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

J. Frédéric Bonnans, Xavier Dupuis, Laurent Pfeiffer (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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...

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