Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-14T13:18:45.647Z Has data issue: false hasContentIssue false
  • English
  • Français

Minimizing the fuel consumption of a vehicle from the Shell Eco-marathon: a numerical study∗

Published online by Cambridge University Press:  21 February 2013

Sophie Jan
Sophie Jan*
Affiliation:
Université de Toulouse & CNRS, Institut de Mathématiques de Toulouse, UMR 5219, 31062 Toulouse Cedex 9, France. sophie.jan@math.univ-toulouse.fr
Get access

Abstract

We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we use once again a nonlinear programming approach.

Keywords

Optimal controlsingular arcsnonlinear programmingcontinuation methodindirect multiple shooting
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 2 , April 2013 , pp. 516 - 532
Copyright
© EDP Sciences, SMAI, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bertrand, R. and Epenoy, R., New smoothing techniques for solving bang-bang optimal control problems – Numerical results and statistical interpretation. Optim. Control Appl. Methods 23 (2002) 171–197. Google Scholar
J.F. Bonnans and F. Silva, Error estimates for the logarithmic barrier method in linear quadratic stochastic optimal control problems. Technical Report, INRIA RR 7455 (2010).
Bonnans, F., Martinon, P. and Trélat, E., Singular arcs in the generalized Goddard’s problem. J. Optim. Theory Appl. 139 (2008) 439–461. Google Scholar
J.-B. Hiriart-Urruty, Les mathématiques du mieux faire, Ellipses. La commande optimale pour les débutants 2 (2008).
L.M. Hocking, Optimal control, An introduction to the theory with applications, Oxford Applied Mathematics and Computing Science Series. The Clarendon Press Oxford University Press (1991).
A. Locatelli, Optimal control, An introduction. Birkhäuser Verlag (2001).
A. Merakeb, F. Messine and M. Aidene, On minimizing the energy consumption of an electrical vehicle. Research Report RT-APO-11-4, IRIT, Université Paul Sabatier, Toulouse (2011).
Robbins, H.M., A generalized Legendre-Clebsch condition for the singular cases of optimal control. IBM J. Research Devel. 11 (1967) 361–372. Google Scholar
Sager, S., Bock, H. G., Diehl, M., Reinelt, G. and Schlöder, J. P., Numerical methods for optimal control with binary control functions applied to a Lotka-Volterra type fishing problem, in Recent advances in optimization, Lect. Notes Econ. Math. Syst. 563 (2006) 269–289. Google Scholar
J. Stoer and R. Bulirsch, Introduction to numerical analysis. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall, Springer-Verlag (1980).
E. Trélat, Contrôle optimal, Mathématiques Concrètes. Vuibert, Paris. Théorie & applications (2005).