Abstract
We study the effect of unmodeled dynamics on the performance of a simple model reference adaptive control mechanism. Exact stability boundaries are computed and different routes to chaotic behavior and global instability are described. Typically, we observed a region of period doubling and Hopf bifurcations similar to those observed in the Ziegler-Nichols approach to PID control design. The analysis applies to higher order and certain nonlinear systems as well.
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