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Journal Articles SIAM Journal on Control and Optimization Year : 2012

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

Daniel Hoehener
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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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Dates and versions

hal-00800528 , version 1 (13-03-2013)

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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, 2012, 50 (3), pp.1139-1173. ⟨10.1137/110828320⟩. ⟨hal-00800528⟩
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