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


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a577142.pdf


Report Date : 23 Nov 2012


Pagination or Media Count : 23


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