Smooth controller design for non-linear systems using multiple fixed models

Multiple model adaptive control (MMAC) with second-level adaptation is a recently proposed methodology for dealing with systems where the parametric uncertainty is large. Compared with the multiple model switching scheme, the new scheme can lead to significant improvements in performance. Some research has been conducted using the new scheme, but all of the results concern linear systems with an adaptive identification model set. In this study, MMAC with second-level adaptation scheme is extended to non-linear systems in strict feedback form, and the fixed identification model set is under consideration. This is motivated by the fact that a smooth controller can lead to smooth performance and the fixed identification model set gains potential advantages over the adaptive identification model set, especially for the case that the parameters of the system change over the time. Design details are presented and the stability of MMAC with second-level adaptation using a fixed identification model set for non-linear systems is given, which has not been discussed before. Finally, two simulations are performed to show that this scheme performs much better than conventional schemes, including adaptive control and multiplemodel switching schemes, in terms of convergence speed and transient performance.