Author:
Benabidallah A.,Cherruault Y.,Tourbier Y.
Abstract
Decomposition of several variables functions by means of functions of one variable was a fundamental problem, studied by mathematicians, and the specially by KOLMOGOROV school. This question is closely connected with optimization and optimal control and with multiple integrals calculus. These problems have been investigated by Professor Y. Cherruault and colleagues, using the ALIENOR method, which is based on α‐dense curves. The decomposition method of Adomian can be coupled with global optimization for solving optimal control problems. Aim is to calculate multiple integrals by a special decomposition of the function using an orthonormal basis of functions. Presents also new methods for approximating a n‐variables function by means of the sum of product of n functions only depending on a single variable. Applications to multi‐variables optimization problems and optimal control system are described.
Subject
Computer Science (miscellaneous),Social Sciences (miscellaneous),Theoretical Computer Science,Control and Systems Engineering,Engineering (miscellaneous)
Reference12 articles.
1. Abbaoui, K. (1995), Les fondements mathématiques de la méthode decompositionnelle d'Adomian et applications à la résolution de problèmes issus de la biologie et de la médecine. These de l'université PARIS VI‐4‐10‐1995‐Laboratoire MEDIMAT.
2. Abbaoui, K. and Cherruault, Y. (1994), “New ideas for solving identification and optimal control problems related to biomedical systems”, Int. J. of Biomed. Comp., Vol. 36, pp. 181–6.
3. Cherruault, Y. (1998), Modeles et méthodes mathématiques pour les sciences du vivant. P.U.F.
4. Cherruault, Y. (1999), Optimisation‐Méthodes locales et globales. P.U.F.
5. Kolmogorov, A.N. (1957), On the representation of continuous functions of several variables in the form of superposition of continuous functions of one variable and addition. Dokl. Akad. SSSR., Vol. 114, pp. 953–956 (Amer. Math. Soc. Trans., Vol. 28 (1963) pp. 55–59).
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. A recursive implementation of the ALIENOR optimization method;International Journal of Intelligent Computing and Cybernetics;2021-01-25