A Consensus Approach to Dynamic Programming. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Laurini, Mattia; Consolini, Luca; Locatelli, Marco
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 8435
• Page End: 8440
• Publication Date: 2017-07
• Subjects: dynamic programming -- communication networks -- directed graphs -- optimization problems -- nonlinear systems -- numerical methods -- convergence proofs; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.735
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: 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.