将数据辅助控制引入哈密顿系统,分治处理不确定性和控制优化。
On the Generalization of Data-Assisted Control in port-Hamiltonian Systems (DAC-pH)
- 用虚拟端口分离系统动态,分别处理内在动力学与外部输入不确定性
- 强化学习在可耗散部分学习最优控制策略,提升系统鲁棒性
- 保留系统结构特性,便于安全约束和状态可观测性分析
本文提出一种针对端口-哈密顿(pH)系统的假设性混合控制框架,采用基于数据辅助控制(DAC)的动态分解。系统演化分为两部分:右端(RHS)为处理最坏参数不确定性的固有哈密顿流,左端(LHS)为应对结构与参数不确定性的耗散/输入流。一个虚拟端口变量Π作为两部分的接口。非线性控制器管理内在哈密顿流,确定期望端口控制值Π_c;同时,强化学习应用于耗散/输入流,学习将Π_c映射到实际系统输入的最优策略。该混合方法有效应对RHS不确定性,同时保持系统内在结构。优势包括通过LHS控制器参数调节性能、利用Π提升AI可解释性、通过硬/软约束保证安全性与状态可达性、相比端到端方案降低学习假设类复杂度、并借助LHS先验知识与系统哈密顿量改善部分可观测下的状态/参数估计。论文详细阐述pH建模、推导分解机制,并展示模块化控制器架构。进一步研究了稳定性与鲁棒性分析与综合,为深入理论探索奠定基础。通过非线性摆的动力学模拟案例,验证了该方法在实证与现象层面的优势,适用于未来研究。
原文摘要 · Abstract (English)
This paper introduces a hypothetical hybrid control framework for port-Hamiltonian (p$\mathcal{H}$) systems, employing a dynamic decomposition based on Data-Assisted Control (DAC). The system's evolution is split into two parts with fixed topology: Right-Hand Side (RHS)- an intrinsic Hamiltonian flow handling worst-case parametric uncertainties, and Left-Hand Side (LHS)- a dissipative/input flow addressing both structural and parametric uncertainties. A virtual port variable $Π$ serves as the interface between these two components. A nonlinear controller manages the intrinsic Hamiltonian flow, determining a desired port control value $Π_c$. Concurrently, Reinforcement Learning (RL) is applied to the dissipative/input flow to learn an agent for providing optimal policy in mapping $Π_c$ to the actual system input. This hybrid approach effectively manages RHS uncertainties while preserving the system's inherent structure. Key advantages include adjustable performance via LHS controller parameters, enhanced AI explainability and interpretability through the port variable $Π$, the ability to guarantee safety and state attainability with hard/soft constraints, reduced complexity in learning hypothesis classes compared to end-to-end solutions, and improved state/parameter estimation using LHS prior knowledge and system Hamiltonian to address partial observability. The paper details the p$\mathcal{H}$ formulation, derives the decomposition, and presents the modular controller architecture. Beyond design, crucial aspects of stability and robustness analysis and synthesis are investigated, paving the way for deeper theoretical investigations. An application example, a pendulum with nonlinear dynamics, is simulated to demonstrate the approach's empirical and phenomenological benefits for future research.
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