Well-Posedness of the Shooting Algorithm for State Constrained Optimal Control Problems with a Single Constraint and Control
作者： J. Frédéric Bonnans , Audrey Hermant
DOI: 10.1137/06065756X
关键词: Boundary value problem 、 Constrained optimization 、 Stability (learning theory) 、 Control theory 、 Mathematics 、 Optimal control 、 Jacobian matrix and determinant 、 Optimality criterion 、 Applied mathematics 、 Constraint (information theory) 、 Boundary (topology)
摘要: This paper deals with the shooting algorithm for optimal control problems a scalar and regular state constraint. Additional conditions are displayed, under which so-called alternative formulation is equivalent to Pontryagin's minimum principle. The appears be well-posed (invertible Jacobian) iff (i) no-gap second-order sufficient optimality condition holds, (ii) when constraint of order $q \geq 3$, there no boundary arc. Stability sensitivity results without strict complementarity at touch points derived using Robinson's strong regularity theory, minimal condition. directional derivatives obtained as solutions linear quadratic problem.
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