Date of Original Version

1999

Type

Conference Proceeding

Abstract or Description

We investigate new approaches to dynamic-programming-based optimal control of continuous time-and-space systems. We use neural networks to approximate the solution to the Hamilton-Jacobi-Bellman (HJB) equation which is a first-order, nonlinear, partial differential equation. We derive the gradient descent rule for integrating this equation inside the domain, given the conditions on the boundary. We apply this approach to the “car-on-the-hill” which is a 2D highly nonlinear control problem. We discuss the results obtained and point out a low quality of approximation of the value function and of the derived control. We attribute this bad approximation to the fact that the HJB equation has many generalized solutions other than the value function, and our gradient descent method converges to one among these functions, thus possibly failing to find the correct value function. We illustrate this limitation on a simple 1D control problem

Comments

"©1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." "This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder."

Included in

Robotics Commons

Share

COinS
 

Published In

International Joint Conference on Neural Networks.