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Revisiting the analysis of optimal control problems with several state constraints

Bonnans J. F., Hermant A.

Control and Cybernetics

2009

Vol. 38, no 4A

1021-1052

This paper improves the results of and gives shorter proofs for the analysis of state constrained optimal control problems than presented by the authors in Bonnans and Hermant (2009b), concerning second order optimality conditions and the well-posedness of the shooting algorithm. The hypothesis for the second order necessary conditions is weaker, and the main results are obtained without reduction to the normal form used in that reference, and without analysis of high order regularity results for the control. In addition, we provide some numerical illustration. The essential tool is the use of the "alternative optimality system".