Fast and low-frequency adaptation in neural network control

In adaptive neural network (NN) control, fast adaptation through high-gain learning rates can cause high-frequency oscillations in control response resulting in system instability. This study presents a simple adaptive NN with proportional derivative (PD) control strategy to achieve fast and low-frequency adaptation for a class of uncertain non-linear systems. Variable-gain PD control without the knowledge of plant bounds is proposed to semi-globally stabilise the plant, so that NN approximation is applicable. A low-pass filter-based modification is applied to the adaptive law to filter out high-frequency content, so that tracking performance can be safely improved by the increase of learning rates. The novelties of this study with respect to adaptive NN control are as follows: (i) semi-global practical asymptotic tracking can be achieved by a simple adjustment of control parameters; and (ii) fast and low-frequency adaptation can be obtained via high-gain learning rates under guaranteed system stability. Simulation studies have demonstrated that the proposed approach can outperform its non-filtering counterpart in terms of tracking accuracy, energy cost and control smoothness.