Viability theory
Differential inclusions and target problems
SIAM Journal on Control and Optimization
Introduction to Hybrid Dynamical Systems
Introduction to Hybrid Dynamical Systems
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Computing invariance kernels of polygonal hybrid systems
Nordic Journal of Computing
Algorithmic analysis of polygonal hybrid systems, Part II: Phase portrait and tools
Theoretical Computer Science
Comparing forward and backward reachability as tools for safety analysis
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Proceedings of the 14th international conference on Hybrid systems: computation and control
Static analysis for state-space reduction of polygonal hybrid systems
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
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We investigate, for constrained controlled systems with impulse, the subset of initial positions contained in a set K from which starts at least one run viable in K - the hybrid viability kernel - eventually until it reaches a given closed target in finite time - the hybrid capture basin. We define a constructive algorithm which approximates this set. The knowledge of this set is essential for control problem since it provides viable hybrid feed-backs and viable runs. We apply this method for approximatingt he Minimal Time-to-reach Function in the presence of both constraints and impulses. Two examples are presented, the first deals with a dynamical system revealingthe complexity of the structure of hybrid kernels, the second deals with a Minimal Time problem with impulses.