Adaptive back-stepping control of high-order uncertain nonlinear systems that a funnel control scheme with uncertain dynamics

For a class of high order nonlinear uncertain systems with uncertain dynamics, a novel adaptive funnel back-stepping control scheme is proposed to ensure the convergence of small overshoot of tracking error. Although the classical funnel performance control method can guarantee the transient performance of the system, the control strategy depends on the symbol of the initial tracking error, and the overshoot and convergence speed are difficult to control. Firstly, a new performance function which does not depend on the initial value of the tracking error is designed to constrain the tracking error. No matter what the tracking error is, it can ensure that the overshoot of the tracking error response process is small or even zero. Then, in order to facilitate the controller design, a new error conversion method is designed, which replaces the initial tracking error with the conversion error, and transforms the “constrained” system into an equivalent “unconstrained” system. Then, combined with back-stepping control theory, the adaptive back-stepping controller is designed. Through the stability analysis of the system, the semi global uniformly bounded stability of the closed-loop control system is guaranteed. Numerical simulation and experimental results verify the superior performance of the control method.