Algorithms | Viability Theory

Viability algorithms

Algorithms play a central role in the study and application of viability theory. They allow us to simulate, explore, and determine viable dynamic trajectories according to imposed constraints. This section presents the main algorithms used in this field, accompanied by explanatory diagrams to better understand their logic.

Viability Kernel Algorithm

Purpose: To numerically approximate the viability kernel of a discrete or continuous system.

Principle:

Discretize time and space.
Progressively eliminate points in the constraint set that do not allow for a viable evolution.

Simplified steps:

Input: Grille d’états G ⊂ K, dynamique F, pas de temps h
Output: Approximation de Viab_F(K)

1. Viab := G
2. Repeat
    a. Pour chaque point x ∈ Viab
        i. Calculer les successeurs possibles via F(x)
        ii. Si aucun successeur ∉ Viab alors supprimer x
3. Until convergence
4. Return Viab

Loading content ...