A Robust Adaptive Controller for Continuous Time Systems
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abstract
The stability of an adaptively controlled continuous-time plant of relative degree one in the presence of unmodeled dynamics is proved. Specifically, it is shown that if the unmodeled dynamics are small in some sense, then all the signals in the closed-loop system remain bounded. Robust performance is achieved, in the sense that the mean-square tracking error converges to zero linearly with the unmodeled dynamics. In the absence of unmodeled dynamics, the tracking error asymptotically goes to zero. The adaptation law considered is the usual gradient update law with projection. This indicates that modifications such as normalization or relative dead-zones are not necessary to achieve stability in the presence of unmodeled dynamics.
