Robust continuous-time adaptive control by parameter projection
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We consider the problem of adaptive control of a continuous-time plant of arbitrary relative degree, in the presence of bounded disturbances as well as unmodeled dynamics. The adaptation law we consider is the usual gradient update law with parameter projection, the latter being the only robustness enhancement modification employed. We show that if the unmodeled dynamics, which consists of multiplicative as well as additive system uncertainty, is small enough, then all the signals in the closed-loop system are bounded. This shows that extra modifications such as, for example, normalization or relative dead zones, are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics. In the nominal case, where unmodeled dynamics and disturbances are absent, the asymptotic error in tracking a given reference signal is zero. Moreover, the performance of the adaptive controller is also robust in that the mean-square tracking error is quadratic in the magnitude of the unmodeled dynamics and bounded disturbances, when both are present.