Fast and low‐frequency adaptation in neural network control

Abstract

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.

Robust adaptive control for unmatched systems with guaranteed parameter estimation convergence

“…This is clearly different to the -modification 11 and e-modification 12 methods. Moreover, the leakage term N proposed in this paper is also different to those introduced in the works of Yucelen and Haddad 8 and Pan et al, 15 ie,Ŵ −Ŵ withŴ being the filtered version ofŴ, which aims to filter out the high-frequency content in the adaptive law and enhance the tracking performance using high-gain learning rate. In fact, it is noted that with the leakage termŴ −Ŵ , only the convergence of the tracking error e can be claimed, while the convergence of the estimation errorW cannot be retained in the aforementioned works.…”

“…1 In this framework, although asymptotic convergence of the estimation error can be proved provided that the regressor is persistently excited, there is a potential parameter drift and bursting issue. 8,15 It is noted that the above adaptive laws cannot guarantee the convergence of the estimated parameters to their true values due to the induced forgetting factors, though the robustness stemming from the system uncertainties can be enhanced. However, with these robust adaptive laws, the estimated parameters may stay around the preset values only due to the induced damping terms, which in turn will slow down the convergence of adaptive laws and thus degrade the tracking control response.…”

“…In addition, low-pass filter operations were added in the adaptive laws to filter out the high-frequency contents embedded in the tracking error. 8,15 It is noted that the above adaptive laws cannot guarantee the convergence of the estimated parameters to their true values due to the induced forgetting factors, though the robustness stemming from the system uncertainties can be enhanced. In fact, it is known that the fast accurate parameter estimation of unknown parameters can largely improve the overall performance of adaptive control systems.…”

Peaking-Free Output-Feedback Adaptive Neural Control Under a Nonseparation Principle

“…Applying (8), (15), (16), and (18) to the above expression, we obtain the state estimation error dynamics as follows:…”

“…It was proved in [2] that the combination of high-gain observers with control saturation enables output-feedback control to recover the trajectories of its state-feedback counterpart if the observer gain is sufficiently high. For nonlinear systems with functional uncertainties, output-feedback approximation-based adaptive control (AAC) using high-gain observers and fuzzy systems/neural networks (NNs) has also been intensively studied [3]- [8] to overcome the limitations of state-feedback AAC [9]- [15]. Yet, due to static-gain and linear properties, highgain observers are usually subject to some limitations as follows [1]: 1) noise rejection ability can be degraded while the observer gain is too high; and 2) peaking responses can occur in the absence of control saturation.…”