一种基于注意力的方法,用于库普曼对非线性系统的建模和预测控制
Meixi Wang1, Xuyang Lou1, Baotong Cui1
1Institute of System Engineering, Jiangnan University, Wuxi 214122, China.
ISA transactions
|April 28, 2025
概括
我们介绍了一种新的深度学习方法,使用注意力机制来建模用于预测控制的非线性系统. 这种方法准确地构建了库普曼固有函数,比现有技术提高了预测性能.
科学领域:
- 控制理论 控制理论
- 机器学习 机器学习
- 动态系统 动态系统
背景情况:
- 对非线性系统的准确建模对于有效的预测控制至关重要.
- 传统的方法与非线性动态的复杂性作斗争.
- 识别非线性和线性系统之间的拓连接是一个关键的挑战.
研究的目的:
- 开发一种创新的基于注意力的深度学习方法,用于构建库普曼自身函数.
- 准确建模非线性系统,以提高预测控制.
- 确定非线性动力学与它们的线性化对应物之间的拓联的二次形态.
主要方法:
- 一种基于注意力的深度学习方法,利用具有条件亲缘合层的可逆神经网络.
- 使用注意力机制来捕捉复杂层次相互作用的差异形态的近似.
- 采用可逆解码神经网络与冷解码器用于精细的二元形态近似的替代策略.
主要成果:
- 库普曼固有函数和固有值的构造从学习的二元形态学.
- 通过多步骤的误差最小化开发一个带有优化的输入矩阵的升高线性系统.
- 与基于动态模式分解的方法相比,在数值示例和物理实验中展示了优异的预测性能.
结论:
- 提出的基于注意力的深度学习框架有效地模拟了用于预测控制的非线性系统.
- 该方法通过利用库普曼固有函数和扩展的强大的线性模型预测控制框架来实现卓越的预测准确性.
- 这种方法在现有的动态模式分解技术上为非线性系统分析和控制提供了显著的进步.
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