Adaptive Neural Control With Guaranteed Performance for Mechanical Systems Under Uncertain Initial Conditions: A Time-Varying Neuron Approach

This article proposes a new adaptive neural control scheme with guaranteed performance for mechanical systems under dynamic uncertainties and uncertain initial conditions. Employing the novel time-varying neuron (TVN) approach and a shifting function, the control method developed in this article can systematically solve two crucial problems: one is how to construct a variable structure network to improve the approximation ability while the online tuning parameters do not increase with the number of neurons, and the other is how to achieve the predetermined tracking performance for multi-input multi-output (MIMO) mechanical systems under any bounded initial tracking errors. To approximate uncertain dynamics, the TVN approach is first presented to instruct the process of adding new neurons for better-learning capability, where the online updating parameters in the neural network (NN) unit are compressed by the vector projection technique, yielding an NN approximator with low-computational burden. By virtue of a shifting function, the uncertain initial tracking error is converted to zero such that a speed function with predetermined convergence performance can be efficiently employed to constrain the tracking trajectory without considering the initial condition. Moreover, to obviate the differentiation operation for the virtual stabilizing function, the dynamic surface technique is adopted to derive the presented control scheme for facilitating practical implementation. Finally, the effectiveness and benefits of the presented control are verified via theoretical analysis and a two-link manipulator.