An α‐variable model‐free prescribed‐time control for nonlinear system with uncertainties and disturbances

Abstract In this article, an ‐variable model‐free prescribed‐time controller (‐MFPTC) is proposed for a nonlinear system with uncertainties and disturbances. First, an ultra‐local model is employed to formulate the plant dynamic by using input and output data. Second, to observe the state variables and compensate for the lumped uncertainties, a linear extended state observer (LESO) is designed. Then, a corresponding LESO‐based ‐fixed model‐free controller (LESO‐iPD) is proposed. Third, based on LESO‐iPD, a prescribed‐time sub‐controller (PTC) is adopted to converge tracking error within a prescribed finite time. Furthermore, an adaptive RBF neural network compensator is constructed to approximate and compensate for LESO error. Correspondingly, an ‐fixed model‐free prescribed‐time controller (‐MFPTC) is proposed. Fourth, based on ‐MFPTC, a tracking error‐based ‐variable method is applied to improve the controller performance, and an ‐variable model‐free prescribed‐time controller (‐MFPTC) is subsequently proposed. Moreover, stability and prescribed‐time convergence of closed‐loop system with ‐MFPTC are analyzed by using the Lyapunov theorem. Ultimately, to demonstrate the performance and effectiveness of the proposed control strategy, the numerical simulation with sliding mode control, LESO‐iPD, ‐MFPTC, and ‐MFPTC and co‐simulation results on quadrotor have been obtained.