Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free method - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Control and Optimization Année : 2014

Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free method

Résumé

Max-plus based methods have been recently explored for solution of first-order Hamilton--Jacobi--Bellman equations by several authors. Among several max-plus numerical methods, McEneaney's curse-of-dimensionality--free method applies to the equations where the Hamiltonian takes the form of a (pointwise) maximum of linear/quadratic forms. In previous works of McEneaney and Kluberg, the approximation error of the method was shown to be $O(1/(N\tau))$+$O(\sqrt{\tau})$, where $\tau$ is the time discretization step and $N$ is the number of iterations. Here we use a recently established contraction result for the indefinite Riccati flow in Thompson's part metric to show that under different technical assumptions, still covering an important class of problems, the error is only of order $O(e^{-\alpha N\tau})+O(\tau)$ for some $\alpha>0$. This also allows us to obtain improved estimates of the execution time and to tune the precision of the pruning procedure, which in practice is a critical element of the method.

Dates et versions

hal-01112251 , version 1 (02-02-2015)

Identifiants

Citer

Zheng Qu. Contraction of Riccati flows applied to the convergence analysis of a max-plus curse of dimensionality free method. SIAM Journal on Control and Optimization, 2014, 52 (5), pp.2677-2709. ⟨10.1137/130906702⟩. ⟨hal-01112251⟩
96 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More