Multiple Model Adaptive Mixing Control: The Discrete-Time Case

Most of the work in multiple model adaptive control with various forms of switching focused on continuous-time systems. The purpose of this technical note is to extend the results of one approach, the adaptive mixing control (AMC), to discrete-time systems. Further, the technical note solves the tracking problem which has not been addressed in most schemes of this class. Stability and robustness properties of the AMC scheme for discrete-time systems are analyzed. It is shown that in the ideal case, when no disturbances or unmodeled dynamics are present, the tracking error converges to zero. In the non ideal case, the mean-square tracking error is of the order of magnitude of the modeling error provided the unmodeled dynamics satisfy a norm-bound condition. While these robustness results are conceptually similar to those of traditional robust adaptive control, the proposed scheme does not suffer from the drawback of stabilizability of the estimated plant and in addition performs much better in simulation studies. Furthermore, it allows well developed results from robust control to be incorporated in the design.