Exploiting Sparse Structures in Nonlinear Model Predictive Control with Hypergraphs
Exploiting Sparse Structures in Nonlinear Model Predictive Control with Hypergraphs
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DOI：
10.1109/aim.2018.8452378
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Christoph Rösmann;Maximilian Krämer;Artemi Makarow;F. Hoffmann;T. Bertram
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文献类型：
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作者：
Christoph Rösmann;Maximilian Krämer;Artemi Makarow;F. Hoffmann;T. Bertram
本文提出了一个求解MPC问题的超图公式。超图方法在导数计算中利用了稀疏结构。因此，与密集公式相比，它在多次射击，搭配和完全离散化方法的情况下计算效率更高。实时优化的最新进展依赖于自动微分（AD）来计算导数。在两个基准控制问题上，对MPC变体与超图和AD进行了广泛的分析。尽管AD需要计算开销来建立问题结构，但在每次迭代中求解非线性程序的速度很快。超图方法的开销可以忽略不计，求解阶段的计算工作量不如AD，但与AD相当。这一观察结果有利于具有非静态问题结构的MPC问题的超图表示。
This paper proposes a hypergraph formulation for solving MPC problems. The hypergraph approach exploits the sparse structure in the calculation of derivatives. It is therefore computationally more efficient in case of multiple-shooting, collocation and full-discretization methods compared to a dense formulation. Recent advances in realtime optimization rely on automatic differentiation (AD) to compute derivatives. An extensive analysis compares MPC variants with both hypergraph and AD on two benchmark control problems. Even though AD requires a computational overhead to set up the problem structure, solving the nonlinear program at each iteration is fast. The overhead in the hypergraph approach is negligible, and computational effort in the solving phase is inferior but comparable to AD. This observation favors the hypergraph representation for MPC problems with non-static problem structure.