A high-order semi-Lagrangian/finite volume scheme for Hamilton-Jacobi-Bellman-Isaacs equations

Maurizio Falcone (1) , Dante Kalise (2)

1 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
2 RICAM - Johann Radon Institute for Computational and Applied Mathematics

We present a numerical scheme for the approximation of Hamilton-Jacobi-Bellman-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.

Mots clés: Hamilton-Jacobi-Bellman-Isaacs equations; high-order schemes; semi-Lagrangian schemes; finite volume schemes; optimal control; differential games

Domaines: Optimisation et contrôle [math.OC]

Maurizio Falcone, Dante Kalise. A high-order semi-Lagrangian/finite volume scheme for Hamilton-Jacobi-Bellman-Isaacs equations. System Modeling and Optimization, System Modeling and Optimization (444), Springer, pp.105-117, 2014, IFIP Advances in Information and Communication Technology, 978-3-662-45503-6. ⟨hal-01122940⟩