We present a numerical scheme for the approximation of Hamilton-Jacobi-Isaacs equations related to optimal control problems and differential games. In the first case, the Hamiltonian is convex with respect to the gradient of the solution, whereas the second case corresponds to a non convex (minmax) operator. We introduce a scheme based on the combination of semi-Lagrangian time discretization with a high-order finite volume spatial reconstruction. The high-order character of the scheme provides an efficient way towards accurate approximations with coarse grids. We assess the performance of the scheme with a set of problems arising in minimum time optimal control and pursuit-evasion games.
A high-order semi-Lagrangian/finite volume scheme for Hamilton-Jacobi- Isaacs equations / Falcone, Maurizio; D., Kalise. - STAMPA. - 443(2014), pp. 105-117. [10.1007/978-3-662-45504-3_10].
A high-order semi-Lagrangian/finite volume scheme for Hamilton-Jacobi- Isaacs equations
FALCONE, Maurizio;
2014
Abstract
We present a numerical scheme for the approximation of Hamilton-Jacobi-Isaacs equations related to optimal control problems and differential games. In the first case, the Hamiltonian is convex with respect to the gradient of the solution, whereas the second case corresponds to a non convex (minmax) operator. We introduce a scheme based on the combination of semi-Lagrangian time discretization with a high-order finite volume spatial reconstruction. The high-order character of the scheme provides an efficient way towards accurate approximations with coarse grids. We assess the performance of the scheme with a set of problems arising in minimum time optimal control and pursuit-evasion games.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
