measuring the Output Derivatives, Dokl. Ross. Akad. Nauk, 1994, vol. 337, no. 5, pp. 592–594.
Andrievsky, B.R. and Fradkov, A.L., Adaptive Controllers with Implicit Reference Models Based on Feedback Kalman-Yakubovich Lemma, Proc. 3rd IEEE Conf. Control Appl., Glasgow, 1994, pp. 1171–1174.
Author information
Authors and Affiliations
Additional information
This work was supported by the grant for young researchers of the leading pedagogical teams of the institutes of higher education and the scientific institutions of the Russian Ministry of Education, project no. PD02-2.8-53.
Translated from Avtomatika i Telemekhanika, No. 1, 2005, pp. 118–129.
Original Russian Text Copyright © 2005 by Bobtsov, Nikolaev.
Rights and permissions
About this article
Cite this article
Bobtsov, A.A., Nikolaev, N.A. Fradkov theorem-based design of the control of nonlinear systems with functional and parametric uncertainties. Autom Remote Control 66, 108–118 (2005). https://doi.org/10.1007/s10513-005-0010-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10513-005-0010-8