## Needle Variations that Cannot be Summed

- Rosa-Maria Bianchini, Matthias Kawski
- SIAM J. Control and Optimization
- 2003

@inproceedings{Bianchini2002LackOC, title={Lack of convexity for tangent cones of needle variations 1}, author={Rosa-Maria Bianchini and Matthias Kawski}, year={2002} }

- Published 2002

Cones of tangent vectors (generated by families of control variations) are the principal analytical tool for obtaining necessary and sufficient conditions for optimality and nonlinear controllability. Unlike the classical Pontryagin cone, it is known that in general high-order variational cones may fail to be convex. For control variations that converge in L to the reference control, this was shown in 1985 by Bressan. This article announces a counter example for high order tangent vectors… CONTINUE READING