Advancement: A Deep Learning Framework for Optimal Feedback Control of High-Dimensional Nonlinear Systems

Speaker Name: 
Tenavi Nakamura-Zimmerer
Speaker Title: 
PhD Candidate (Advisor: Qi Gong)
Speaker Organization: 
Applied Mathematics
Start Time: 
Friday, October 11, 2019 - 1:30pm
Location: 
Engineering 2, Room 475
Organizer: 
Professor Qi Gong

Abstract:

Computing optimal feedback controls for nonlinear dynamical systems generally requires numerically solving Hamilton-Jacobi-Bellman (HJB) equations. This is notoriously difficult when the state dimension is large. Existing strategies for high-dimensional problems generally rely on specific, restrictive problem structures, are valid only locally around some nominal trajectory, or provide no easy way to validate the solution accuracy. To address these challenges, we introduce a data-driven method to approximate semi-global solutions to HJB equations for general high-dimensional nonlinear systems and compute optimal feedback controls in real-time. We model solutions to HJB equations with neural networks (NNs) trained on data generated without discretizing the state space. Training is made more effective and data-efficient by leveraging the known physics of the problem and using the partially-trained NN to aid in adaptive data generation. We demonstrate the effectiveness of our method by learning solutions to HJB equations corresponding to the attitude control of a six-dimensional nonlinear rigid body, and nonlinear systems of dimension up to 30 arising from the stabilization of a Burgers'-type partial differential equation. The trained NNs are then used for real-time optimal feedback control of these systems.

Event Type: 
Event
Advisor: 
Professor Qi Gong