论文标题
QRNET：具有LQR增强神经网络的最佳调节器设计
QRnet: optimal regulator design with LQR-augmented neural networks
论文作者
论文摘要
在本文中，我们提出了一种新的计算方法，用于设计用于高维非线性系统的最佳调节器。所提出的方法利用物理知识的机器学习来解决在最佳反馈控制中产生的高维汉密尔顿 - 雅各比 - 贝尔曼方程。具体而言，我们通过神经网络增强线性二次调节器来处理非线性。我们在生成的数据上训练增强模型，而无需离散状态空间，从而使其适用于高维问题。我们使用拟议的方法来设计候选最佳调节剂以进行不稳定的汉堡方程，并通过此示例证明了与现有的神经网络配方相比提高了鲁棒性和准确性。
In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman equations arising in optimal feedback control. Concretely, we augment linear quadratic regulators with neural networks to handle nonlinearities. We train the augmented models on data generated without discretizing the state space, enabling application to high-dimensional problems. We use the proposed method to design a candidate optimal regulator for an unstable Burgers' equation, and through this example, demonstrate improved robustness and accuracy compared to existing neural network formulations.
