Weak Hamiltonian finite element method for optimal control problems
Weak Hamiltonian finite element method for optimal control problems
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DOI：
10.2514/3.20616
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发表时间：
1991-02
影响因子：
2.6
通讯作者：
D. Hodges;Robert R. Bless
中科院分区：
文献类型：
--
作者：
D. Hodges;Robert R. Bless
基于Hamilton弱原理的混合形式，提出了一种求解动力学和最优控制问题的时域有限元方法。混合形式的汉密尔顿的弱原理包含位移和动量作为主要变量，展开的节点值和简单的多项式形函数。然而，与其他形式的汉密尔顿原理不同，动量和位移的时间导数并不出现在其中;相反，只有虚动量和虚位移相对于时间微分。基于观察到的对偶存在于汉密尔顿的弱原理和变分原理的混合形式之间的经典最优控制问题，后者的时间有限元制定可以在一个相当简单的方式。在动力学和最优控制的几个著名的问题进行了说明。示例动力学问题涉及时间推进问题。作为最优控制的例子，基本的轨迹优化问题进行处理。
A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated.