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Simulation based reachability analysis for nonlinear and hybrid systems and applications

The computation of reachable sets for hybrid systems with nonlinear dynamics for the continuous part is still a very challenging problem. The main obstacle is the curse of dimensionality which states that the number of operations to be performed is exponential in the number of continuous variables. For linear dynamics, the use of special set representations (ellipsoids, zonotopes etc) can break this curse but in the general case, there is still no "ideal" solution. Recently, we proposed an approach based on numerical simulation and sensitivity analysis which approximates the reachable set by using a finite number of trajectories augmented with reachable "tubes". The main advantage is that it reports the curse of dimensionality from the number of continuous variables to the number of uncertain initial parameters. Thus high dimensional systems can be dealt with provided that we focus on a small number of uncertain parameters. In this talk, I will detail this approach and its more recent developments and applications. In particular, I will present a variant of our reachability analysis algorithm that can be used to solve a "parameter synthesis" problem, which consists in partitioning a given set of parameters into subsets of safe, unsafe and uncertain parameters, depending on whether they induce behaviors that avoid, approach or cross a given set of bad states. A nice feature of this technique is that it can be used directly on Simulink models. It was also applied to different models of nonlinear differential equations arising from the domain of system biology. Finally, I will discuss ongoing works and perspectives.

Type of Seminar:
IfA Internal Seminar
Dr. Alexandre Donzé
Laboratoire Verimag 2, Avenue de Vignate 38610 Gières, France
Aug 12, 2009   14.15

ETL K 25
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Biographical Sketch:
From Oct. 2008 Post-Doctoral Position at VERIMAG laboratory, Grenoble, with Oded Maler 2007–2008 Post-Doctoral Position at the School of Computer Science of Carnegie Mellon University, Pittsburgh, with Pr. Edmund Clarke and Pr. Bruce Krogh June 2007 Ph.D. in Mathematics and Computer Science at the University of Grenoble (Université Joseph Fourier) under the supervision of Oded Maler and Thao Dang 2002–2003 Master of Science Degree in Computer Science at the University of Grenoble 2001–2002 Master of Science Degree in Applied Mathematics at the University of Grenoble 1999–2002 Engineering Master Degree in computer science and applied mathematics at the ´Ecole Nationale Supérieure d’Informatique et de Mathématiques Appliquées (ENSIMAG), Technological University of Grenoble