Summary This paper studies adaptive parameter estimation and control for nonlinear robotic systems based on parameter estimation errors. A framework to obtain an expression of the parameter estimation error is proposed first by introducing a set of auxiliary filtered variables. Then three novel adaptive laws driven by the estimation error are presented, where exponential error convergence is proved under the conventional persistent excitation (PE) condition; the direct measurement of the time derivatives of the system states are avoided. The adaptive laws are modified via a sliding mode technique to achieve finite‐time convergence, and an online verification of the alternative PE condition is introduced. Leakage terms, functions of the estimation error, are incorporated into the adaptation laws to avoid windup of the adaptation algorithms. The adaptive algorithm applied to robotic systems permits that tracking control and exact parameter estimation are achieved simultaneously in finite time using a terminal sliding mode (TSM) control law. In this case, the PE condition can be replaced with a sufficient richness requirement of the command signals and thus is verifiable a priori. The potential singularity problem encountered in TSM controls is remedied by introducing a two‐phase control procedure. The robustness of the proposed methods against disturbances is investigated. Simulations based on the ‘Bristol‐Elumotion‐Robotic‐Torso II’ (BERT II) are provided to validate the efficacy of the introduced methods. Copyright © 2014 John Wiley & Sons, Ltd.

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SUMMARYAn alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.

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