To overcome the drawback of overparametrization in existing nonlinear adaptive control design with multiple unknown control directions, we propose a new algorithm which combines nonlinear integrator backstepping, tuning function design and a logic-based switching mechanism that tunes the control directions online in a switching manner. Global asymptotic tracking control is achieved for parametric-strict-feedback systems without overparametrization. The logic-based switching criterion is based on monitoring incremental errors caused during two consecutive switching moments, and thus can identify the true control direction quickly.
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