题 目：Deep learning algorithms forHamilton-Jacobi-Bellman equations and optimal control

主讲人：陈国元副教授

时 间：2021年5月27日（周四）13：30-14：30

地 点：6号学院楼500

主办单位：yh86银河国际 浙江省2011“数据科学与大数据分析协同创新中心”

摘要：

In this talk,wegive an introduction toa deep learning method to approximate the stable manifolds of the Hamilton-Jacobi-Bellman(HJB) equations from nonlinearoptimalcontrol systems based on some mathematically rigorous asymptotic analysis, and then numerically compute optimal feedback controls. The algorithm is devised from geometric features of the stable manifolds, and relies on adaptive data generation by finding trajectories of two-point boundary value problems (BVP) for the associated Hamiltonian systems of the HJ equations. A number of samples are chosen on each trajectory according to exponential distribution with respect to the time. Some adaptive samples are selected near the points with large errors after the previous round of training. These may make the training of the neural network (NN) approximations more efficient.

Our algorithm is causality-free basically, hence it has a potential to apply to various high-dimensional nonlinear systems.Here we illustrate the effectiveness of our method by swinging up and stabilizing the Reaction Wheel Pendulums.Furthermore, such method can be applied to more complicated problems with high dimensional, e.g., 3D pendulum control, multi-agent, PDE control, etc.

主讲人简介：

陈国元，博士，毕业于南开大学陈省身数学研究所基础数学专业，现任yh86银河国际副教授，硕士生导师。主要研究领域为非线性分析，偏微分方程，动力系统，控制论，及相关的人工智能交叉应用。主持（完成）国家自然科学基金项目1项，浙江省自然科学基金目2项。以第一作者在《Journal of Differential Equations》、《Nonlinearity》、《Discrete and Continuous Dynamical Systems》、《Science China-Mathematics》、《Journal of Mathematical Physics》等国内外权威学术期刊发表论文10多篇。

欢迎各位老师和同学踊跃参加！