ABSTRACT Explicit model predictive control (EMPC) moves the online computational burden of linear model predictive control (MPC) to offline computation by using multi-parametric programming which produces control laws defined over a set of polyhedral regions in the state space. The online computation of EMPC is to find the corresponding control law according to a given state, this is called the point location problem. This paper deals with efficient point location in larger polyhedral data sets. The authors propose a hybrid data structure, grid k-d tree (GKDT), which is constructed by the k-dimensional tree (k-d tree), hash table and binary search tree (BST). The main part of GKDT is a multiple branch tree which constructs subtrees by splitting the polyhedral region into several equal grids based on the k-d tree and is traversed by the hash function on each level. GKDT has a high search efficiency, even though it needs much more storage memory. A complexity analysis of the approach in the runtime and storage requirements is provided. Advantages of the method are supported by two examples in the paper.

中文翻译：

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多面体数据集中点位置的网格 Kd 树方法 - 显式 MPC 的应用

摘要 显式模型预测控制 (EMPC) 通过使用多参数编程将线性模型预测控制 (MPC) 的在线计算负担转移到离线计算，该编程产生在状态空间中的一组多面体区域上定义的控制律。EMPC 的在线计算就是根据给定的状态寻找相应的控制律，这称为点定位问题。本文处理较大多面体数据集中的有效点定位。作者提出了一种混合数据结构，网格kd树（GKDT），它由k维树（kd tree）、哈希表和二叉搜索树（BST）构建而成。GKDT的主要部分是一个多分支树，它基于kd树将多面体区域分裂成几个相等的网格来构造子树，并在每一层上通过哈希函数遍历。GKDT 具有很高的搜索效率，尽管它需要更多的存储内存。提供了该方法在运行时和存储要求方面的复杂性分析。论文中的两个例子支持了该方法的优点。