带有约束的新纯的多序分数最佳控制问题:QP和LP方法
1Aerospace and Mechanical Engineering Group Ronin Institute, Montclair, NJ 07043, USA.
ISA transactions
|August 23, 2024
概括
新的方法通过将它们转换成二次编程 (QP) 和线性编程 (LP) 模型来简化分数最佳控制问题. 这种方法消除了复杂的步骤,为分数控制系统提供了高效的解决方案.
科学领域:
- 控制理论 控制理论
- 应用数学 应用数学 应用数学
- 数字分析 数字分析
背景情况:
- 分数最佳控制问题 (FOCPs) 由于其复杂的数学公式,存在独特的挑战.
- 现有的方法往往需要复杂的步骤,如定义成本变量和推导最佳性条件,限制实际应用.
研究的目的:
- 引入新的,简化的方法来解决FOCPs与里曼-利乌维尔性能指数和卡普托衍生系统.
- 将FOCP转换为可解决的二次编程 (QP) 和线性编程 (LP) 模型.
- 为了使直接的数值解决方案使用标准解决器,如MATLAB的QP和LP解决器.
主要方法:
- 分数二进制的最佳控制问题被重新制定为使用一种新的状态控制参数化的QP问题.
- 分数线性最佳控制问题被建模为没有离散的LP问题.
- 引入了新的概念,包括分数边界和里曼-利乌维尔等比约束.
主要成果:
- 拟议的QP和LP模型允许使用MATLAB解决器直接计算最佳控制.
- 消除传统的复杂性,如成本变量定义和最佳性条件导出.
- 成功地应用于分数/整数线性控制问题,包括大爆炸和最小燃料系统.
结论:
- 开发的方法为解决一类FOCPs提供了显著的简化.
- QP和LP建模方法为最佳控制解决方案提供了高效和可访问的途径.
- 该研究表明,这些方法适用于现实世界的问题,如容器起重机和化疗药物调度.
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