Evaluation of Crisis, Reversibility, Alert Management for Constrained Dynamical Systems Using Impulse Dynamical Systems

Authors:
Patrick Saint-Pierre
Affiliations:
-
Venue:
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
Year:
2002

Citing 4
Cited 0

Viability theory

Viability theory
Differential inclusions and target problems

SIAM Journal on Control and Optimization
Hybrid Kernels and Capture Basins for Impulse Constrained Systems

HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Guaranteed Overapproximations of Unsafe Sets for Continuous and Hybrid Systems: Solving the Hamilton-Jacobi Equation Using Viability Techniques

HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control

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Abstract

Considering constrained dynamical systems characterized by a differential inclusion x驴驴 F(x), we are interested in studying the situation where, for various reasons, the state leaves the constrain domain K either because the initial position does not belong to the Viability Kernel of K for F or it belongs to a "sustainable or tolerable" but not comfortable" domain. This question appears in numerous models in Social Sciences or in Genetics as well as for controlling security in Automatics and Robotics, like Aircraft landing, rolling and taking off. After recalling basic concepts in Viability Theory and using hybrid calculus, we show how to evaluate and manage crisis in general cases.