Second-order sufficient conditions for strong solutions to optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 3, p. 704-724

In this article, given a reference feasible trajectory of an optimal control problem, we say that the quadratic growth property for bounded strong solutions holds if the cost function of the problem has a quadratic growth over the set of feasible trajectories with a bounded control and with a state variable sufficiently close to the reference state variable. Our sufficient second-order optimality conditions in Pontryagin form ensure this property and ensure a fortiori that the reference trajectory is a bounded strong solution. Our proof relies on a decomposition principle, which is a particular second-order expansion of the Lagrangian of the problem.

DOI : https://doi.org/10.1051/cocv/2013080
Classification:  49K15,  34K35,  90C48
Keywords: optimal control, second-order sufficient conditions, quadratic growth, bounded strong solutions, Pontryagin multipliers, pure state and mixed control-state constraints, decomposition principle
@article{COCV_2014__20_3_704_0,
author = {Fr\'ed\'eric Bonnans, J. and Dupuis, Xavier and Pfeiffer, Laurent},
title = {Second-order sufficient conditions for strong solutions to optimal control problems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {20},
number = {3},
year = {2014},
pages = {704-724},
doi = {10.1051/cocv/2013080},
zbl = {1293.49039},
mrnumber = {3264220},
language = {en},
url = {http://www.numdam.org/item/COCV_2014__20_3_704_0}
}

Frédéric Bonnans, J.; Dupuis, Xavier; Pfeiffer, Laurent. Second-order sufficient conditions for strong solutions to optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 20 (2014) no. 3, pp. 704-724. doi : 10.1051/cocv/2013080. http://www.numdam.org/item/COCV_2014__20_3_704_0/

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