Adaptive Global Asymptotic Control for Time-Varying Complex Systems with Input Saturation Under Prescribed Performance Constraints

In this work, an adaptive control problem is formulated for a class of time-varying complex systems with input saturation and unknown disturbances. A prescribed performance control (PPC) scheme is developed, incorporating a distinctive type of funnel function and the barrier Lyapunov function (BLF) method. This approach enhances robustness and performance in systems significantly affected by input saturation. The proposed method ensures asymptotic tracking, achieving more than bounded-error tracking performance, and offers a reliable and effective control solution under input saturation. To address nonlinearity from input saturation, a smooth approximation of the saturation function is applied to the control input signal. This control strategy employs PPC techniques to mitigate the effects of input saturation. A Lyapunov-based framework is used to ensure system stability, with a control law that guarantees convergence even in the presence of saturation. The focus is on achieving global adaptive asymptotic control of time-varying complex nonlinear systems, emphasizing PPC to ensure both stability and superior transient performance. Additionally, an adaptive control strategy is introduced, ensuring that all closed-loop signals remain globally uniformly ultimately bounded. Finally, simulation results confirm the proposed method's effectiveness in delivering high-performance control.