不确定离散线性系统的鲁棒单调反馈–前馈迭代学习控制

Robust monotonically convergent feedback-forward iterative learning control for uncertain linear discrete systems

针对一类不确定离散线性系统,提出一种沿迭代方向鲁棒单调收敛和沿时间方向有界输入有界输出(bouned-input bounded-output,BIBO)稳定的反馈–前馈迭代学习控制策略.首先,将不确定反馈–前馈迭代学习系统表示为不确定二维Roesser模型系统;然后,把二维系统沿迭代方向的鲁棒单调收敛问题转化成一维系统的H∞干扰抑制控制问题,并给出系统的稳定性证明和用线性矩阵不等式(linear matrix inequality,LMI)表示的沿迭代方向鲁棒单调收敛的充分条件,该LMI充分条件不仅可以用于确定反馈–前馈控制器的增益矩阵,而且还可以保证系统沿时间轴方向是BIBO稳定的;最后,仿真结果证明了该反馈–前馈迭代学习控制策略的有效性.

For a class of uncertain linear discrete systems,a feedback feed-forward iterative learning control （ILC） scheme is proposed,which can ensure the system to be robust monotonically convergent along the iteration direction and bouned-input bounded-output （BIBO） stable along the time direction.First,the uncertain feedback feed-forward iterative learning system is presented by an uncertain two dimensional Roesser model system.Then,the robust monotonic convergence problem along the iteration direction is converted to a H∞ disturbance attenuation problem of a one-dimensional system.Furthermore,the stability analysis is presented and the robust monotonically convergent conditions are given by linear matrix inequality （LMI）.The LMI conditions can not only determine gain matrix of the feedback feed-forward iterative learning controller,but also guarantee the system is BIBO stable along the time direction.Finally,the simulation results are presented to demonstrate the effectiveness of the proposed scheme.