Differential games: a viability approach
SIAM Journal on Control and Optimization
Viability theory
Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations
SIAM Journal on Control and Optimization
Conductance-based integrate-and-fire models
Neural Computation
A dynamical theory of spike train transitions in networks of integrate-and-fire oscillators
SIAM Journal on Applied Mathematics
Neural Networks and Qualitative Physics: A Viability Approach
Neural Networks and Qualitative Physics: A Viability Approach
Introduction to Hybrid Dynamical Systems
Introduction to Hybrid Dynamical Systems
Dynamical Qualitative Analysis of Evolutionary Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
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The main purpose of viability theory is to explain the evolution of the state of a control system, governed by nondeterministic dynamics and subjected to viability constraints, to reveal the concealed feedbacks which allow the system to be regulated and provide selection mechanisms for implementing them. It assumes implicitly an "opportunistic" and "conservative" behavior of the system: a behavior which enables the system to keep viable solutions as long as its potential for exploration (or its lack of determinism) -- described by the availability of several evolutions -- makes possible its regulation.Examples of viability constraints are provided by architectures of networks imposing constraints described by connectionist tensors operating on coalitions of actors linked by the network. The question raises how to modify a giving dynamical system governing the evolution of the signals, the connectionist tensors and the coalitions in such a way that the architecture remains viable.