scholarly journals APPLICATION OF THE PONTRYAGIN MAXIMUM PRINCIPLE TO CONTROL TUMOR ANGIOGENESIS

2021 ◽  
Vol 6 (12(62)) ◽  
pp. 51-55
Author(s):  
Cherif Abdelillah Otmane
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Tumor Angiogenesis ◽  
Pontryagin Maximum Principle ◽  
Optimal Trajectory ◽  
Minimum Principle ◽  
Pontryagin Minimum Principle ◽  
Sample Application ◽  
Control Tumor ◽  
The Pontryagin Maximum Principle

We present a sample application covering several cases using an extension of the Pontryagin Minimum Principle (PMP) [3]. We are interested in the management of tumor angiogenesis, that is, the therapeutic management of the proliferation of cancer cells that develop new blood vessels. Let us formulate the problem and derive the optimal control and apply the Pontryagin maximum principle to our optimal trajectory, and we derive the theorem and check it with an example. Then we will study stabilization.

WHY REGULARIZATION OF LAGRANGE PRINCIPLE AND PONTRYAGIN MAXIMUM PRINCIPLE IS NEEDED AND WHAT IT GIVES

2018 ◽  
pp. 757-775
Author(s):  
Mikhail Iosifovich Sumin
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Mathematical Programming ◽  
Optimality Conditions ◽  
Pontryagin Maximum Principle ◽  
Lagrange Principle ◽  
Convex Problems ◽  
The Pontryagin Maximum Principle

We consider the regularization of the classical Lagrange principle and the Pontryagin maximum principle in convex problems of mathematical programming and optimal control. On example of the “simplest” problems of constrained infinitedimensional optimization, two main questions are discussed: why is regularization of the classical optimality conditions necessary and what does it give?

scholarly journals Regularized classical optimality conditions in iterative form for convex optimization problems for distributed Volterra-type systems

2021 ◽  
Vol 31 (2) ◽  
pp. 265-284
Author(s):  
V.I. Sumin ◽  
M.I. Sumin
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Pontryagin Maximum Principle ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Lagrange Principle ◽  
The Pontryagin Maximum Principle

We consider the regularization of the classical optimality conditions (COCs) — the Lagrange principle and the Pontryagin maximum principle — in a convex optimal control problem with functional constraints of equality and inequality type. The system to be controlled is given by a general linear functional-operator equation of the second kind in the space $L^m_2$, the main operator of the right-hand side of the equation is assumed to be quasinilpotent. The objective functional of the problem is strongly convex. Obtaining regularized COCs in iterative form is based on the use of the iterative dual regularization method. The main purpose of the regularized Lagrange principle and the Pontryagin maximum principle obtained in the work in iterative form is stable generation of minimizing approximate solutions in the sense of J. Warga. Regularized COCs in iterative form are formulated as existence theorems in the original problem of minimizing approximate solutions. They “overcome” the ill-posedness properties of the COCs and are regularizing algorithms for solving optimization problems. As an illustrative example, we consider an optimal control problem associated with a hyperbolic system of first-order differential equations.

scholarly journals An Optimal Treatment Control of TB-HIV Coinfection

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Fatmawati ◽  
Hengki Tasman
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Optimal Control Theory ◽  
Hiv Infections ◽  
Treatment Control ◽  
Hiv Coinfection ◽  
Existence And Stability ◽  
Disease Free ◽  
The Pontryagin Maximum Principle

An optimal control on the treatment of the transmission of tuberculosis-HIV coinfection model is proposed in this paper. We use two treatments, that is, anti-TB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TB-HIV coinfection model. The model exhibits four equilibria, namely, the disease-free, the HIV-free, the TB-free, and the coinfection equilibria. We further obtain two basic reproduction ratios corresponding to TB and HIV infections. These ratios determine the existence and stability of the equilibria of the model. The optimal control theory is then derived analytically by applying the Pontryagin Maximum Principle. The optimality system is performed numerically to illustrate the effectiveness of the treatments.

scholarly journals KONTROL OPTIMAL PADA PEYEBARAN TUBERKULOSIS DENGAN EXOGENOUS REINFECTION

2019 ◽  
Vol 16 (1) ◽  
pp. 42-50
Author(s):  
J Nainggolan ◽  
F J Iswar ◽  
Abraham Abraham
Keyword(s):  
Numerical Simulation ◽  
Optimal Control ◽  
Mycobacterium Tuberculosis ◽  
Maximum Principle ◽  
Pontryagin Maximum Principle ◽  
Pontryagin’S Maximum Principle ◽  
Pontryagin's Maximum Principle ◽  
Simulation Results ◽  
The Pontryagin Maximum Principle ◽  
Exogenous Reinfection

Tuberculosis is a disease caused by Mycobacterium tuberculosis. Tuberculosis can be controlled through treatment, chemoprophylaxis and vaccination. Optimal control of treatment in the exposed compartment can be done in an effort to reduce the number of exposed compartments individual into the active compartment of tuberculosis. Optimal control can be completed by the Pontryagin Maximum Principle Method. Based on numerical simulation results, optimal control of treatment in the exposed compartment can reduce the number of infected compartments individual with active TB.Keywords : Exogenous Reinfection, Optimal Control, Pontryagin's Maximum Principle, Spread Of Tuberculosis.

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