基于学习的最佳边界控制,用于具有执行器动态的抛物线分布式参数系统
Jingyi Sun1, Biao Luo1, Xiaodong Xu1
1School of Automation, Central South University, Changsha 410083, China.
ISA transactions
|November 28, 2024
概括
本研究介绍了一种新的数据驱动的最佳控制器,用于具有执行器动态的复杂部分微分方程 (PDE) 和普通微分方程 (ODE) 系统,实现稳定的控制. 该方法确保了通过模拟验证的合PDE-ODE系统的统一无边形稳定性.
科学领域:
- 控制理论 控制理论
- 应用数学 应用数学 应用数学
- 化学工程是化学工程的重要组成部分.
背景情况:
- 研究合的部分微分方程 (PDE) 和普通微分方程 (ODE) 系统,这些系统在建模复杂过程中很常见.
- 解决了影响边界条件的执行器动态的挑战,这是控制设计中的一个困难方面.
- 突出了在结合的希尔伯特空间中优化无限维的性能指数的复杂性.
研究的目的:
- 为结合PDE-ODE系统开发一种新的数据驱动的边界最佳控制器,其中包含执行器动力学.
- 为了应对ODE执行器动态中的边界输入的挑战,并简化边界条件的减少.
- 首次在诺曼边界条件下解决与执行器动力学合的PDE-ODE系统在诺曼边界条件下的最佳控制问题.
主要方法:
- 将合的PDE-ODE系统重构为具有同质边界条件的系统,并推导出其无限维的单一扰动形式.
- 设计了一个无模型的代学习最佳控制算法,使用加权剩余技术的批评者和演员网络.
- 采用任意控制策略来增强探索和放松持久激发条件.
主要成果:
- 成功解决了在诺曼边界条件下与执行器动力学合的PDE-ODE系统的最佳控制问题.
- 证明了闭环系统在无限维希尔伯特空间中的均非对称稳定性,用于每个学习代.
- 通过对扩散反应过程的模拟,验证了拟议方法的有效性.
结论:
- 开发的数据驱动的代学习最佳控制算法有效地处理与执行器动力学合的PDE-ODE系统.
- 这种方法确保了统一的非对称稳定性,提供了强大的控制解决方案.
- 这项工作在控制具有挑战性的动态和边界条件的复杂系统方面取得了重大进展.
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