一类极小能控制与广义样条函数

本文讨论由一般微分方程确定的时不变线性系统的一类极小能控制问题。首先,通过引入降阶逆向系统揭示了原系统的输入与输出是由某个积分-微分算子联系着的,并利用该算子建立了极小能控制与广义样条的联系;然后在对于输出端的一类较广泛的约束条件下,导出了其输出空间与文[1]的输出空间具有类似的构造性质,从而建立了与文[1]类似的投影公式与递推公式。

On a Class of Minimum Energy Controls and Generalized Splines

In this paper, the problem of minimum-energy control of linear systems determinedin terms of two differential operators is investigated. By introducing the reduced-orderinverse of the system discussed in this paper, we reveal that the input and output of thesystem are connected by a integro-differential operator. This operator is used to definethe correspondence between the optimal controls and certain generalized splines. Finally,the formulas and the recursive algorithm, similar to those in [1], for the optimal controlsand the generalized splines are obtained.