安全的物理信息机器学习以实现最佳预定义时间稳定:基于利亚普诺夫的方法
概括
这项研究为非线性系统引入了安全的预定义时间稳定性,确保状态保持边界,并在设定的时间内达到平衡. 一个新的基于物理的机器学习算法解决了最佳控制问题,以提高系统安全性和性能.
科学领域:
- 控制理论 控制理论
- 非线性动态系统非线性动态系统
- 优化优化 优化优化
背景情况:
- 在有限的,预先确定的时间内定义稳定性对于许多工程应用至关重要.
- 确保系统轨迹保持在安全运行范围内,是控制设计的一个关键挑战.
- 最佳控制旨在尽量减少性能指标,同时满足系统约束.
研究的目的:
- 介绍并定义参数依赖的非线性系统的"安全预定义时间稳定性".
- 开发一个基于Lyapunov的定理,以保证安全的预定义时间稳定性.
- 使用反控制器解决最佳安全的预定义时间稳定问题.
主要方法:
- 使用Lyapunov函数,制定安全的预定义时间稳定条件.
- 反控制器的合成,以实现闭环安全的预定义时间稳定性.
- 运用基于物理的机器学习来解决稳定状态的汉密尔顿-雅各比-贝尔曼 (HJB) 方程以获得最佳性.
主要成果:
- 建立了一个Lyapunov定理,为安全的预定义时间稳定提供了足够的条件.
- 控制器是合成的,以确保闭环系统具有安全的预定义时间稳定性.
- 一个基于物理的机器学习算法有效地学习了HJB方程的最佳稳定解决方案.
结论:
- 拟议的框架允许在预先定义的时间内设计可保证安全性和融合的系统控制器.
- 开发的算法提供了解决非线性系统中复杂的最佳控制问题的实用方法.
- 模拟结果验证了基于物理的机器学习方法在安全的预定义时间稳定方面的有效性.
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