Exploiting Sparsity in the Direct Transcription Method for Optimal Control
Exploiting Sparsity in the Direct Transcription Method for Optimal Control
复制标题
利用直接转录方法中的稀疏性实现最佳控制
DOI：
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发表时间：
1999
影响因子：
2.2
通讯作者：
W. Huffman
中科院分区：
文献类型：
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作者：
J. Betts;W. Huffman
在直接转录法中，通过对状态变量和控制变量的离散化构造了最优控制问题的近似解。因此，控制问题被转化为具有有限数量变量的大规模约束优化问题。为了尽可能高效地求解离散化过程中产生的非线性规划问题，研究的重点是在相关的雅可比矩阵和Hessian矩阵为稀疏矩阵时求解底层NLP的方法。然而，很少有人关注雅可比矩阵和黑森矩阵的计算，特别是对于需要有限差分技术的应用。通常假设这些矩阵具有块结构，并且当使用标准有限差分估计时，此操作是一个主要的计算开销。本文描述了如何有效地构造雅可比矩阵和黑森矩阵，并利用问题固有的稀疏性。当原最优控制问题具有多个状态变量和控制变量时，该方法可以显著减少计算量。
In the direct transcription method an approximation to an optimal control problem is constructed by discretization of the state and control variables. The control problem is thus transcribed into a large scale constrained optimization problem with a finite number of variables. It is necessary to solve the nonlinear programming (NLP) problem produced by the discretization as efficiently as possible, and research has focused on methods for solving the underlying NLP when the relevant Jacobian and Hessian matrices are sparse. However little attention has been given to computing the Jacobian and Hessian, particularly for applications that require finite difference techniques. Typically it is assumed that these matrices have a block structure, and when standard finite difference estimates are used this operation is a major computational expense. This paper describes how to actually construct the Jacobian and Hessian matrices efficiently, and exploit sparsity inherent in the problem. This new technique can significantly reduce the computational costs when the original optimal control problem has many state and control variables.