控制混乱的地图使用下一代水库计算
Robert M Kent1, Wendson A S Barbosa1, Daniel J Gauthier1,2
1Department of Physics, The Ohio State University, 191 W. Woodruff Ave., Columbus, Ohio 43210, USA.
Chaos (Woodbury, N.Y.)
|February 2, 2024
概括
本研究介绍了一种新的控制器,将非线性系统控制与预测动态系统的储计算合并为预测动态系统. 该方法有效地控制混乱系统,使用最小的数据,显示对噪声和错误的稳定性.
科学领域:
- 动态系统和控制理论.
- 机器学习和人工智能的人工智能
- 非线性动力学是一种非线性动力学.
背景情况:
- 动态系统具有复杂的行为,难以预测和控制.
- 传统的控制方法经常与混乱或高维系统作斗争.
- 储计算提供了一个强大的框架来建模和预测来自动态系统的时间序列数据.
研究的目的:
- 开发和评估一种新的控制器,将非线性系统控制与水库计算集成在一起.
- 为了证明控制器在管理复杂的动态系统中的有效性,特别是混乱的Hénon地图.
- 在数据要求,速度和稳定性方面评估控制器的性能.
主要方法:
- 结合了非线性系统控制技术和下一代储计算.
- 采用一个混乱的亨农地图作为控制任务的基准.
- 使用最小的数据集 (十个数据点) 训练控制器.
主要成果:
- 在不稳定的固定点和更高阶周期轨道之间成功控制了亨农地图.
- 实现了对任意所需状态的稳定.
- 在单个代中证明了对所需轨迹的控制.
- 展示了控制器对噪声和建模错误的稳定性.
结论:
- 拟议的控制器,合并非线性控制和储计算,对动态系统非常有效.
- 这种方法需要最小的训练数据,并表现出快速,稳健的性能.
- 这种方法推进了机器学习在控制复杂的非线性系统中的应用.
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