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

J. Frederic Bonnans(frederic.bonnans***at***inria.fr)
Xavier Dupuis(xavier.dupuis***at***cmap.polytechnique.fr)
Laurent Pfeiffer(laurent.pfeiffer***at***polytechnique.edu)

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.

Keywords: Optimal control; second-order sufficient conditions; quadratic growth; bounded strong solutions; Pontryagin multipliers; pure state and mixed control-state constraints; decomposition principle.

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Published as the Inria Research Report No 3807.

Download: [PDF]

Entry Submitted: 05/23/2013
Entry Accepted: 05/23/2013
Entry Last Modified: 05/23/2013

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