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Delay Dynamics of Cancer and Immune Cell Model

D. Adongo, K.R. Fister (2012)

Mathematical Modelling of Natural Phenomena

We investigate optimal control of a cancer-immune cell interactive model with delay in the interphase compartment. By applying the optimal control theory, we seek to minimize the cost associated with the chemotherapy drug, minimize the accumulation of cancer cells, and increase the immune cell presence. Optimality conditions and characterization of the control are provided. Numerical analyses are given to enhance the understanding of the difficulties...

Deterministic state-constrained optimal control problems without controllability assumptions

Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position x. In the constrained...

Deterministic state-constrained optimal control problems without controllability assumptions

Olivier Bokanowski, Nicolas Forcadel, Hasnaa Zidani (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider nonlinear optimal control problems with constraints on the state of the system. We are interested in the characterization of the value function without any controllability assumption. In the unconstrained case, it is possible to derive a characterization of the value function by means of a Hamilton-Jacobi-Bellman (HJB) equation. This equation expresses the behavior of the value function along the trajectories arriving or starting from any position x. In...

Domaine de victoire et stratégies viables chez les pêcheurs décrits par l'anthropologue Fredrik Barth

Noël Bonneuil, Patrick Saint-Pierre (1998)

Mathématiques et Sciences Humaines

L'anthropologue Fredrik Barth a analysé l'émergence des formes sociales chez les pêcheurs norvégiens. Sa perspective est bien modélisée par les outils mathématiques de la théorie de la viabilité, grâce auxquels on peut calculer l'ensemble des états à partir desquels la survie du système est encore possible, ainsi que la bonne décision à prendre à chaque instant, entre explorer ou suivre les autres bateaux. En outre, il se trouve que, techniquement, la condition de compacité des images de la correspondance...

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