The Hamilton-Jacobi-Bellman (HJB) equation provides a general method to solve optimal control problems. Since the HJB equation is a nonlinear partial differential equation, a closed form solution does not exist for the general case and various numerical procedures have been developed for its solution. Some recent approaches, after some simplifications, convert the problem into a fixed-point iteration. One problem related to the iteration is that its convergence speed is rather poor. We propose a Jacobi-like acceleration that allows to improve the convergence speed. As an application, we compute the minimum-time solution of a parking maneuver for a car-like vehicle with bounded velocity and steering angle.

A Jacobi-like acceleration for dynamic programming / Laurini, Mattia; Micelli, Piero; Consolini, Luca; Locatelli, Marco. - ELETTRONICO. - (2016), pp. 7371-7376. (Intervento presentato al convegno 55th IEEE Conference on Decision and Control, CDC 2016 tenutosi a ARIA Resort and Casino, usa nel 2016) [10.1109/CDC.2016.7799408].

A Jacobi-like acceleration for dynamic programming

Abstract

The Hamilton-Jacobi-Bellman (HJB) equation provides a general method to solve optimal control problems. Since the HJB equation is a nonlinear partial differential equation, a closed form solution does not exist for the general case and various numerical procedures have been developed for its solution. Some recent approaches, after some simplifications, convert the problem into a fixed-point iteration. One problem related to the iteration is that its convergence speed is rather poor. We propose a Jacobi-like acceleration that allows to improve the convergence speed. As an application, we compute the minimum-time solution of a parking maneuver for a car-like vehicle with bounded velocity and steering angle.
Scheda breve Scheda completa Scheda completa (DC)
2016
9781509018376
A Jacobi-like acceleration for dynamic programming / Laurini, Mattia; Micelli, Piero; Consolini, Luca; Locatelli, Marco. - ELETTRONICO. - (2016), pp. 7371-7376. (Intervento presentato al convegno 55th IEEE Conference on Decision and Control, CDC 2016 tenutosi a ARIA Resort and Casino, usa nel 2016) [10.1109/CDC.2016.7799408].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11381/2825151`
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