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Reports (Research Report) Year : 2007

Second-order Analysis for Optimal Control Problems with Pure and Mixed State Constraints

Abstract

This paper deals with the optimal control problem of an ordinary differential equation with several pure state constraints, of arbitrary orders, as well as mixed control-state constraints. We assume (i) the Hamiltonian to be strongly convex and the mixed constraints to be convex w.r.t. the control variable, and (ii) a linear independence condition of the active constraints at their respective order to hold. We give a complete analysis of the smoothness and junction conditions of the control and of the constraints multipliers. This allow us to obtain, when there are finitely many nontangential junction points, a theory of no-gap second-order optimality conditions and a characterization of the well-posedness of the shooting algorithm. These results generalize those obtained in the case of a scalar-valued state constraint and a scalar-valued control.
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Dates and versions

inria-00148946 , version 1 (23-05-2007)
inria-00148946 , version 2 (24-05-2007)

Identifiers

  • HAL Id : inria-00148946 , version 2

Cite

Frédéric J. Bonnans, Audrey Hermant. Second-order Analysis for Optimal Control Problems with Pure and Mixed State Constraints. [Research Report] RR-6199, INRIA. 2007. ⟨inria-00148946v2⟩
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