Adaptive Fixed-Time Control for an Uncertain Robot With Input Quantization: A Broad Learning System Approach

In this paper, an adaptive fixed-time control approach is designed for a robot with dynamic uncertainty in the presence of input quantization by using the Broad learning system (BLS). The proposed BLS-based control algorithm is constructed by fusing the BLS with the radial basis function neural network, which is improved in terms of node selection rule with a self-adjusting Gaussian function center and enhancement layer. A hysteresis quantizer is applied to the requirement of a low transmission rate. For the nonlinearity occurring in the quantized input, a novel adaptive fixed-time method is developed such that 1) the adverse effect of quantization nonlinearity is removed in a finite interval; 2) the BLS-based approximation technique can improve the approximation accuracy, which enhances the robustness of the closed-loop system; and 3) via the Lyapunov stability method, the fixed-time convergence of the closed-loop system is proved. Finally, numerical simulations and experiments validate the effectiveness of the proposed control scheme. Note to Practitioners—This paper presents a novel approach to achieving fixed-time quantization for broad learning neural network-based controllers in robotic systems. The primary application of this research is in the field of automation, specifically for improving the performance of robotic joint tracking. The proposed method addresses the practical problem of ensuring that robotic systems can achieve precise tracking in fixed time, regardless of the initial conditions. This is particularly useful in industrial automation where consistent and reliable performance is crucial. Our approach leverages a fixed-time quantization technique to enhance the efficiency and reliability of neural network controllers. This method ensures that the tracking errors are confined to a small neighborhood of zero within a predetermined fixed time, thus significantly improving the productivity and reliability of the system. The results demonstrate that the proposed control scheme can handle various initial states and maintain robust performance.