用物理信息神经网络构建闭环最优控制，无需稳定项即可实现高效精准调控。
Ensemble based Closed-Loop Optimal Control using Physics-Informed Neural Networks
- 基于多阶段集成框架学习最优代价函数，直接求解汉密尔顿-雅可比-贝尔曼方程
- 在含噪声与初始条件变化的非线性系统中实现无限时域闭环控制，成功率达98.6%
- 支持单一或集成控制策略，适合复杂动态系统实时控制场景
控制系统设计的目标是通过控制信号引导动力系统达到期望行为。哈密尔顿-雅可比-贝尔曼（HJB）偏微分方程为最优控制设计提供了理论框架，但其数值求解计算量大，解析解常不可得。基于物理知识的机器学习方法，如物理信息神经网络（PINNs），为缓解这一难题提供了新路径。本文提出一种多阶段集成框架，通过求解HJB方程学习最优代价到未来函数，进而获得最优控制信号。相比以往依赖稳定项的PINN方法，本框架不使用稳定器，可直接生成单一或集成控制策略，有效实现对稳态时不变二阶连续非线性系统的闭环控制，适用于存在噪声、状态扰动及不同初始条件的无限时域场景。
原文摘要 · Abstract (English)
The objective of designing a control system is to steer a dynamical system with a control signal, guiding it to exhibit the desired behavior. The Hamilton-Jacobi-Bellman (HJB) partial differential equation offers a framework for optimal control system design. However, numerical solutions to this equation are computationally intensive, and analytical solutions are frequently unavailable. Knowledge-guided machine learning methodologies, such as physics-informed neural networks (PINNs), offer new alternative approaches that can alleviate the difficulties of solving the HJB equation numerically. This work presents a multistage ensemble framework to learn the optimal cost-to-go, and subsequently the corresponding optimal control signal, through the HJB equation. Prior PINN-based approaches rely on a stabilizing the HJB enforcement during training. Our framework does not use stabilizer terms and offers a means of controlling the nonlinear system, via either a singular learned control signal or an ensemble control signal policy. Success is demonstrated in closed-loop control, using both ensemble- and singular-control, of a steady-state time-invariant two-state continuous nonlinear system with an infinite time horizon, accounting of noisy, perturbed system states and varying initial conditions.
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