Minimizing the fuel consumption of a vehicle from the shell eco-marathon: a numerical study. (English) Zbl 1263.49034
Summary: 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.
MSC:
49M37 | Numerical methods based on nonlinear programming |
49J15 | Existence theories for optimal control problems involving ordinary differential equations |
49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
90C30 | Nonlinear programming |
49N90 | Applications of optimal control and differential games |
90C90 | Applications of mathematical programming |