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首页> 外文期刊>Control Systems Technology, IEEE Transactions on >Flexible Piecewise Function Evaluation Methods Based on Truncated Binary Search Trees and Lattice Representation in Explicit MPC
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Flexible Piecewise Function Evaluation Methods Based on Truncated Binary Search Trees and Lattice Representation in Explicit MPC

机译：基于截断二叉搜索树和格表示的柔性分段函数评估方法

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摘要

Efficient methods for evaluation of piecewise functions defined over convex polyhedral partitions are proposed. As an important application, the explicit model predictive control problem is considered which requires a piecewise affine (PWA) control law to be evaluated online. The widely used binary search tree (BST) method is modified to be able to deal with a wider class of problems for which the BST method becomes prohibitive in terms of preprocessing time or memory requirements. The proposed method combines an orthogonal truncated binary search tree (OTBST) and lattice representation for PWA functions in a unified structure enjoying the advantages of both approaches. Both OTBST and Lattice-based OTBST (LOTBST) methods enable the designer to tradeoff between preprocessing time, storage requirement, and online computation time. The OTBST approach can be applied to more general partitions, e.g., discontinues and overlapping, while the LOTBST is directed towards more efficient evaluation of PWA functions, associated to the explicit MPC solutions. The key feature of the proposed methods is that the exact solution can be computed with predefined worst case online computation time guarantees. The computations are readily implementable using fixed-point arithmetic on a low cost microcontroller since there is no recursive accumulation of round-off errors, and the online algorithm is simple with a small footprint suitable for formal verification of correctness of implementation. Using several examples it is shown that the proposed LOTBST leads to a considerably less preprocessing time and memory requirement comparing to the pure BST and less online computation time comparing to the pure lattice representation.
机译：提出了一种有效的方法来评估凸多面体分区上定义的分段函数。作为一个重要的应用，考虑了显式模型预测控制问题，该问题需要分段仿射（PWA）控制律进行在线评估。修改了广泛使用的二叉搜索树（BST）方法，使其能够处理更广泛的问题，从预处理时间或内存要求的角度来看，BST方法变得无法实现。所提出的方法结合了正交截断的二进制搜索树（OTBST）和PWA函数的晶格表示，并具有统一的结构，同时兼有两种方法的优点。 OTBST和基于格子的OTBST（LOTBST）方法都使设计人员能够在预处理时间，存储需求和在线计算时间之间进行权衡。 OTBST方法可以应用于更通用的分区，例如不连续和重叠，而LOTBST则是针对与显式MPC解决方案相关的PWA功能的更有效评估。所提出的方法的关键特征是可以在预定义的最坏情况在线计算时间保证的情况下计算精确的解决方案。由于不存在舍入误差的递归积累，因此可以在低成本微控制器上使用定点算法轻松实现计算，并且在线算法简单，占用空间小，适合形式验证正确性。通过几个示例可以看出，与纯BST相比，建议的LOTBST导致预处理时间和内存需求明显减少，与纯晶格表示相比，在线计算时间更少。

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