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首页> 外文期刊>Control Systems Technology, IEEE Transactions on >A Comparison of the Embedding Method With Multiparametric Programming, Mixed-Integer Programming, Gradient-Descent, and Hybrid Minimum Principle-Based Methods
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A Comparison of the Embedding Method With Multiparametric Programming, Mixed-Integer Programming, Gradient-Descent, and Hybrid Minimum Principle-Based Methods

机译：嵌入方法与多参数编程，混合整数编程，梯度下降和基于混合最小原理的方法的比较

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摘要

In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical nonlinear optimization, has not been extensively compared with alternative solution approaches. The goal of this paper is thus to compare the embedding approach with multiparametric programming, mixed-integer programming [mixed integer programming (MIP), commercial (CPLEX)], and gradient-descent-based methods in the context of five recently published examples: 1) a spring-mass system; 2) moving-target tracking for a mobile robot; 3) two-tank filling; dc–dc boost converter; and 5) skid-steered vehicle. A sixth example, an autonomous switched 11-region linear system, is used to compare a hybrid minimum principle method and traditional numerical programming. For a given performance index (PI) for each case, cost and solution times are presented. It is shown that there are numerical advantages of the embedding approach: lower PI cost (except in some instances when autonomous switches are present), generally faster solution time, and convergence to a solution when other methods may fail. In addition, the embedding method requires no ad hoc assumptions (e.g., predetermined mode sequences) or specialized control models. Theoretical advantages of the embedding approach over the other methods are also described; guaranteed existence of a solution under mild conditions, convexity of the embedded hybrid optimization problem (under the customary conditions on the PI), solvability with traditional techniques (e.g., sequential quadratic programming) avoiding the combinatorial complexity in the number of modes/discrete variables of MIP, applicability to affine nonlinear systems, and no need to explicitly assign discrete/mode variables to autonomous switches. Finally, common misconceptions regarding the embedding approa- h are addressed, including whether it uses an average value control model (no), whether it is necessary to tweak the algorithm to obtain bang-bang solutions (no), whether it requires infinite switching to implement embedded solution (no), and whether it has real-time capability (yes).
机译：近年来，在一系列论文中已经开发了用于解决切换最优控制问题的嵌入方法。然而，尚未将嵌入方法（其将混合最优控制问题有利地转换为经典的非线性优化）与替代解决方案进行了广泛的比较。因此，本文的目的是在五个最近发布的示例的背景下，将嵌入方法与多参数编程，混合整数编程[混合整数编程（MIP），商用（CPLEX）]和基于梯度下降的方法进行比较： 1）弹簧质量系统； 2）移动机器人的运动目标跟踪； 3）两罐灌装； dc-dc升压转换器； 5）滑移式车辆。第六个例子是一个自治的11区切换线性系统，用于比较混合最小原理方法和传统的数值编程。对于每种情况下的给定性能指标（PI），将显示成本和解决时间。结果表明，嵌入方法具有数字上的优势：较低的PI成本（某些情况下存在自主交换机除外），通常更快的求解时间以及在其他方法可能失败时收敛到解决方案。另外，嵌入方法不需要 ad hoc 假设（例如预定模式序列）或专门的控制模型。还介绍了嵌入方法相对于其他方法的理论优势；在温和条件下保证解的存在，嵌入式混合优化问题的凸性（在PI的常规条件下），传统技术的可求解性（例如，顺序二次编程）避免了模式/离散变量的组合复杂性MIP，适用于仿射非线性系统，无需将离散/模式变量明确分配给自主开关。最后，解决了关于嵌入方法的常见误解，包括是否使用平均值控制模型（否），是否需要对算法进行调整以获取爆炸解（否），是否需要无限切换至实施嵌入式解决方案（否），以及是否具有实时功能（是）。

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