Nagumo type condition for partial differential inclusions
Non-Linear Analysis
Viability theory
Mathematical problems arising in qualitative simulation of a differential equation
Artificial Intelligence
Neural Networks and Qualitative Physics: A Viability Approach
Neural Networks and Qualitative Physics: A Viability Approach
Viability Kernels and Capture Basins of Sets Under Differential Inclusions
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
Path-Dependent Impulse and Hybrid Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Formal descriptions of developing systems
Qualitative simulation and related approaches for the analysis of dynamic systems
The Knowledge Engineering Review
Lost in Translation: Hybrid-Time Flows vs. Real-Time Transitions
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
On simulations and bisimulations of general flow systems
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Fuzzy differential equations without fuzzy convexity
Fuzzy Sets and Systems
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Kuipers' QSIM algorithm for tracking the monotonicity properties of solutions to differential equations has been revisited by Dordan by placing it in a rigorous mathematical framework. The Dordan QSIM algorithm provides the transition laws from one qualitative cell to the others.We take up this idea and revisit it at the light of recent advances in the field of "hybrid systems" and, more generally, "impulse differential equations and inclusions".Let us consider a family of "qualitative cells Q(a)" indexed by a parameter a 驴 A: We introduce a dynamical system on the discrete set of qualitative states prescribing an order of visit of the qualitative cells and an evolutionary system govening the "continuous" evolution of a system, such as a control system. The question arises to study and characterize the set of any pairs of qualitative and quantitative initial states from which start at least one order of visit of the qualitative cells and an continuous evolution visiting the qualitative cells in the prescribed order. This paper is devoted to the issues regarding this question using tools of set-valued analysis and viability theory.