Second-order sufficient conditions for strong solutions to optimal control problems∗
Received: 23 May 2013
Revised: 16 September 2013
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.
Mathematics Subject Classification: 49K15 / 34K35 / 90C48
Key words: 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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