\documentclass{abstract}
\begin{document}

\title{Software for verification of collision avoidance algorithms via Optimal Control Techniques. }
\author{I. Xausa}
\institute{Volkswagen A.G.}
\email{ilaria.xausa@volkswagen.de}
\coauthor{R. Baier, \and M. Gerdts} % comment out if not needed

\mymaketitle

\section{Abstract}
The goal of the talk is to present a verification procedure for car collision avoidance algorithms using reachable set information and optimal control techniques. After defining the car models and the scenarios with avoidable objects, consistent with the measured data provided by Volkswagen, we create an algorithm which is able to give an output data comparable with the ones of the Volkswagen algorithms. To do this it is needs to define mathematically when a collision will occur or not. This definition is based on reachable set information and optimal control problem solutions. Moreover we take into account sensor perturbations in relation to their mathematical model. The task is to find sensor tolerance ranges guaranteeing that a certain failure rate probability is not exceeded.


\begin{thebibliography}{9} 


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Numerical Algebra, Control and Optimization, 3 (3) 2013, pp.~519--548.

\bibitem{bok-for-zid-2010-2}
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\bibitem{Ger06b}{\sc M.~Gerdts},
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Optimal Control, Applications and Methods, 27(3) (2006), pp.~169--182.


\bibitem{ifip}
{\sc M.~Gerdts and I.~Xausa}, 
{\em Collision Avoidance Using Reachable Sets and Parametric Sensitivity Analysis}, 
In System Modeling and Optimization.
25th IFIP TC 7 conference on system modeling and optimization, CSMO 2011, Berlin, Germany, September 12–16, 2011. Revised Selected Papers, D. Hömberg, F. Tröltzsch (eds.)
IFIP Advances in Information and Communication Technology, 391 (2013),  pp.~491--500.


\bibitem{mit-bay-tom-2005}
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\bibitem{mtns}
{\sc I.~Xausa, R.~Baier, M.~Gerdts, M.~Gonter and C.~Wegwerth}, 
{\em Avoidance Trajectories for Driver Assistance Systems via Solvers for Optimal Control Problems}, 
Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems, Melbourne, Australia, 294 (2012), 8 pages.


\end{thebibliography}

\end{document}