Application of Pontryagin maximum principle

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Table of contents

1 Introduction 
1.1 Bioprocesses and bioremediation
1.2 Mathematical models of bioreactors and classical results
1.2.1 Mathematical models
1.2.2 Classical results on chemostats
1.2.3 Classical results on SBRs
1.2.4 Stochastic models of bioreactors
1.3 Model of inhomogeneous lake
1.4 Singular perturbations
1.5 Contributions of the thesis
1.5.1 Deterministic optimal control for continuous bioremediation processes
1.5.2 Study of stochastic modeling of sequencing batch reactors
2 Bioremediation of natural water resources via Optimal Control techniques 
2.1 Introduction
2.2 Mathematical model
2.2.1 Description of the dynamics
2.2.2 Preliminary results on the dynamics
2.2.3 Minimal time optimal control problem
2.3 Application of Pontryagin maximum principle
2.4 The effect of recirculation
2.5 Numerical Simulations
2.6 Conclusion
3 Optimal feedback synthesis and minimal time function for the bioremediation of water resources with two patches 
3.1 Introduction
3.2 Definitions and preliminaries
3.3 Study of the relaxed problem
3.4 Synthesis of the optimal strategy
3.5 Study of the minimal-time function
3.6 Numerical illustrations
3.7 Conclusion
4 Minimal-time bioremediation of natural water resources with gradient of polluxiitant 
4.1 Introduction
4.2 Definitions and preliminaries
4.3 Optimal control problem
4.4 Numerical simulations
4.5 Conclusions
5 Stochastic modelling of sequencing batch reactors for wastewater treatment 
5.1 Introduction
5.2 Stochastic SBR model
5.3 Existence of solutions of the controlled stochastic model
5.4 The optimal reach-avoid problem
5.5 Numerical simulations and conclusions
6 Conclusions and perspectives 
Bibliography