On modified parameter estimators for identification and adaptive control. A unified framework and some new schemes
Résumé
A key assumption in the development of system identification and adaptive control schemes is the availability of a regression model which is linear in the unknown parameters (of the plant and/or the controller). Applying standard— e.g., gradient descent-based—parameter estimators leads to a linear time-varying equation for the parameter errors, whose stability relies on the usually stringent persistency of excitation assumption. As suggested in Kreisselmeier (1977) and Lion (1967), with the inclusion of linear filters, it is possible to generate alternative regression models, whose parameter error equations have different stability properties. In Duarte and, Narendra (1989), Panteley, Ortega,and Moya, (2002) and Slotine and Li, (1989) estimators that combine tracking and identification errors, to generate new parameter error equations, were proposed. The main objectives of this paper are: first, based on the two key developments mentioned above, provide a unified framework for the analysis and design of parameter estimators and, in particular, show that they lie at the core of some modified schemes recently proposed in the literature. Second, extend the realm of application of these estimators to the class of nonlinear systems considered in Panteley et al. (2002). Third, use this framework to propose some new schemes with relaxed conditions for convergence and improved transient performance. Particular attention is given to the task of obviating the persistency of excitation assumption, which is rarely verified in applications and is, certainly not, the only way to ensure robustness of the schemes.