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Nonlinear boundary control problem of hyperbolic systems

Journal of Control and Decision 2024年第1期11卷 73-83页

作者： A.Bouhamed a.el kabouss H.Bouzahir ISTI Lab Ibn Zohr UniversityENSAAgadirMorocco Faculty of sciences Moulay Ismail UniversityMeknesMorocco

The paper is devoted to the study of optimal control of a hyperbolic system,where the control enters the system through the *** hyperbolic system is the wave equation on a smooth and open domain,where the boundary condition involves the normal derivative at the boundary of z,the time derivative of z times a constant k,and a nonlinear term ***,z is the state and u is the control,satisfying some boundedness condition depending on *** functional cost consists of the energy and the difference between the solution of the system at final time,and a desired state in *** a closed convex set,we prove the existence of an optimal control that minimises the cost functional using a priori ***,using the differentiability of the cost functional with respect to the control,we establish the characterisation by deriving necessary conditions that an optimal control must satisfy.A numerical approach is successfully illustrated by simulations.

关键词： Non-linear system hyperbolic system boundary control optimal control controllability

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Tuberculosis among Chronic Hemodialysis Patients: A Senegalese Single Center Experience

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Open Journal of Nephrology 2015年第4期5卷 117-122页

作者： Mouhamadou Moustapha Cisse Rachid el kabouss Yaya Kane Sidy Mouhamed Seck Ahmed Tall Lemrabott Maria Faye el Hadji Fary Ka Ansoumana Diatta Abdou Niang Boucar Diouf Nephrology Department of Teaching Hospital Aristide le Dantec Dakar Senegal Department of Nephrology Assane Seck University Ziguinchor Senegal Department of Nephrology Gaston Berger University Saint Louis Senegal

Summary: Tuberculosis is a common infectious disease in chronic hemodialysis due to alteration of the immune system associated with chronic kidney disease. The objectives of this study are to determine the prevalence of tuberculosis in chronic hemodialysis patients and to identify its diagnostic and therapeutic difficulties. Methods and patients: This was a descriptive retrospective study over a period of 20 years (1994-2014). It includes the records of periodic hemodialysis patients in the Nephrology Department of the Aristide Le Dantec University Teaching Hospital in Dakar which clinical symptoms and laboratory favor tuberculosis. Results: Of 258 chronic hemodialysis patients treated in Hospital Aristide Le Dantec hemodialysis center, 29 cases (11.4%) of tuberculosis disease are diagnosed. The mean age is 43.21 ± 12.48 years, and the sex-ratio is 0.8. The median time to onset of tuberculosis after initiation of hemodialysis is 22.86 ± 28.86 months. The diagnosis of tuberculosis is sure only in 17% of cases. Extra-pulmonary sites are found in 79% of cases. The average duration of treatment is 9.39 ± 1.64 months (6 - 13 months). Various treatment protocols are adopted. Mortality is 21%, 50% due to disseminated tuberculosis. Conclusion: The diagnosis of tuberculosis in the chronic hemodialysis patients is often difficult due to the atypical symptoms, the frequency of extra-pulmonary location and the lack of evidence of sure diagnosis.

关键词： Tuberculosis Hemodialysis Dakar

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