论文标题
直接拍摄方法等同于间接方法
A Direct Shooting Method is Equivalent to an Indirect Method
论文作者
论文摘要
我们表明，在某些一阶条件的意义上，直接拍摄方法在数学上等同于间接方法。得出了与直接射击方法与间接方法的等效性有关的特定数学公式。我们还表明，如果将参数化的最佳控制问题简单地修补为非线性编程求解器，则理论在等效性不一定会转化为实际等效性。为这种修补的非线性编程方法的成功和失败提供了数学解释。为了更稳定地生成正确的解决方案，必须通过哈密顿编程方法更换或增强传统直接方法中使用的非线性编程求解器。本文得出的理论结果进一步增强了计算最佳控制，深度学习和自动分化之间的联系。
We show that a direct shooting method is mathematically equivalent to an indirect method in the sense of certain first-order conditions. Specific mathematical formulas pertaining to the equivalence of a direct shooting method with an indirect method are derived. We also show that a theoretical equivalence does not necessarily translate to practical equivalence if the parameterized optimal control problem is simply patched to a nonlinear programming solver. A mathematical explanation is provided for the successes and failures of such patched nonlinear programming methods. In order to generate the correct solution more consistently, the nonlinear programming solver used in a traditional direct method must be replaced or augmented by a Hamiltonian programming method. The theoretical results derived in this paper further strengthen the connections between computational optimal control, deep learning and automatic differentiation.
