The optimal control theory is applied to investigate interpolating splines associated with arbitrary linear differential operators. The differential operator interpolating splines are considered a linear optimal control problem; the structure and the continuity property of differential operator interpolating splines are derived from the necessary conditions of the optimal control with constrained states. This method not only facilitates the derivation of the well-known structure and the continuity property of differential operator interpolating splines, but also obtains as well the jerk formula at nodes of splines after the operation of the differential operator, further revealing the relation between the differential operator interpolating splines and the optimal control and providing a new approach to the study of structural properties for obstructed operator interpolating splines.%本文将最优控制理论用于微分算子广义插值样条构造性质的研究.通过将微分算子插值样条描述成线性最优控制问题,用带状态约束的一类最优控制的必要条件推导出微分算子插值样条的构造与连续性质.这一方法不仅较容易地导出了微分算子插值样条熟知的构造和连续性质,而且还得到了样条经过微分算子作用后在节点处的跃度公式.进一步揭示了微分算子插值样条与最优控制理论的联系,为带障碍的算子插值样条构造性质的研究提供了新的方法.
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