Differential automata and their discrete simulators
Non-Linear Analysis
Viability theory
Introduction to Hybrid Dynamical Systems
Introduction to Hybrid Dynamical Systems
Qualitative Theory of Hybrid Dynamical Systems
Qualitative Theory of Hybrid Dynamical Systems
Hybrid Dynamical Systems: Controller and Sensor Switching Problems
Hybrid Dynamical Systems: Controller and Sensor Switching Problems
Viability Kernels and Capture Basins of Sets Under Differential Inclusions
SIAM Journal on Control and Optimization
Boundary-Value Problems for Systems of Hamilton--Jacobi--Bellman Inclusions with Constraints
SIAM Journal on Control and Optimization
The Substratum of Impulse and Hybrid Control Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Impulse differential inclusions driven by discrete measures
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
The Substratum of Impulse and Hybrid Control Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Path-Dependent Impulse and Hybrid Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Towards Computing Phase Portraits of Polygonal Differential Inclusions
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Dynamical Qualitative Analysis of Evolutionary Systems
HSCC '02 Proceedings of the 5th International Workshop 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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The behavior of the run of an impulse differential inclusion, and, in particular, of a hybrid control system, is "summarized" by the "initialization map" associating with each initial condition the set of new initialized conditions and more generally, by its "substratum", that is a set-valued map associating with a cadence and a state the next reinitialized state. These maps are characterized in several ways, and in particular, as "set-valued" solutions of a system of Hamilton-Jacobi partial differential inclusions, that play the same role than usual Hamilton-Jacobi-Bellman equations in optimal control.