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Variational Approach to Second-Order Optimality Conditions for Control Problems with Pure State Constraints

Daniel Hoehener 1
1 C&O - Equipe combinatoire et optimisation
IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche
Abstract : For optimal control problems with set-valued control constraints and pure state constraints we propose new second-order necessary optimality conditions. In addition to the usual second-order derivative of the Hamiltonian, these conditions contain extra terms involving second-order tangents to the set of feasible trajectory-control pairs at the extremal process under consideration. The second-order necessary optimality conditions of the present work are obtained by using a variational approach. In particular, we present a new second-order variational equation. This approach allows us to make direct proofs as opposed to the classical way of obtaining second-order necessary conditions by using an abstract infinite dimensional optimization problem. No convexity assumptions on the constraints are imposed and optimal controls are required to be merely measurable.
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https://hal.inria.fr/hal-00800528
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Submitted on : Wednesday, March 13, 2013 - 7:12:45 PM
Last modification on : Thursday, December 10, 2020 - 12:32:42 PM

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Daniel Hoehener. Variational Approach to Second-Order Optimality Conditions for Control Problems with Pure State Constraints. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2012, 50 (3), pp.1139-1173. ⟨10.1137/110828320⟩. ⟨hal-00800528⟩

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