Multiple model adaptive control (MMAC) for nonlinear systems with nonlinear parameterization

A novel dwell-time-switching based multiple model adaptive control (MMAC) scheme is proposed for the state feedback stabilization problem of a class of general nonlinear systems with nonlinear parameterization. One major contribution is that it has advanced Morse´s dwell-time-switching from linear systems to a class of nonlinear systems. Another significant contribution is that it combines the idea of monitoring the adequacy of candidate models (in terms of their estimation performances) in most MMAC schemes with the idea of monitoring the performance of candidate controllers in unfalsified control. Moreover, sufficient conditions for closed-loop stability are established for the proposed dwell-time-switching based MMAC scheme when applied to the considered class of nonlinear systems. To fulfil those sufficient conditions, emphasis has been put on the design of multiple estimators, candidate controllers and monitoring signals. The carefully designed estimators, candidate controllers, and monitoring signals enable us to derive a finite time switching result and provide a characterization on the maximum number of switchings for the dwell-time-switching algorithm proposed. In order to show how the general design of our dwell-time-switching based MMAC scheme can be applied to a particular nonlinear system, a constructive design based on back-stepping is provided for the adaptive control problem for a special class of nonlinearly parameterized systems, which can satisfy all the sufficient conditions to ensure closed-loop stability.