A patchy Dynamic Programming scheme for a class of Hamilton-Jacobi-Bellman equations

Abstract

In this paper we present a new algorithm for the solution of Hamilton-Jacobi-Bellman equations related to optimal control problems. The key idea is to divide the domain of computation into subdomains which are shaped by the optimal dynamics of the underlying control problem. This can result in a rather complex geometrical subdivision, but it has the advantage that every subdomain is invariant with respect to the optimal dynamics, and then the solution can be computed independently in each subdomain. The features of this dynamics-dependent domain decomposition can be exploited to speed up the computation and for an efficient parallelization, since the classical transmission conditions at the boundaries of the subdomains can be avoided. For their properties, the subdomains are patches in the sense introduced by Ancona and Bressan [ESAIM Control Optim. Calc. Var., 4 (1999), pp. 445-471]. Several examples in two and three dimensions illustrate the properties of the new method.

Cited by in corpus (12)

• Adaptive Deep Learning for High-Dimensional Hamilton-Jacobi-Bellman Equations
• QRnet: optimal regulator design with LQR-augmented neural networks
• Causal Domain Restriction for Eikonal Equations
• Reliable optimal controls for SEIR models in epidemiology
• Deep neural network approximations for the stable manifolds of the Hamilton-Jacobi-Bellman equations
• Mitigating the Curse of Dimensionality: Sparse Grid Characteristics Method for Optimal Feedback Control and HJB Equations
• A parallel Heap-Cell Method for Eikonal equations
• A Hybrid control approach to the route planning problem for sailing boats
• A dynamic domain decomposition for a class of second order semi-linear equations
• Reconstruction of Independent Sub-domains for a class of Hamilton Jacobi Equations and its Application to Parallel Computing
• Error analysis for POD Approximations of infinite horizon problems via the Dynamic Programming approach
• An Efficient Policy Iteration Algorithm for Dynamic Programming Equations