Convergence Analysis of the Implicit Euler-discretization and Sufficient Conditions for Optimal Control Problems Subject to Index-one Differential-algebraic Equations
Convergence Analysis of the Implicit Euler-discretization and Sufficient Conditions for Optimal Control Problems Subject to Index-one Differential-algebraic Equations
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DOI：
10.1007/s11228-018-0471-x
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发表时间：
2019-06-01
影响因子：
1.6
通讯作者：
Gerdts, Matthias
中科院分区：
文献类型：
--
作者：
Martens, Bjoern;Gerdts, Matthias
对于受半显式形式的指数一微分代数方程影响的最优控制问题，我们讨论了考虑双范数差异的矫顽力条件形式的二阶充分条件。此外，我们引入了相关的 Riccati 型和 Legendre-Clebsch 条件，它们足以证明矫顽力条件的有效性。我们使用隐式欧拉离散化逼近最优控制问题，并应用Stetter通用收敛框架分析离散化最优控制问题的局部最小原理解的收敛性，这要求离散化方法是连续的、一致的和稳定的。
For optimal control problems subject to index-one differential-algebraic equations in semi-explicit form we discuss second order sufficient conditions in form of a coercivity condition taking into account the two-norm discrepancy. Furthermore we introduce a related Riccati-type and Legendre-Clebsch condition which are sufficient for the validity of the coercivity condition. Using the implicit Euler-discretization we approximate the optimal control problem and analyze the convergence of solutions of the local minimum principle for the discretized optimal control problem by applying the general convergence framework of Stetter, which requires the discretization method to be continuous, consistent, and stable.