Disturbed time-delay nonlinear systems with practical predefined-time control

The presence of time delays prevents the controller from responding to disturbances promptly, resulting in excessive overshoot and prolonged adjustment times, which in turn deteriorate system stability. To address the issue, a practical predefined-time control approach is proposed for systems with state time delays. The Lyapunov–Krasovskii functional method is employed, without the use of trigonometric or exponential functions. Additionally, a practical predefined-time observer is developed to estimate mismatched disturbances, enhancing the robustness of nonlinear time-delay systems. A practical predefined-time neural network is also used to estimate system uncertainty. The proposed approach is validated through experiments. The impact of delays on the system is analyzed under multiple scenarios. Compared to traditional control methods, the results show a reduction in computational costs and improved control performance in the presence of time delays. The proposed method outperforms the conventional predefined-time control algorithm by 7.5% and shows an improvement of approximately 20% over the fixed-time control method.