Second order analysis of control-affine problems with scalar state constraint
arXiv:1411.171919 citationsh-index: 21
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Provides theoretical advancements for optimal control theory, specifically for problems with state constraints, but is incremental in nature.
The paper establishes new second-order necessary and sufficient optimality conditions for control-affine problems with scalar state constraints, extending the Goh transform to the constrained state framework.
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.