Analysis of adaptive identifiers in the presence of unmodeled dynamics: averaging and tuned parameters
- 1 January 1988
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 33 (10) , 969-976
- https://doi.org/10.1109/9.7258
Abstract
The authors analyze the behavior of a standard identifier when the plant contains additional dynamics, called unmodeled dynamics, which invalidate the known order assumption. The first result of the analysis is an input richness condition which does not depend on the order of the unmodeled dynamics to guarantee persistency of excitation of the regressor. Then it is shown that the persistently exciting (PE) condition leads to a BIBO (bounded-input bounded-output) stability property for the identifier. The method of averaging is used to formally define the notion of tuned parameters as the equilibrium of the identifier averaged system. It is shown that the tuned parameters always exist and that the actual parameters converge to some neighborhood of the tuned parameters. From the definition of the tuned parameters, an explicit expression to calculate and interpret them as the fixed parameter values that minimize the mean-squared output error is derived.Keywords
This publication has 16 references indexed in Scilit:
- Necessary and sufficient conditions for parameter convergence in adaptive controlAutomatica, 1986
- Integral manifolds of slow adaptationIEEE Transactions on Automatic Control, 1986
- New stability theorems for averaging and their application to the convergence analysis of adaptive identification and control schemesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1985
- A stability-instability boundary for disturbance-free slow adaptation with unmodeled dynamicsIEEE Transactions on Automatic Control, 1985
- Averaging Methods in Nonlinear Dynamical SystemsPublished by Springer Nature ,1985
- On Algorithms for Solving f(x)=0Communications on Pure and Applied Mathematics, 1979
- Adaptive observers with exponential rate of convergenceIEEE Transactions on Automatic Control, 1977
- Stable adaptive observers and controllersProceedings of the IEEE, 1976
- Stable adaptive schemes for state estimation and identification of linear systemsIEEE Transactions on Automatic Control, 1974
- A new canonical form for an adaptive observerIEEE Transactions on Automatic Control, 1974