# Homogeneous tangent vectors and high-order necessary conditions for optimal controls

@article{Ancona1997HomogeneousTV,
title={Homogeneous tangent vectors and high-order necessary conditions for optimal controls},
author={Fabio Ancona},
journal={Journal of Dynamical and Control Systems},
year={1997},
volume={3},
pages={205-240}
}
AbstractAn extension of the classical Pontryagin maximum principle for Mayer problems without terminal constraints, subject to affine control systems $$\dot x = X_0 (x) + \sum\nolimits_{j = 1}^m u _j X_j (x)$$ , is proved. In connection with a suitable dilation on the state space ℝn, we introduce a class of “homogeneous tangent vectors” which provide a nonlinear, high-order approximation of the attainable set in the case where the usual linear approximation proves to be inadequate. By studying… CONTINUE READING

## Preasymptotic Stability and Homogeneous Approximations of Hybrid Dynamical Systems

• Mathematics, Computer Science
• SIAM Review
• 2010
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