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.

Second-order sufficient conditions for strong solutions to optimal control problems / Bonnans, J. Frédéric; Dupuis, Xavier; Pfeiffer, Laurent. - In: ESAIM. COCV. - ISSN 1292-8119. - 20:3(2014), pp. 704-724. [10.1051/cocv/2013080]

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

DUPUIS, XAVIER;
2014

Abstract

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.
Second-order sufficient conditions for strong solutions to optimal control problems / Bonnans, J. Frédéric; Dupuis, Xavier; Pfeiffer, Laurent. - In: ESAIM. COCV. - ISSN 1292-8119. - 20:3(2014), pp. 704-724. [10.1051/cocv/2013080]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11385/160727
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