ABSTRACT

This paper presents an adaptive neural control to solve the tracking problem of a class of pure-feedback systems with non-differentiable non-affine functions in the presence of unknown periodically time-varying disturbances. To handle with the design difficulty from non-affine structure of pure-feedback system, a continuous and positive control gain function is constructed to model the periodically disturbed non-affine function as a form that facilitates the control design. As a result, the non-affine function is not necessary to be differentiable with respect to control variables or input. In addition, the bounds of non-affine function are unknown functions, and some appropriate compact sets are introduced to investigate the bounds of non-affine function so as to cope with the difficulty from these unknown bounds. It is proven that the closed-loop control system is semi-globally uniformly ultimately bounded by choosing the appropriate design parameters. Finally, comparative simulations are provided to illustrate the effectiveness of the proposed control scheme.

摘要

本文提出了一种自适应神经控制来解决一类具有不可微分非仿射函数的纯反馈系统在存在未知周期性时变扰动的情况下的跟踪问题。针对纯反馈系统的非仿射结构设计困难，构造了一个连续正控制增益函数，将周期性扰动的非仿射函数建模为一种便于控制设计的形式。因此，非仿射函数不必相对于控制变量或输入是可微的。此外，非仿射函数的边界是未知函数，引入一些合适的紧集来研究非仿射函数的边界，以解决这些未知边界带来的困难。通过选择合适的设计参数，证明了闭环控制系统是半全局一致最终有界的。最后，提供了比较仿真来说明所提出的控制方案的有效性。