Algorithms of Data Development For Deep Learning and Feedback Design

Abstract

Recent research reveals that deep learning is an effective way of solving high dimensional Hamilton-Jacobi-Bellman equations. The resulting feedback control law in the form of a neural network is computationally efficient for real-time applications of optimal control. A critical part of this design method is to generate data for training the neural network and validating its accuracy. In this paper, we provide a survey of existing algorithms that can be used to generate data. All the algorithms surveyed in this paper are causality-free, i.e., the solution at a point is computed without using the value of the function at any other points. At the end of the paper, an illustrative example of optimal feedback design using deep learning is given.

arXiv comment15 pages, 1 figure

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Cited by in corpus (5)

• Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning
• Neural Network Optimal Feedback Control with Guaranteed Local Stability
• Deep neural network approximations for the stable manifolds of the Hamilton-Jacobi-Bellman equations
• Neural network optimal feedback control with enhanced closed loop stability
• Progressive Optimal Path Sampling for Closed-Loop Optimal Control Design with Deep Neural Networks