Bursting Scenaria and Performance Limitations of Adaptive Algorithms in the Absence of Excitation

Kostas S. Tsakalis

Supported in part by ARPA under grant F49620-93-1-0062 and in part by NSF under RIA grant ECS-9111346.

Presented at the 3rd IEEE Mediterranean Symposium on New Directions in Control and Automation, July 1995
Published in KYBERNETIKA, V.33, 1, 17-40, 1997; related results in Automatica, V.32, 4, 549-560, 1996; also in Int. J. of Adaptive Control and Signal Processing, V.8, 173-199, 1994 (Asymptotic Performance Guarantees in Adaptive Control, with Suttipan Limanond). 


A simple, yet general, bursting scenario is developed for a wide class of parameter estimation and system identification algorithms in the absence of sufficient excitation. This allows for an analytical derivation of a lower bound on the worst-case performance of such algorithms in the presence of perturbations. Simple examples are constructed, illustrating the implications of these results in adaptive control. 
Click here to see a brief description of the main result, a bursting example and some simulation results.