نوع مقاله : مقاله پژوهشی
نویسندگان
گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه تربیت مدرس، تهران، ایران
چکیده
کلیدواژهها
موضوعات
عنوان مقاله [English]
نویسندگان [English]
In this paper, we presented an optimal control problem for the least myofibroblast diffusion
in order to prevent the formation of fibrotic tissue in the repair process in lung tissue. Since transforming
growth factor-beta causes the proliferation and activation of myofibroblast, we considered this factor as
the control function of the optimal control problem. By presenting a theorem, the optimal control of the
above issue is guaranteed. In order to solve the problem of optimal control, there is a need to convert
an equation with partial derivatives into a system of linear ordinary differential equations. Therefore,
we solved this problem by using the central finite difference method. Then, using two methods of the
maximum principle (Hamiltonian equations ) and the calculus of variations (Euler–Lagrange equation) in
optimal linear regulator problem, we controlled the most important factor, i.e. transforming growth factor-beta, which is common to all fibrotic tissues. In a theorem, we prove that the solution of the optimal linear
regulator problem is the same for both methods. Finally, we compared the calculation results with the two
presented methods.
کلیدواژهها [English]
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