在残余误差下对非线性H2和H∞最佳控制问题进行稀疏连续近似
Zhong Wang1, Yan Li1, Yuqing Qiu1
1Department of Navigation, Guidance, and Control, Northwestern Polytechnical University, Xi'an, 710129, PR China.
ISA transactions
|December 9, 2023
概括
本研究介绍了一种稀疏连续近似方法,用于解决非线性最佳控制问题 (OCP),使用汉密尔顿-雅各比-贝尔曼 (HJB) 和汉密尔顿-雅各比-伊萨克斯 (HJI) 方程. 该方法提高了H2和H-infinity控制的融合和计算效率.
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:
- 顺序近似技术对于在最佳控制问题 (OCP) 中解决非线性汉密尔顿 - 雅各比 - 贝尔曼 (HJB) 和汉密尔顿 - 雅各比 - 艾萨克斯 (HJI) 方程至关重要.
- 由于非线性H2和H-infinity OCPs中的残余错误和计算复杂性,现有的方法面临着趋同的挑战.
研究的目的:
- 为无限地平线的非线性H2和H-infinity OCPs提出一个统一的表述和一种新的稀疏连续近似方法.
- 解决由剩余错误引起的融合问题,并减少现有数值方法的计算负担.
主要方法:
- 在非线性H2和H-无限OCP中,HJB/HJI部分微分方程 (PDEs) 的统一公式.
- 不线性PDEs转换为线性PDEs的序列,可通过初始值问题在点上解决.
- 纳入额外的约束,以确保结合,尽管残余错误.
- 利用稀疏的基于网格的拼接点和基础函数,以实现高效的数值实现.
主要成果:
- 提出的方法将复杂的非线性PDEs转换为一系列更简单的线性PDEs.
- 即使存在剩余错误,通过额外的约束来保证趋同.
- 使用稀疏网格技术实现了高效的数值实现.
- 模拟证明了拟议方法的有效性.
结论:
- 稀疏连续近似方法为解决非线性H2和H无限度OCP提供了有效和计算效率高的方法.
- 统一的表述和趋同保证使该方法在实际应用中具有稳定性.
- 使用稀疏网格显著提高了解决HJB/HJI方程的数值处理能力.
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