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Second order analysis of state-constrained control-affine problems

M. Soledad Aronna(aronna***at***impa.br)
J. Frederic Bonnans(Frederic.Bonnans***at***inria.fr)
Bean San Goh(bsgoh***at***curtin.edu.my)

Abstract: In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition. We propose a shooting algorithm to solve numerically this class of problems and we provide a sufficient condition for its local convergence. We provide examples to illustrate the theory.

Keywords: control-affine systems, second order condition, singular arc, shooting algorithm

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: hal-01081111

Download: [PDF]

Entry Submitted: 11/07/2014
Entry Accepted: 11/07/2014
Entry Last Modified: 11/07/2014

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