THIS paper presents a design approach based on error minimization in adaptive control for improving the rate of adaptation and allowing under certain conditions exponential convergence of the error dynamics. Global stability results are given for the case of perfectly parameterized uncertainty. The approach relies on the fact that the unknown weights in any linearly parameterized representation of uncertainty satisfy an integral equation involving the state and control variables. The equation is used to formulate an error minimization problem, the solution for which can be incorporated in the adaptive law. The paper extends an idea originally developed in (1) for the case of scalar uncertainty to the vector case. The results are conceptually similar to the notion of composite adaptation (2), and techniques developed for state estimation (3). The main difference is that these approaches use different signals. The effect of the modified adaptive components is illustrated on a dynamical model of an aircraft in which uncertainty is present both in control effectiveness and non-linear state dependent terms.
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