All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 142

Showing per page

Control variational method approach to bending and contact problems for Gao beam

Jitka Machalová, Horymír Netuka (2017)

Applications of Mathematics

This paper deals with a nonlinear beam model which was published by D. Y. Gao in 1996. It is considered either pure bending or a unilateral contact with elastic foundation, where the normal compliance condition is employed. Under additional assumptions on data, higher regularity of solution is proved. It enables us to transform the problem into a control variational problem. For basic types of boundary conditions, suitable transformations of the problem are derived. The control variational problem...

Curve cuspless reconstruction via sub-riemannian geometry

Ugo Boscain, Remco Duits, Francesco Rossi, Yuri Sachkov (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the problem of minimizing ∫ 0 ℓ ξ 2 + K 2 ( s ) d s ∫ 0 ℓ ξ 2 + K 2 ( s )   d s for a planar curve having fixed initial and final positions and directions. The total lengthℓ is free. Here s is the arclength parameter, K(s) is the curvature of the curve and ξ > 0 is a fixed constant. This problem comes from a model of geometry of vision due to Petitot, Citti and Sarti. We study existence of local and global minimizers for this problem. We prove that if for a certain choice of boundary conditions there...

Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*

Yuri L. Sachkov (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. In the previous works [Moiseev and Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009004; Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009031], extremal trajectories were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping is described. On this basis an explicit characterization of the cut locus and Maxwell set is obtained....

Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*

Yuri L. Sachkov (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. In the previous works [Moiseev and Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009004; Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009031], extremal trajectories were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping is described. On this basis an explicit characterization of the cut locus and Maxwell set is obtained....

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...

Evolution inclusions of the subdifferential type depending on a parameter

Dimitrios A. Kandilakis, Nikolaos S. Papageorgiou (1992)

Commentationes Mathematicae Universitatis Carolinae

In this paper we study evolution inclusions generated by time dependent convex subdifferentials, with the orientor field F depending on a parameter. Under reasonable hypotheses on the data, we show that the solution set S ( λ ) is both Vietoris and Hausdorff metric continuous in λ ∈ Λ . Using these results, we study the variational stability of a class of nonlinear parabolic optimal control problems.

Evolution of structure for direct control optimization

Maciej Szymkat, Adam Korytowski (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and...

Existence d'un contrôle optimal via l'analyse non standard.

Patricia Spinelli, Georges Solay Rakotonirayni (1991)

Collectanea Mathematica

In this article, we want to show that it is possible to give a complete theory about the existence of an optimal control, without introducing any functional space, by means of the Non Standard Analysis.

Currently displaying 21 – 40 of 142