Abstract: A sufficient conditions for the convergence of D-type open-loop iterative learning controller is proposed for multiple input multiple output continuous repeat system in the presence of bounded external state disturbance and actuator failure. Under the conditions of the initial state is equal and the initial state exist bounded offset, based on λ-norm, this paper proposed the sufficient conditions for the convergence of the iterative learning controller respectively. It is proved that in the sense of λ norm, under the two conditions, the convergence conditions of the iterative controller are the same, only the upper bound of tracking error between the output of fault system and the expected trajectory is different. Based on Schur's complement principle, linear matrix inequality is given to determine the optimal control gain at a given convergence rate. Numerical simulations verify the effectiveness and feasibility of the proposed control strategy.

Key words: Nonlinear dynamics, iterative learning, fault-tolerant control, process control, algorithm

摘要： 对存在状态干扰和执行器故障的连续线性时不变系统，给出了D型开环迭代学习控制律收敛的充分条件。在λ范数意义下，分别给出了系统状态和理想状态之间的初值相等和初值存在有界偏移时，D型开环迭代学习控制律收敛的充分条件；理论证明，在λ范数意义下，初值相等和初值存在有界偏移，迭代控制律的收敛条件相同，仅故障系统输出与期望轨迹的跟踪误差上界存在差别。基于Schur补原理，给出确定迭代控制增益的线性矩阵不等式，以快速计算给定收敛速度下的最优控制增益。数值仿真验证了该控制策略的容错性和鲁棒性。

关键词: 非线性动力学, 迭代学习, 容错控制, 过程控制, 算法