输入约束不确定系统的点对点迭代学习控制与优化

Point-to-point iterative learning control and optimization for uncertain systems with constrained input

为解决工业过程中机械臂等特殊重复运行系统的输出在有限时间内无需实现全轨迹跟踪,仅需跟踪期望轨迹上某些特殊关键点的控制问题,针对线性时不变离散系统提出一种基于范数最优的点对点迭代学习控制算法.通过输入输出时间序列矩阵模型变换构建综合性多目标点性能指标函数,求解二次型最优解得到优化迭代学习控制律,同时给出模型标称和不确定情形下最大奇异值形式鲁棒控制算法收敛的充分条件,并进一步推广得到输入约束系统优化控制算法的收敛性结果,最后在三轴龙门机器人模型上验证算法的有效性.

In order to solve the problem that the output of special repetitive operation systems, like manipulators in industrial process, only needs to track some special key points on the desired trajectory rather than realize full trajectory tracking in limited time, a norm-optimal point-to-point iterative learning control algorithm is proposed for a linear time-invariant discrete system. By transforming the matrix model of the input and output time series, a comprehensive multi-objective point performance index function is constructed. Thus, the optimal iterative learning control law can be obtained through the quadratic optimal solution. At the same time, the sufficient conditions for convergence of the robust control algorithm in the form of largest singular value are given in the case of model nominal and uncertain. Moreover,the convergence results of the optimal control algorithm for systems with input signal constraints are further generalized.Finally, the effectiveness of the algorithm is verified on the three-axis gantry robot model.