论文标题
Lyapunov的基于屏障功能的时间变化的方法获得了高阶滑动模式控制器
A Lyapunov Approach to Barrier-Function Based Time-Varying Gains Higher Order Sliding Mode Controllers
论文作者
论文摘要
在本文中，我们为{\ color {\ color {black} fast}稳定具有有界不确定性的集成器链链的稳定。我们将此类控制器称为{\ color {black}时间变化}高阶滑动模式控制器，因为它们是为具有有界不确定性的非线性单输入单输出（SISO）系统设计的，因此不确定性界限是未知的。 ％{\ color {blue} old：我们的主要结果指出，给定的任何邻域$ \ varepsilon $，我们确定一个控制器确保每个不确定性界限，相应的闭环系统的每个轨迹都会进入$ \ varepsilon $，并最终留在那里。 Furthermore, based on the homogeneity property, a new asymptotic accuracy, which depends on the size of $\varepsilon$, is presented.} We provide a time varying control feedback law insuring verifying the following: there exists a family $(D(t))_{t\geq 0}$ of time varying open sets decreasing to the origin as $t$ tends to infinity, such that, for任何不明的不确定性界限和相应系统的轨迹$ z（\ cdot）$，都存在$ z（t_z）\ in d（t_z）$和$ z（t）$的$ z（t_z）\ in d（t_z）\ in d（t）\ in D（t）\ in d（t）$ in d \ t（t）$的$ t \ t \ egeq t_z t_z $。 ％在所有轨迹的有限时间内进入融合到一个变化的域$ d（t）$缩小到原点及其维护的时间。因此，由于函数$η（t）$趋于零，因此这会导致所有轨迹的渐近收敛趋于零。通过模拟说明了这些控制器的有效性。
In this paper, we present Lyapunov-based {\color{black}time varying} controllers for {\color{black}fast} stabilization of a perturbed chain of integrators with bounded uncertainties. We refer to such controllers as {\color{black}time varying} higher order sliding mode controllers since they are designed for nonlinear Single-Input-Single-Output (SISO) systems with bounded uncertainties such that the uncertainty bounds are unknown. %{\color{blue} OLD: Our main result states that, given any neighborhood $\varepsilon$ of the origin, we determine a controller insuring, for every uncertainty bounds, that every trajectory of the corresponding closed loop system enters $\varepsilon$ and eventually remains there. Furthermore, based on the homogeneity property, a new asymptotic accuracy, which depends on the size of $\varepsilon$, is presented.} We provide a time varying control feedback law insuring verifying the following: there exists a family $(D(t))_{t\geq 0}$ of time varying open sets decreasing to the origin as $t$ tends to infinity, such that, for any unknown uncertainty bounds and trajectory $z(\cdot)$ of the corresponding system, there exists a positive positve $t_z$ for which $z(t_z)\in D(t_z)$ and $z(t)\in D(t)$ for $t\geq t_z$. %enters convergence in finite time of all the trajectories to a time varying domain $D(t)$ shrinking to the origin and their maintenance there. Hence, since the function $η(t)$ tends to zero, this leads the asymptotic convergence of all the trajectories to zero. The effectiveness of these controllers is illustrated through simulations.
