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Titre : Study of a cancer therapy model using Dynamic Programming Method Type de document : texte imprimé Auteurs : Islem Akkouche, Auteur ; Mohamed Hammi ; Sofiane Lamri ; Touffik Bouremani, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2024 Importance : 1 vol (39 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Non-smooth analysis
Autonomous optimal control problem
The Dynamic Programming Algorithm
Bolza Problem.Index. décimale : 510-Mathématique Résumé :
In this note we use a dynamic programming method to study a mathematical model of cancer. This study is based on recent results of non-differentiable analysis, applying a generalized algorithm to obtain a complete, justified and rigorous solution.Note de contenu :
Sommaire
INTRODUCTION . ................................ 1
I NONSMOOTHANALYSISANDAPPLICATIONS . ........ 4
1.1 Introduction.................................4
1.2 PreliminaryNotions.............................4
1.2.1 Di¤erentiablemappingsonsubmanifoldsof Rn . ........4
1.2.2 StratiÂ…edsetsandmapping....................8
1.3 Conesandgeneralizedderivative......................11
1.4 Monotonicityofrealfunctions.......................12
1.4.1 Generalmonotonicityresult....................13
IISUFFICIENTCONDITIONOFNONAUTONOMOUSOPTIMAL
CONTROLPROBLEMS . .......................... 16
2.1 Introduction.................................16
2.2 FormulationsandclassiÂ…cationsofnon-autonomousoptimalcontrolprob-
lems .....................................16
2.2.1 Non-autonomousBolzaproblemfordi¤erentialinclusions...16
2.2.2 Non-autonomousBolzaproblemparameterized.........19
2.2.3 Lagrangeoptimalcontrolproblem.................21
2.2.4 Mayeroptimalcontrolproblem..................21
2.2.5 OptimalcontrolproblemwithÂ…xedterminaltime........21
2.2.6 Minimumtimeproblem......................22
2.2.7 Problemofvariationalcalculation.................22
2.2.8 InÂ…nitehorizonoptimalcontrolproblems.............22
2.3 VeriÂ…cationTheoremsforanon-autonomousoptimalcontrolproblem.22
2.4 Generalalgorithmforsolvinganautonomousoptimalcontrolproblem25
IIISTUDYOFACANCERTHEARAPYMODELUSINGDYNAMIC
PROGRAMMINGMETHOD . ...................... 29
3.1 Introduction.................................29
3.2 MathematicalModel............................29
3.2.1 Dynamicprogrammingformulation................30
3.2.2 CharacterizationoftheHamiltonian...............30
3.2.3 Setoftransversalityterminalpoints................31
3.3 GeneralizedHamiltonianÂ…eld.......................32
3.3.1 Hamiltoniansystemonthestratum Z???? . .............33
3.3.2 Generalizedcharacteristic‡ow...................36
3.4 Valuefunctionandoptimaltrajectories..................37
3.5 Conclusionandcoments...........................37Côte titre : MAM/0724 Study of a cancer therapy model using Dynamic Programming Method [texte imprimé] / Islem Akkouche, Auteur ; Mohamed Hammi ; Sofiane Lamri ; Touffik Bouremani, Directeur de thèse . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (39 f.) ; 29 cm.
Langues : Anglais (eng)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Non-smooth analysis
Autonomous optimal control problem
The Dynamic Programming Algorithm
Bolza Problem.Index. décimale : 510-Mathématique Résumé :
In this note we use a dynamic programming method to study a mathematical model of cancer. This study is based on recent results of non-differentiable analysis, applying a generalized algorithm to obtain a complete, justified and rigorous solution.Note de contenu :
Sommaire
INTRODUCTION . ................................ 1
I NONSMOOTHANALYSISANDAPPLICATIONS . ........ 4
1.1 Introduction.................................4
1.2 PreliminaryNotions.............................4
1.2.1 Di¤erentiablemappingsonsubmanifoldsof Rn . ........4
1.2.2 StratiÂ…edsetsandmapping....................8
1.3 Conesandgeneralizedderivative......................11
1.4 Monotonicityofrealfunctions.......................12
1.4.1 Generalmonotonicityresult....................13
IISUFFICIENTCONDITIONOFNONAUTONOMOUSOPTIMAL
CONTROLPROBLEMS . .......................... 16
2.1 Introduction.................................16
2.2 FormulationsandclassiÂ…cationsofnon-autonomousoptimalcontrolprob-
lems .....................................16
2.2.1 Non-autonomousBolzaproblemfordi¤erentialinclusions...16
2.2.2 Non-autonomousBolzaproblemparameterized.........19
2.2.3 Lagrangeoptimalcontrolproblem.................21
2.2.4 Mayeroptimalcontrolproblem..................21
2.2.5 OptimalcontrolproblemwithÂ…xedterminaltime........21
2.2.6 Minimumtimeproblem......................22
2.2.7 Problemofvariationalcalculation.................22
2.2.8 InÂ…nitehorizonoptimalcontrolproblems.............22
2.3 VeriÂ…cationTheoremsforanon-autonomousoptimalcontrolproblem.22
2.4 Generalalgorithmforsolvinganautonomousoptimalcontrolproblem25
IIISTUDYOFACANCERTHEARAPYMODELUSINGDYNAMIC
PROGRAMMINGMETHOD . ...................... 29
3.1 Introduction.................................29
3.2 MathematicalModel............................29
3.2.1 Dynamicprogrammingformulation................30
3.2.2 CharacterizationoftheHamiltonian...............30
3.2.3 Setoftransversalityterminalpoints................31
3.3 GeneralizedHamiltonianÂ…eld.......................32
3.3.1 Hamiltoniansystemonthestratum Z???? . .............33
3.3.2 Generalizedcharacteristic‡ow...................36
3.4 Valuefunctionandoptimaltrajectories..................37
3.5 Conclusionandcoments...........................37Côte titre : MAM/0724 Exemplaires (1)
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