A Consensus Approach to Dynamic Programming

Motivated by the finite element formulation of the Hamilton-Jacobi-Bellman (HJB) equation, we introduce a consensus algorithm to compute the solution of a class of optimization problems that can be solved with a fixed point iteration. The proposed algorithm reduces the computational cost in terms of elementary operations with respect to a complete fixed point iteration. We provide theoretical results on maximum error rate and on the convergence of the algorithm. As an application, we compute the minimum-time solution for a parking maneuver of a car-like vehicle, comparing the fixed point iteration with the consensus iteration.