Second-order sufficient conditions for strong solutions to optimal control problems

Frédéric Bonnans, J.; Dupuis, Xavier; Pfeiffer, Laurent

ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 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.

Classification : 49K15, 34K35, 90C48
Mots clés : 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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