Accession Number:

ADA577142

Title:

Numerical Solution of Hamilton-Jacobi Equations in High Dimension

Descriptive Note:

Final technical rept. 31 Oct 2009-31 Oct 2012

Corporate Author:

UNIVERSITA DI ROMA LA SAPIENZA ROMA (ITALY) DIPARTIMENTO DI MATEMATICA

Personal Author(s):

• Falcone, Maurizio

Report Date:

2012-11-23

Pagination or Media Count:

23.0

Abstract:

The solution of nonlinear optimal control problems and the computation of optimal control laws is a difficult task that requires a fast response in many real applications. During the three years of the AFOSR grant we attacked the problem via the numerical solution of Hamilton-Jacobi equations describing the value function. In the framework of viscosity solutions, the value function is uniquely characterized and it allows for the computation of optimal controls in feedback form. Unfortunately, from a computational point of view, solving real problems in high dimension via Hamilton-Jacobi equations is still a huge task and efficient algorithms are required. Our research has been devoted to the development of new Fast Marching methods and domain decomposition techniques or a combination of them in order to improve CPU times, avoid useless computations and reduce memory requirements.

Descriptors:

• *EQUATIONS
• ALGORITHMS
• HAMILTONIAN FUNCTIONS
• NUMERICAL METHODS AND PROCEDURES

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE