Optimal control of differential‐algebraic equations from an ordinary differential equation perspective
Optimal control of differential‐algebraic equations from an ordinary differential equation perspective
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DOI：
10.1002/oca.2481
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发表时间：
2018-06
影响因子：
1.8
通讯作者：
A. Ilchmann;Leslie Leben;Jonas Witschel;K. Worthmann
中科院分区：
文献类型：
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作者：
A. Ilchmann;Leslie Leben;Jonas Witschel;K. Worthmann
我们研究常规线性微分代数系统的最优控制问题（OCP）。为此，我们引入了输入索引，一方面它允许用类卡尔曼矩阵来表征一致初始值的空间，另一方面允许控制的必要平滑属性。后者对于从数字角度解决问题至关重要。此外，我们推导了一个增强系统，作为使用常微分方程最优控制中众所周知的工具来分析 OCP 的关键。输入索引和增广系统的新概念提供了易于检查的充分条件，确保阶段成本与微分代数系统一致。
We study the optimal control problem (OCP) for regular linear differentialalgebraic systems. To this end, we introduce the input index, which allows, on the one hand, to characterize the space of consistent initial values in terms of a Kalman‐like matrix and, on the other hand, the necessary smoothness properties of the control. The latter is essential to make the problem accessible from a numerical point of view. Moreover, we derive an augmented system as the key to analyze the OCP with tools well known from optimal control of ordinary differential equations. The new concepts of the input index and the augmented system provide easily checkable sufficient conditions, which ensure that the stage costs are consistent with the differential‐algebraic system.