Physics-Informed Neural Networks (PINN) refer to recently defined a class of machine learning algorithms where the learning process for both regression and classification tasks is constrained to satisfy differential equations derived by the straightforward application of known physical laws. Indeed, Deep Neural Networks (DNN) have been successfully employed to solve a variety of ODEs and PDEs arising in fluid mechanics, quantum mechanics, just to mention a few. Optimal control problems, i.e. finding a feasible control that minimize a cost functional while satisfying physical, state and control constraints, are generally difficult to solve and one may nned to resort to specialized numerical methods. The application of Pontryagin minimum principle generates a complex two-point boundary value problem that is very sensitive to the initial guess (“curse of complexity”). The application of dynamic programming principles generate a high-dimensional PDE named Hamilton-Jacobi-Bellman (“Curse of Dimensionality”). In this talk we show the PINN can be employed to solve optimal control problems by tackling their solution using deep and/or shallow NNs. We show that such methods can be coupled with the Theory of Functional Connections (TFC, by Mortari et al.) to create numerical frameworks that generate efficient and accurate solutions with potential for real-time applications.
03/09/2020
Bio
Roberto Furfaro is currently Full Professor at the Department of Systems and Industrial Engineering, Department of Aerospace and Mechanical Engineering, University of Arizona. He is also the Director of the Space Situational Awareness Arizona (SSA-Arizona) Initiative and currently the PI of the AFRL Cooperative Agreement. He published more than 60 peer-reviewed journal papers and more than 200 conference papers and abstracts. He is technical member of the AIAA Astrodynamics Committee, AAS Space Surveillance Committee, and former member of the AAS Space Flight Mechanics Committee. In 2010-2016, he was the systems engineering lead for the Science Processing and Operations Center of the NASA OSIRIS REx Asteroid Sample Return Mission. He is currently the lead for the target follow-up team of the recently selected NASA NEO Surveyor Mission. For his contribution to space missions, the asteroid 2003 WX3 was renamed 133474 Roberto Furfaro.