Abstract
In this paper we present the solution of a long-standing open problem related to adaptive control: a method and its analysis for the recursive estimation of time-varying parameters. The method of analysis is the use of an earlier result in Gerencsér (1988b) on the pathwise stability of random differential equations, which we present (in an improved form) in Section 1.
The paper has been written during a visit to the Department of Electrical Engineering, McGill University, Montreal, Quebec, while being on leave from the Computer and Automation Institute of the Hungarian Academy of Sciences, Budapest. The invitation and support of the organizers of the present conference is also gratefully acknowledged.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Caines, P.E., Lafortune, S., Adaptive Control with Recursive Identification for Stochastic Linear Systems. IEEE Trans on Aut. Cont., Vol. AC-29 (1984), 312–321.
Caines, P.E., Meyn, S.P., A new approach to stochastic adaptive control. Preprint of the Computer Vision and Robotics Laboratory, McGill Research Centre for Intelligent Machines 1986, McGill University Montreal, Quebec.
Djereveckii, D.P., Fradko, A.L., Applied Theory of Discrete Adaptive Control Systems. (In Russian), Nauka, Moscow, 1981.
Gerencsér, L., On a class of mixing processes. Preprint of the Dept. of Math., Chalmers Univ. of Techn. and The Univ. of Göteborg, 1986; 11. To appear in Stochatics, 1988a.
Gerencsér, L., On the exponential stability of the mixture of time-invariant systems. Manuscript, 1988d.
Gerencsér, L., Parameter Tracking of Time-Varying Continuous-Time Linear Stochastic Systems. In modelling, Identification and Robust Control (eds.: Ch. I. Byrnes and A. Lindquist) North Holland, 1986, pp. 581–595. (1986a).
Gerencsér, L., Pathwise stability of random differential equations, Preprint of the Department of Mathematics, Chalmers University of Technology and the University of Göteborg, 1986: 19, b. Revised version submitted to Stochastics, 1988b
Gerencsér, L., Recursive estimation of time-varying parameters. Proc. of the IFAC/IFORS Symposium on Identification and System l'arameter Estimation, Beijing, 1988c.
Hartman, Ph., Ordinary Differential Equations. Wiley and Sons, Inc., New York, 1964.
Ljung, L., Analysis of recursive stochastic algorithms. IEEE Trans. Auto. Cont., AC-22 (1977), 551–575.
Pontryagin, L.S., Ordinary Differential Equations. (In Russian), Nauka, Moscow, 1970.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag
About this paper
Cite this paper
Gerencsér, L. (1989). Pathwise stability of random differential equations and the solution of an adaptive control related problem. In: Christopeit, N., Helmes, K., Kohlmann, M. (eds) Stochastic Differential Systems. Lecture Notes in Control and Information Sciences, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0043780
Download citation
DOI: https://doi.org/10.1007/BFb0043780
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51299-8
Online ISBN: 978-3-540-46188-3
eBook Packages: Springer Book Archive