Looking for globally stable adaptive schemes for discrete-time nonlinear systems without growth restrictions.

G. A. GONZÁLEZ

Campinas

Workshop; CIMPA Workshop on Geometric Non-linear Control.; 2003

CIMPA y Universidade Estatual de Campinas

Since the beginning of the research about adaptive control of discrete-time nonlinear systems, several works have been based on techniques from the literature on adaptive control of linear systems. As a consequence, they only guaranteed global stability under growth conditions on the nonlinearities. The first intend to overcome this drawback was due to Kanellakopoulos in 1994 who developed a modified least-squares estimator with nonlinear weights to globally stabilize a scalar system with a single unknown parameter. Later on, new adaptive scheme based on an orthogonalization process was introduced by this author; globally boundedness and convergence were achieved for scalar systems affected linearly by a vector of unknown parameters. Now it may be seen that it is possible to make progress on that scheme: better stability and robustness properties can be obtained if the estimator is re-designed by means of a mean-squares problem. On the other hand, a great deal of research efforts focuses on nonlinear discrete-time systems in strict-feedback form presented by Yeh and Kokotovic in 1995 by the first time. But again, global results were only obtained for nonlinearities under growth restrictions. More recently, new adaptive algorithms have been introduced that guarantee global boundedness and tracking for this class of systems. A novel approach on this line promises to be the design of a new scheme by combining these last ideas with the ¨least squares problem¨ estimator.