Second order analysis of control-affine problems with scalar state constraint
M. Soledad Aronna, Fr\'ed\'eric Bonnans, Bean San Goh
TL;DR
This paper develops new second order optimality conditions for control-affine problems with scalar control and state constraints, extending classical tools like the Goh transform to this constrained setting.
Contribution
It introduces novel second order necessary and sufficient conditions for control-affine problems with scalar state constraints, extending the Goh transform.
Findings
New second order optimality conditions established
Extension of the Goh transform to constrained state problems
Provides a framework for analyzing control-affine problems with scalar constraints
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.
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