Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control - Order conditions for symplectic partitioned Runge-Kutta schemes (second revision)

Bonnans JF; Laurent-Varin J

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Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control - Order conditions for symplectic partitioned Runge-Kutta schemes (second revision)

机译：辛分区Runge-Kutta方案的有序条件及其最优控制的应用-辛分区Runge-Kutta方案的有序条件（第二版）

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We derive order conditions for the discretization of (unconstrained) optimal control problems, when the scheme for the state equation is of Runge-Kutta type. This problem appears to be essentially the one of checking order conditions for symplectic partitioned Runge-Kutta schemes. We show that the computations using bi-coloured trees are naturally expressed in this case in terms of oriented free tree. This gives a way to compute them by an appropriate computer program.

机译：当状态方程的方案为Runge-Kutta类型时，我们推导了离散化（无约束）最优控制问题的阶条件。这个问题似乎本质上是检查辛分配的Runge-Kutta方案的阶数条件之一。我们表明，在这种情况下，使用有色树的计算自然是根据有向自由树表示的。这提供了一种通过适当的计算机程序来计算它们的方法。

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《Numerische Mathematik》 |2006年第1期|共10页
作者
Bonnans JF; Laurent-Varin J;
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正文语种 eng
中图分类数理逻辑、数学基础;
关键词
CONSTRAINED OPTIMAL-CONTROL;

机译：约束的最佳控制;

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专利

1. Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control - Order conditions for symplectic partitioned Runge-Kutta schemes (second revision) [J] . Bonnans JF, Laurent-Varin J Numerische Mathematik . 2006,第1期

机译：辛分区Runge-Kutta方案的有序条件及其最优控制的应用-辛分区Runge-Kutta方案的有序条件（第二版）
2. SIMULATION OF STOCHASTIC OPTIMAL CONTROL PROBLEMS WITH SYMPLECTIC PARTITIONED RUNGE-KUTTA SCHEME [J] . Fikriye Y?lmaz, Hacer ?z, Gerhard-Wilhelm Weber Dynamics of continuous, discrete & impulsive systems, Series B. Applications & algorithms . 2015,第5a6期

机译：具有辛分割的Runge-Kutta方案的随机最优控制问题的仿真
3. Computation of the eigenvalues of the Schrodinger equation by symplectic and trigonometrically fitted symplectic partitioned Runge-Kutta methods [J] . Monovasilis T, Kalogiratou Z, Simos TE Physics Letters, A . 2008,第5期

机译：用辛和三角拟合辛分割的Runge-Kutta方法计算Schrodinger方程的特征值
4. A Second Order Symplectic Partitioned Runge-Kutta Scheme for Maxwell's Equations [C] . HUANG Zhi-xiang, WU Xian-liang 2005 Asia-Pacific Microwave Conference Proceedings vol.3: Microwaves Make People Closer . 2005

机译：麦克斯韦方程组的二阶辛分区Runge-Kutta格式
5. Interpolation and error control schemes for algebraic differential equations using continuous implicit Runge-Kutta methods. [D] . Nguyen, Pham Hung. 1995

机译：使用连续隐式Runge-Kutta方法的代数微分方程插值和误差控制方案。
6. Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order [O] . Y. H. Cong, C. X. Jiang -1

机译：具有高代数和色散阶的对角隐辛辛格Runge-Kutta方法
7. Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control [O] . Bonnans, J. Frederic, Laurent-Varin, Julien 2004

机译：辛分区Runge-Kutta格式的有序条件计算及其在最优控制中的应用
8. Almost Symplectic Runge-Kutta Schemes for Hamiltonian Systems. [R] . Tan, X. 2004

机译：哈密顿系统的几乎辛Runge-Kutta方案。

Computation of order conditions for symplectic partitioned Runge-Kutta schemes with application to optimal control - Order conditions for symplectic partitioned Runge-Kutta schemes (second revision)

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