论文标题
汉密尔顿 - 雅各比 - 贝尔曼PDES的深度学习求解器的数据驱动初始化
Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs
论文作者
论文摘要
与非线性二次调节剂（NLQR）问题相关的汉密尔顿 - 雅各比 - 贝尔曼部分微分方程（HJB PDE）的近似的深度学习方法。首先使用了依赖于州的Riccati方程控制法来生成一个梯度增强的合成数据集，以进行监督学习。根据HJB PDE的残差，最小化损耗函数的最小化成为一个温暖的开始。监督学习和残留最小化的结合避免了虚假的解决方案，并减轻了仅监督学习方法的数据效率低下。数值测试验证了所提出方法的不同优势。
A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first used to generate a gradient-augmented synthetic dataset for supervised learning. The resulting model becomes a warm start for the minimization of a loss function based on the residual of the HJB PDE. The combination of supervised learning and residual minimization avoids spurious solutions and mitigate the data inefficiency of a supervised learning-only approach. Numerical tests validate the different advantages of the proposed methodology.
