Prescribed-time prescribed performance based BFNN control for strict-feedback nonlinear system with disturbance and uncertainties consideration

This paper investigates the prescribed-time prescribed performance tracking control for nonlinear strict-feedback systems with model uncertainties and external disturbances. First, a prescribed-time prescribed performance function (PTPPF) is constructed to provide a decaying performance envelope that terminates at a user-defined settling time. Then, considering the model uncertainties, an adaptive broad fuzzy neural network (BFNN) with broad learning capability is employed for estimation, which utilizes an incremental node generation mechanism to enhance approximation performance. Furthermore, a disturbance observer (DO) is integrated, which compensates for the lumped disturbance composed of the BFNN approximation error and external disturbances. Subsequently, to suppress control oscillation and smooth the state response, a nonlinear variable gain feedback mechanism is developed based on the small-error large-gain (SELG) and large-error small-gain (LESG) principles. The virtual control signals are designed by using the nonlinear variable gain and BFNN approximation. Meanwhile, an adaptive command filter is introduced, which avoids the explosion of complexity and estimates the unknown derivative bounds of the virtual control signals. Finally, Lyapunov stability analysis proves that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB). Numerical simulations validate the effectiveness and superiority of the proposed method.