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

Abstract : In this report, 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.
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https://hal.inria.fr/hal-00825260
Contributor : Laurent Pfeiffer Connect in order to contact the contributor
Submitted on : Thursday, May 23, 2013 - 12:14:11 PM
Last modification on : Tuesday, April 26, 2022 - 3:11:25 AM
Long-term archiving on: : Saturday, August 24, 2013 - 5:15:21 AM

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Joseph Frederic Bonnans, Xavier Dupuis, Laurent Pfeiffer. Second-order sufficient conditions for strong solutions to optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, 2014, 20 (03), pp.704-724. ⟨10.1051/cocv/2013080⟩. ⟨hal-00825260⟩

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