On the optimal control of hybrid systems: analysis and zonal algorithms for trajectory and schedule optimization

M. S. Shaikh, P. Caines
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引用次数: 35

Abstract

In [M.S. Shaikh, et al., 2002, April 2003, 2003] a class of hybrid optimal control problems was formulated and a set of necessary conditions for hybrid system trajectory optimally was presented. Employing these conditions, we presented and analyzed a class of general hybrid maximum principle (HMP) based algorithms for hybrid systems optimization. In this paper it is first shown how the HMP algorithm class can be extended with discrete search algorithms, which find locally optimal switching schedules and their associated, switching times. We then present the notion of optimality zones; these zones have a well defined geometrical structure and once they have been computed (or approximated) they permit the exponential complexity search for optimal schedule sequences of the first method to be reduced to a complexity level which under reasonable hypotheses is proportional to the number of zones. The algorithm HMP[Z] which performs this optimization is essentially a minor modification of the HMP algorithm and permits one to reach the global optimum in a single run of the HMP[MCS] algorithm. The efficacy of the proposed algorithms is illustrated via computational examples.
混合系统的最优控制:轨迹与调度优化的分析与分区算法
在[硕士Shaikh, et al., 2002, April 2003,2003]构造了一类混合最优控制问题,给出了混合系统轨迹最优的一组必要条件。利用这些条件,提出并分析了一类基于混合极大值原理的混合系统优化算法。本文首先展示了如何将HMP算法类扩展为离散搜索算法,这些算法可以找到局部最优交换调度及其相关的交换时间。然后,我们提出了最优区域的概念;这些区域具有良好定义的几何结构,一旦它们被计算(或近似),它们允许将第一种方法的最优调度序列的指数复杂度搜索降低到在合理假设下与区域数量成正比的复杂性水平。执行此优化的算法HMP[Z]本质上是对HMP算法的一个小修改,并允许在HMP[MCS]算法的单次运行中达到全局最优。通过算例说明了所提算法的有效性。
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