Solution of Two-Point Boundary-Value Problems Using Lagrange Implicit Function Theorem
Solution of Two-Point Boundary-Value Problems Using Lagrange Implicit Function Theorem
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DOI：
10.2514/1.43024
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发表时间：
2009-09
影响因子：
2.6
通讯作者：
M. Majji;J. Turner;J. Junkins
中科院分区：
文献类型：
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作者：
M. Majji;J. Turner;J. Junkins
两点边值问题(TPBVP)是多种多物理建模和控制分析的重要组成部分，包括但不限于航空航天工程的制导、导航和控制问题。到目前为止，已经开发了几种求解TPBVP的技术，而每种技术的核心都是牛顿方法(参见。Bryson和Ho[1])。在这篇注记中，我们提出了一种隐式导数牛顿打靶法来求解一类最优控制问题中最常遇到的两点边值问题。为了推动本文的发展，考虑了最优控制问题。
TWO-POINT boundary-value problems (TPBVPs) form an important ingredient in the solution of several multiphysics modeling and control analyses, including but not limited to guidance, navigation, and control problems of aerospace engineering. Several techniques to solve TPBVPs have been developed so far and the workhorse at the core of each has been Newton’s method (cf. Bryson and Ho [1]). In this Note, we present an implicit derivative Newton’s shooting method to solve a class of two-point boundary-value problems, most often encountered in the solution of optimal control problems. To motivate the developments of the paper, consider the optimal control problem