输入受限不确定离散系统的灰色滑模控制

Grey Sliding Mode Control for Uncertain Discrete Systems with Input Constraints

对于输入受限离散系统,首先构造出输入受限条件的等效约束矩阵,然后基于线性矩阵不等式给出了满足输入受限条件的切换函数时变参数的构造方法。采用离散趋近控制,结合李雅普诺夫函数和线性矩阵不等式方法提出了滑动模态渐近稳定的充分条件,对不确定部分建立灰色估计模型,证明了闭环系统的稳定性。理论和仿真表明,不仅利用到基于等效控制的滑模控制器构造简单、易于实现等优点,而且满足输入受限条件,克服了传统基于等效控制的滑模控制器瞬时输出量过大的缺点,有效地消除了系统抖振和不确定因素的影响。

The sliding mode control problem a class of uncertain discrete systems with input constraints is discussed. An equivalent matrix is constructed for input constraints. The control strategy combing discrete quasi-sliding mode control with discrete equivalent control is presented. A sufficient condition for the existence of time-varying sliding surfaces is given in terms of LMIs and Lyapunov function. Grey estimate model is built for the uncertain part. The proposed method utilizes the merits of sliding mode controller based on equivalent control. The simulation results show that the existence large instantaneous output in the traditional sliding mode control is overcome.