Workshop I: High Dimensional Hamilton-Jacobi Methods in Control and Differential Games

March 30 - April 3, 2020

All times in this Schedule are Pacific Time (PT)

Monday, March 30, 2020 | |

8:45 - 9:00 | Welcome & Opening Remarks: Dean Miguel García-Garibay (Dean of Physical Sciences, UCLA) and Dima Shlyakhtenko (Director, IPAM) |

9:00 - 9:50 | Qi Gong (University of California, Santa Cruz (UC Santa Cruz)) Nonlinear optimal feedback control - a model-based learning approach |

10:00 - 10:30 | Break |

10:30 - 11:20 | Weinan E (Princeton University) High Dimensional PDEs: Theory and Numerical Algorithms |

11:30 - 12:00 | Break |

12:00 - 12:50 | Kyriakos G Vamvoudakis (Georgia Institute of Technology) Solving Game-Theoretic Hamilton-Jacobi Equations in a Model-Free Way |

1:00 - 2:00 | Lunch (on your own) |

2:00 - 2:50 | Arthur Krener (Naval Postgraduate School) Albrekht’s Method in Infinite Dimensions |

3:00 - 3:30 | Break |

3:30 - 4:20 | Claire Tomlin (University of California, Berkeley (UC Berkeley)) To Be Announced |

Tuesday, March 31, 2020 | |

9:00 - 9:50 | Helene Frankowska (Centre National de la Recherche Scientifique (CNRS)) Abnormal Hamilton-Jacobi Equations arising in Inﬁnite Horizon Problems |

10:00 - 10:30 | Break |

10:30 - 11:20 | Maurizio Falcone (Università di Roma “La Sapienza”) A discrete time Dynamic Programming approach on a tree structure for ﬁnite horizon optimal control problems |

11:30 - 12:00 | Break |

12:00 - 12:50 | Richard Tsai (University of Texas at Austin) Learning optimal strategies for line-of-sight based games |

1:00 - 2:00 | Lunch (on your own) |

2:00 - 2:50 | Yat Tin Chow (University of California, Riverside (UC Riverside)) A numerical method of solving high dimensional Hamilton-Jacobi equations with generalized Hopf-Lax formula |

3:00 - 3:30 | Break |

3:30 - 4:20 | Gang George Yin (Wayne State University) High-Dimensional HJBs: Mean-Field Limits and McKean-Vlasov Equations |

Wednesday, April 1, 2020 | |

9:00 - 9:50 | Christian Chilan (University of Illinois at Urbana-Champaign) Optimal Nonlinear Control Using Hamilton–Jacobi–Bellman Viscosity Solutions on Quasi-Monte Carlo Grids |

10:00 - 10:30 | Break |

10:30 - 11:20 | Jerome Darbon (Brown University) Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architectures |

11:30 - 12:00 | Break |

12:00 - 12:50 | Karl Kunisch (Universität Graz ) Solution Concepts for Optimal Feedback Control of Nonlinear Partial Differential Equations |

1:00 - 2:00 | Lunch (on your own) |

2:00 - 2:50 | Stanley Osher (University of California, Los Angeles (UCLA)) Solving high dimensional HJ equations using generalized Hopf-Lax formulas vs using Machine Learning. Presenting with Samy Wu Fung. |

3:00 - 3:30 | Break |

3:30 - 4:20 | Mac McEneaney (University of California, San Diego (UCSD)) Exact Conversion of Second-Order HJ PDE Problems to First-Order HJ PDE Problems |

Thursday, April 2, 2020 | |

9:00 - 9:50 | Wei Kang (Naval Postgraduate School) Data Development and Deep Learning for HJB Equations |

10:00 - 10:30 | Break |

10:30 - 11:20 | Alex Lin (University of California, Los Angeles (UCLA)) To Be Announced |

11:30 - 12:00 | Break |

12:00 - 12:50 | Mo Chen (Simon Fraser University) A Multi-Pronged Approach to Computational Challenges in HJ Reachability |

1:00 - 2:00 | Lunch (on your own) |

2:00 - 2:50 | Ivan Egorov (Yegorov) (North Dakota State University) Attenuation of the curse of dimensionality in continuous-time nonlinear optimal feedback stabilization problems |

3:00 - 3:30 | Break |

3:30 - 4:20 | Matthew Kirchner (University of California, Santa Barbara (UCSB)) Numeric Methods for Reachability with Applications to Vehicle Problems. |

Friday, April 3, 2020 | |

9:00 - 9:50 | Marianne Akian (Institut National de Recherche en Informatique et Automatique (INRIA)) Probabilistic max-plus schemes for solving Hamilton-Jacobi-Bellman equations |

10:00 - 10:30 | Break |

10:30 - 11:20 | Sylvia Herbert (University of California, Berkeley (UC Berkeley)) Scalability for Hamilton-Jacobi Reachability Analysis: Decomposition, Warm-Start Initialization, and Model Reduction |

11:30 - 12:00 | Break |

12:00 - 12:50 | Somil Bansal (University of California, Berkeley (UC Berkeley)) Scaling Hamilton-Jacobi Reachability Analysis for Robotics: Multi-agent Systems to Real-time Computation |