Numerical Solution of Hamilton-Jacobi Equations in High Dimension

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 23, 2012
Accession Number
ADA577142

Entities

People

  • Maurizio Falcone

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Anisotropy
  • Boundaries
  • Boundary Value Problems
  • Computations
  • Computer Programming
  • Construction
  • Control Systems
  • Convergence
  • Cooperative Games
  • Differential Equations
  • Dynamic Programming
  • Equations
  • Game Theory
  • Non-Cooperative Games
  • Parallel Computing
  • Partial Differential Equations

Readers

  • Calculus or Mathematical Analysis
  • Computational Fluid Dynamics (CFD)
  • Operations Research