Adaptive multi-dimensional Taylor network dynamic surface control for a class of strict-feedback uncertain nonlinear systems with unmodeled dynamics and output constraint

Abstract

Unmodeled dynamics and output constraint are very often experienced in many physical applications, while few studies on them simultaneously are constructed. This study concentrates on the problem of adaptive multi-dimensional Taylor network dynamic surface control (MTN-DSC) for a class of strict-feedback uncertain nonlinear systems subjected to unmodeled dynamics and output constraint. The purpose is to make this study more practical, and design a controller with simple structure to improve the system performance. A barrier Lyapunov function is used to restrict the system output to within the prescribed constraint. At each step during the backstepping design process, an MTN is applied to approach the generated unknown composite function stemming from the unknown functions and uncertain disturbances, rather than individually; this simplifies the structure and reduces the complexity of the controllers. Meanwhile, the computational burden is further reduced, as only one parameter is adjusted online, which has the minimum number of parameters to be adjusted. Additionally, DSC technique is introduced to eliminate the inherent “explosion of complexity” problem in traditional backstepping design procedure. Furthermore, it is proved that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and that the output constraint is never violated. The validity of the proposed control scheme is illustrated through the numerical and applied simulation examples.