By Topic

Using Persistent Excitation with Fixed Energy to Stabilize Adaptive Controllers and Obtain Hard Bounds for the Parameter Estimation Error

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Radenkovic, M.S. ; Department of Electrical Engineering, University of Colorado at Denver, Denver Colorado 80204. ; Ydstie, B.E.

We show that persistent excitation with fixed and finite energy can be used as a tool to stabilize adaptive control algorithms and obtain hard bounds for the parameter estimation errors. Two important instability problems in certainty equivalence adaptive control are solved by applying excitation. The first instability is parameter drift due to an unstable manifold which appears when the excitation level is not high enough. This problem has previously been studied using averaging and local analysis. Our results are global. The second instability is numerical, and due to a division with zero in the adaptive law. In the paper we show that the system parameters are estimated when the level of excitation is sufficiently high relative to the magnitudes of the external disturbances and the unmodelled dynamics. It follows that the singularity problem only can occur during the transient. The consequence of this is that we can implement a direct adaptive controller without requiring knowledge of the sign of the high frequency gain. The approach can be generalized to more complex adaptive laws and this, together with the fact that we obtain hard bounds for the parameter estimation error opens up for the possibility of designing robust controllers that are adaptive.

Published in:

American Control Conference, 1993

Date of Conference:

2-4 June 1993