Sequential Type-2 Fuzzy Wavelet for Robust Online Control Applications

Abstract

Controlling nonlinear systems in real-time applications, such as robotics, aerospace, and industrial automation, poses significant challenges due to their complex dynamics, strong nonlinearities, and susceptibility to external disturbances and parameter uncertainties. Traditional intelligent control methods often struggle with these complexities, particularly in uncertain environments, leading to issues with accuracy, stability, and adaptability. Existing approaches, including fuzzy logic-based control and extreme learning machines (ELMs), offer promising solutions but still face limitations such as noise sensitivity, sensitivity to random initialization, lack of robustness in parameter updates, and inadequate robustness in real-time scenarios. This paper presents a novel robust intelligent control framework to tackle challenges in online learning and uncertainty management for nonlinear systems. An online updating method that integrates the Householder block exact QR decomposition-based recursive least squares algorithm is proposed, improving numerical stability and robustness during parameter updates, especially under noisy and uncertain conditions. By applying this method, the model becomes less sensitive to random initialization and more resilient to outliers. Building on this, a new robust online controller based on a sequential type-2 fuzzy wavelet is developed. This controller combines interval type-2 fuzzy logic for uncertainty modeling, wavelet neural networks for time-frequency localization, and an extreme learning machine for fast, one-pass learning. Architecture supports dynamic and robust parameter adaptation while keeping the hidden layer fixed, enhancing efficiency and adaptability in real-time applications. Additional contributions include an adaptive residual weighting strategy, regularized QR decomposition, and a recursive update scheme using Householder transformations. The proposed system significantly reduces sensitivity to random initialization and outliers, offering improved adaptability and performance in real-time applications. The numerical performance indices demonstrate that the ROC-ST2FWELM outperforms existing control methods, including online sequential type-2 fuzzy wavelet extreme learning machine (OS-T2FWELM) and fractional order PID combined with extended state observer (FOPID-ESO), across different real-world and simulated systems, including the Twin Rotor MIMO System (TRMS) and the backhoe hydraulic system. Specifically, the TRMS results show a Root Mean Square Error (RMSE) of the preposed controller for at 0.0988 and 0.0621, OS-T2FWELM at 0.2631 and 0.2334, and FOPID-ESO at 0.3324 and 0.3261 for the yaw angle and the pitch angle, respectively.