固定初值下广义系统的迭代学习控制

Iterative Learning Control for Singular Systems with Fixed Initial Value

针对一类在有限时间区间上重复运动的线性广义系统,提出了一种在固定初始学习状态下的闭环PD型迭代学习控制算法,给出了该算法的收敛条件,并在理论上对算法进行了收敛性分析。初态学习允许在每次迭代开始时,其初始状态为固定值在PD型闭环学习律的作用下,线性广义系统的迭代输出会收敛于极限轨迹,可以在D型算法的基础上有效的减少固定偏差。数值仿真结果验证了闭环PD型迭代学习控制算法在固定初值下算法的有效性。

For a class of linear singular systems operating repeatedly on finite interval, the paper proposes a PD-type closed-loop iterative learning control algorithm with fixed initial learning states. Besides, the paper gives the convergence conditions and proves the convergence of the algorithm theoretically. The initial state learning principle promises fixed value at the beginning of each iteration. By using the closed-loop PD-type algorithm, the iterative input is convergent to a limiting trajectory, which can reduce fixed deviation on the basis of the D-type algorithm. The effectiveness of the closed-loop PD-type iterative learning control algorithm with fixed initial value is proved by the illustrative example.