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26 results on '"Carlini, E"'

26. An efficient algorithm for Hamilton–Jacobi equations in high dimension

Author

Roberto Ferretti, Elisabetta Carlini, Maurizio Falcone, Carlini, E, Falcone, M, and Ferretti, Roberto

Subjects
Optimal control, problem viscosity solution, optimal trajectory, differential game, Jacobi equation, problem viscosity solution, Mathematical optimization, optimal trajectory, Jacobi equation, Numerical analysis, General Engineering, Optimal control, Hamilton–Jacobi equation, Theoretical Computer Science, Range (mathematics), Computational Theory and Mathematics, Dimension (vector space), Modeling and Simulation, Differential game, Applied mathematics, differential game, Computer Vision and Pattern Recognition, Viscosity solution, Software, Interpolation, Mathematics
Abstract

In this paper we develop a new version of the semi-Lagrangian algorithm for first order Hamilton–Jacobi equations. This implementation is well suited to deal with problems in high dimension, i.e. in Rm with m ≥ 3, which typically arise in the study of control problems and differential games. Our model problem is the evolutive Hamilton–Jacobi equation related to the optimal control finite horizon problem. We will give a step-by-step description of the algorithm focusing our attention on two critical routines: the interpolation in high dimension and the search for the global minimum. We present some numerical results on test problems which range from m = 3 to m = 5 and deal with applications to front propagation, aerospace engineering, ecomomy and biology.

Published
2004

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