Vertex based calculation of explicit MPC laws
Vertex based calculation of explicit MPC laws
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基于顶点的显式 MPC 定律计算
DOI：
10.1109/acc.2012.6315197
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
M. Jost
中科院分区：
文献类型：
--
作者：
M. Mönnigmann;M. Jost
我们探索了一种新的方法来计算严格凸成本的线性二次MPC问题的显式解。其核心思想是计算状态空间多面体的顶点，并仅从顶点构造分段仿射控制律。我们表明，在顶点处计算的信息足以推断围绕给定顶点的控制律。因此，不需要计算构造和评估多面体内部的点。该方法只涉及简单的线性代数，如秩检验和求解线性方程组。关于面到面属性，不需要任何假设。该方法已成功地应用于一些标准的显式MPC的例子。
We explore a new approach to calculating explicit solutions of linear-quadratic MPC problems with strictly convex cost. The central idea is to calculate the vertices of the state space polytopes, and to construct the pieces of the piecewise affine control law from only the vertices. We show that information calculated at the vertex suffices to infer the control laws that surround a given vertex. Consequently, it is not necessary to computationally construct and evaluate points in the interior of the polytopes. The approach only involves simple linear algebra such as rank testing and solving linear systems of equations. No assumptions are necessary regarding the facet-to-facet property. The approach has successfully been applied to a number of standard explicit MPC examples.