Abstract
Many physical phenomena are modeled by stochastic systems. Typically some parameters of the system are unknown so that these parameters must be estimated and often it is required to control this system. In this paper the parameter estimation problem is considered for this combined adaptive control problem. The unknown parameters appear affinely in the drift term of the stochastic differential equation that describes the nonlinear stochastic system. It is shown that the family of maximum likelihood estimates based on the observations of the system for increasing time are strongly consistent.
Research partially supported by NSF Grant ECS-8403286-A01.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Borkar and A. Bagchi, Parameter estimation in continuous—time stochastic processes, Stochastics 8 (1982), 193–212.
T. Duncan and P. Varaiya, On the solutions of a stochastic control system, SIAM J. Control 9 (1971), 354–371.
T. Duncan and P. Variaya, On the solutions of a stochastic control system II, SIAM J. Control 13 (1975), 1077–1092.
T. E. Duncan and B. Pasik—Duncan, Adaptive control of continuous time linear systems, preprint.
T. E. Duncan and B. Pasik—Duncan, Adaptive control of linear delay time systems, preprint.
P. Hall and C. C. Heyde, Martingale Limit Theory and Its Applications, Academic Press, 1980.
K. It6 and H. P. McKean, Duffusion Processes and their Sample Paths, Springer—Verlag, 1965.
T. S. Lee and F. Kozin, Almost sure asymptotic likelihood theory for diffusion processes, J. Appl. Prob. 14 (1977), 527–537.
R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes II Applications, Springer—Verlag, 1978.
P. Mandl, The use of optimal stationary policies in the adaptive control of linear systems, Proc. Symp. to Honour Jerzy Heyman, Warsaw, 1974, 223–243.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Duncan, T.E., Pasik-Duncan, B. (1986). A Parameter Estimate Associated with the Adaptive Control of Stochastic Systems. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systems. Lecture Notes in Control and Information Sciences, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007585
Download citation
DOI: https://doi.org/10.1007/BFb0007585
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16729-7
Online ISBN: 978-3-540-39856-1
eBook Packages: Springer Book Archive