Continuous and Discrete Composite Adjoints for the Hessian of the Lagrangian in Shooting Algorithms for Dynamic Optimization
Continuous and Discrete Composite Adjoints for the Hessian of the Lagrangian in Shooting Algorithms for Dynamic Optimization
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动态优化射击算法中拉格朗日 Hessian 的连续和离散复合伴随
DOI：
10.1137/080714518
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
W. Marquardt
中科院分区：
文献类型：
--
作者：
Hannemann;W. Marquardt
用直接法解决最优控制问题的一种方法是所谓的序贯法或单次打靶法。只有控制变量被离散化，产生一个非线性规划（NLP），可以用SQP或内点法求解。本文提出了一种新的方法来有效地提供的拉格朗日的Hessian的NLP。该算法是基于二阶伴随方法，并引入了新的复合伴随的概念，以减少计算工作量的海森评估。虽然这种贡献是为了简单起见，仅限于单次射击，但同样的方法也可以很容易地应用于多次射击。
One approach to solve optimal control problems by direct methods is the so-called sequential approach or single shooting. Only the control variables are discretized resulting in a nonlinear program (NLP) which can be solved with SQP or interior point methods. This paper presents a new methodology to efficiently provide the Hessian of the Lagrangian of that resulting NLP. The algorithm is based on the second-order adjoint method and introduces the novel concept of composite adjoints to reduce the computational effort of a Hessian evaluation. Though this contribution is for the sake of simplicity restricted to single shooting, the same methodology can also be easily applied to multiple shooting.