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

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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 : 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 
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     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},
     pages = {704--724},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {3},
     year = {2014},
     doi = {10.1051/cocv/2013080},
     mrnumber = {3264220},
     zbl = {1293.49039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2013080/}
}
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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, Tome 20 (2014) no. 3, pp. 704-724. doi: 10.1051/cocv/2013080

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