摘要:
本文给出了方块脉冲函数的一些运算性质.利用这些性质求解线性时变系统的状态方程
和基于二次型性能指标的最优控制规律,得出了便于应用的均匀分段恒定解答.较沃尔什函
数逼近法容易导出形式简明的递推算法,且子区间的分段数可选取任意整数,因而节省计算机
内存和机时,有助于提高计算和控制的精度.
Abstract:
Some useful operational properties of the block-pulse functions are developed. By
applying these properties to the analysis and optimal control of time-varying linear systems
with a quadratic performance index, the piecewise constant solutions equally distributed,
which are simple in form and convenient for use or implementation, are
obtained. Another advantage of this method is that any positive integer can be chosen
as the number of sub-intervals, whereas in the case of Walsh function approximation the
choice can only be made from 2, 4, 8, 16, 32, and so on. Therefore, in many practical
situations computation and control of higher precision can be achieved without expending
excessive memory capacity and calculating time. The recursive algorithms of the solutions
are illustrated by appropriate examples.
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