论文标题
使用平滑控制
Adaptive Backstepping Control for Fractional-Order Nonlinear Systems with External Disturbance and Uncertain Parameters Using Smooth Control
论文作者
论文摘要
在本文中，我们考虑控制一类具有参数不确定性和外部干扰的单输入单输出（SISO）分数非线性系统。基于反向替代方法，提出了一种自适应控制器，其适应性定律用于估计未知系统参数和未知干扰的界限。不用使用不连续的函数，例如$ \ mathrm {sign} $函数，而是使用辅助功能来获得平滑的控制输入，该输入仍然能够在存在有限干扰的情况下实现完美的跟踪。实际上，通过使用分数有向的lyapunov方法证明，所有闭环信号和分数系统输出的渐近完美跟踪的全局界限都可以证明。为了验证所提出的控制方法的有效性，提出了示例示例。
In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller is proposed with adaptive laws that are used to estimate the unknown system parameters and the bound of unknown disturbance. Instead of using discontinuous functions such as the $\mathrm{sign}$ function, an auxiliary function is employed to obtain a smooth control input that is still able to achieve perfect tracking in the presence of bounded disturbances. Indeed, global boundedness of all closed-loop signals and asymptotic perfect tracking of fractional-order system output to a given reference trajectory are proved by using fractional directed Lyapunov method. To verify the effectiveness of the proposed control method, simulation examples are presented.
