通过多任务人工神经网络解决非线性和复杂的最佳控制问题
Ali Emami Kerdabadi1, Alaeddin Malek2
1Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, 14115-134, Iran.
Scientific reports
|July 14, 2025
概括
本研究介绍了一种新的多任务学习框架,使用神经网络来解决复杂的最佳控制问题. 该方法确保了哈密尔顿的最佳性,并通过流行病学和电网模型进行了验证.
科学领域:
- 计算数学 计算数学 计算数学
- 控制理论 控制理论
- 人工智能的人工智能
背景情况:
- 在各种科学和工程领域,最佳控制问题至关重要.
- 解决非线性和复杂的最佳控制问题仍然是一个重大挑战.
- 现有的方法往往在高维度和复杂的动态方面扎.
研究的目的:
- 提出一种新的多任务学习框架,用于解决非线性和复杂的最佳控制问题.
- 开发一种基于神经网络的统一方法,整合状态,控制和附加动态.
- 为了确保满足哈密尔顿的最佳性条件.
主要方法:
- 神经网络框架旨在统一状态,控制和附加动态.
- 哈密尔顿式是嵌入到神经网络结构使用Pontryagin最大原则.
- 提出了一种代算法,用于顺序和并行神经网络学习.
- 神经网络解决方案与最佳控制解决方案的融合已被证明.
主要成果:
- 提出的框架成功地解决了两个非线性复杂的最佳控制问题.
- 应用包括流行病学建模和电网稳定.
- 数字结果和图形表示证明了该方法的有效性.
- 通过神经网络的解决方案来满足哈密尔顿的最佳性条件.
结论:
- 多任务学习框架为复杂的最佳控制提供了一种有效的方法.
- 神经网络集成提供了一个强大的和融合的解决方案.
- 该方法对各种领域的现实应用具有前景.
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