In this paper we deal with the strong local optimality of a triplet satisfying Pontryagin Maximum Principle in the minimum time problem between two given manifolds. The reference control is assumed to be bang-bang with a double switching time. Our methods are based on a topological technique for the inversion of the projected maximised flow.
DOI : 10.1051/cocv/2015021
Mots clés : Hamiltonian methods, bang-bang controls, sufficient second order conditions
@article{COCV_2016__22_3_688_0,
author = {Poggiolini, Laura and Spadini, Marco},
title = {Bang-bang trajectories with a double switching time in the minimum time problem},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {688--709},
publisher = {EDP-Sciences},
volume = {22},
number = {3},
year = {2016},
doi = {10.1051/cocv/2015021},
zbl = {1344.49037},
mrnumber = {3527939},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2015021/}
}
TY - JOUR AU - Poggiolini, Laura AU - Spadini, Marco TI - Bang-bang trajectories with a double switching time in the minimum time problem JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 688 EP - 709 VL - 22 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015021/ DO - 10.1051/cocv/2015021 LA - en ID - COCV_2016__22_3_688_0 ER -
%0 Journal Article %A Poggiolini, Laura %A Spadini, Marco %T Bang-bang trajectories with a double switching time in the minimum time problem %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 688-709 %V 22 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015021/ %R 10.1051/cocv/2015021 %G en %F COCV_2016__22_3_688_0
Poggiolini, Laura; Spadini, Marco. Bang-bang trajectories with a double switching time in the minimum time problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 688-709. doi : 10.1051/cocv/2015021. http://archive.numdam.org/articles/10.1051/cocv/2015021/
, Applications of the theory of quadratic forms in Hilbert space to calculus of variations. Pacific J. Math 1 (1951) 525–581. | DOI | MR | Zbl
L. Poggiolini, On local state optimality of bang-bang extremals in a free horizon Bolza problem. Rendiconti del Seminario Matematico dell’Università e del Politecnico di Torino (2006). | MR | Zbl
L. Poggiolini and M. Spadini, Sufficient Optimality Conditions for a Bang-bang Trajectory in a Bolza Problem. In Mathematical Control Theory and Finance, edited by A. Sarychev, A. Shiryaev, M. Guerra and M. do Rosário Grossinho. Springer, Berlin, Heidelberg (2008) 337–357. | MR | Zbl
L. Poggiolini and M. Spadini, Bang-bang trajectories with a double switching time: sufficient strong local optimality conditions. Preprint (2010). | arXiv
and , Strong local optimality for a bang-bang trajectory in a Mayer problem. SIAM J. Control Optim. 49 (2011) 140–161. | DOI | MR | Zbl
and , Local inversion of planar maps with nice nondifferentiability structure. Adv. Nonlin. Stud. 13 (2013) 411–430. | DOI | MR | Zbl
and , State-local optimality of a bang-bang trajectory: a Hamiltonian approach. Syst. Control Lett. 53 (2004) 269–279. | DOI | MR | Zbl
and , Bang-singular-bang extremals: sufficient optimality conditions. J. Dyn. Control Syst. 17 (2011) 469–514. | DOI | MR | Zbl
G. Stefani and P. Zezza, Time-Optimality of a Bang-bang Trajectory with Maple. In 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (2003). | MR
Cité par Sources :
