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.

A Consensus Approach to Dynamic Programming / Laurini, Mattia; Consolini, Luca; Locatelli, Marco. - 50:1(2017), pp. 8435-8440. [10.1016/j.ifacol.2017.08.735]

A Consensus Approach to Dynamic Programming

Laurini, Mattia;Consolini, Luca;Locatelli, Marco
2017

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.
A Consensus Approach to Dynamic Programming / Laurini, Mattia; Consolini, Luca; Locatelli, Marco. - 50:1(2017), pp. 8435-8440. [10.1016/j.ifacol.2017.08.735]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2836806
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