scholarly journals An optimal control problem of immuno-chemotherapy in presence of gene therapy

2021 ◽  
Vol 6 (10) ◽  
pp. 11530-11549
Author(s):  
Kaushik Dehingia ◽  
◽  
Hemanta Kumar Sarmah ◽  
Kamyar Hosseini ◽  
Khadijeh Sadri ◽  
...  
Keyword(s):  
Gene Therapy ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Tumor Cells ◽  
Equilibrium Points ◽  
Time Interval ◽  
Drug Induced ◽  
Effector Cells ◽  
Proposed Model

<abstract><p>This study addresses a cancer eradication model involving effector cells in the presence of gene therapy, immunotherapy, and chemotherapy. The main objective of this study is to understand the optimal effect of immuno-chemotherpay in the presence of gene therapy. The boundedness and positiveness of the solutions in the respective feasible domains of the proposed model are verified. Conditions for which the equilibrium points of the system exist and are stable have been derived. An optimal control problem for the system has been constructed and solved to minimize the immuno-chemotherapy drug-induced toxicity to the patient. Amounts of immunotherapy to be injected into a patient for eradication of cancerous tumor cells have been found. Numerical and graphical results have been presented. From the results, it is seen that tumor cells can be eliminated in a specific time interval with the control of immuno-chemotherapeutic drug concentration.</p></abstract>

scholarly journals An Optimal Control Problem of Chemotherapy In Presence of Gene and Immunotherapy

2021 ◽  
Author(s):  
kaushik dehingia
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Tumor Cells ◽  
Equilibrium Points ◽  
Time Interval ◽  
Chemotherapeutic Drug ◽  
Drug Induced ◽  
Effector Cells ◽  
Proposed Model

Abstract In this study, a cancer eradication model involving effector cells in the presence of gene therapy, immunotherapy, and chemotherapy has been proposed. Boundedness and positiveness of the solutions in the respective feasible domains of the proposed model are verified. Conditions for which the equilibrium points of the system are stable have been derived. Amounts of immunotherapy to be injected to a patient for eradication of cancerous tumor cells have been found. To minimize the chemotherapy drug-induced toxicity to the patient, an optimal control problem for the system has been constructed and solved. Numerical and graphical results have been presented. Through the investigation, it was seen that tumor cells can be eliminated in a specific time interval with the control of chemotherapeutic drug concentration.

scholarly journals On Optimal Retirement

2014 ◽  
Vol 51 (02) ◽  
pp. 333-345 ◽  
Author(s):  
Philip A. Ernst ◽  
Dean P. Foster ◽  
Larry A. Shepp
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Time Interval ◽  
Investment Strategies ◽  
Net Worth ◽  
New Model ◽  
Ito Process

We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function f and our current net worth X(t) for any t, we invest an amount f(X(t)) in the market. We need a fortune of M ‘superdollars’ to retire and want to retire as early as possible. We model our change in net worth over each infinitesimal time interval by the Itô process dX(t) = (1 + f(X(t)))dt + f(X(t))dW(t). We show how to choose the optimal f = f 0 and show that the choice of f 0 is optimal among all nonanticipative investment strategies, not just among Markovian ones.

Discrete-time interval optimal control problem

2017 ◽  
Vol 92 (8) ◽  
pp. 1778-1784 ◽  
Author(s):  
J. R. Campos ◽  
E. Assunção ◽  
G. N. Silva ◽  
W. A. Lodwick ◽  
M. C. M. Teixeira
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Discrete Time ◽  
Time Interval

scholarly journals Stabilization and Analytic Approximate Solutions of an Optimal Control Problem

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 476-487 ◽  
Author(s):  
Camelia Pop ◽  
Camelia Petrişor ◽  
Remus-Daniel Ene
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Equilibrium Points ◽  
Approximate Solutions ◽  
Linear Control ◽  
Runge Kutta Method ◽  
The Stability ◽  
Stability Results

Abstract This paper analyses a dynamical system derived from a left-invariant, drift-free optimal control problem on the Lie group SO(3) × ℝ3 × ℝ3 in deep connection with the important role of the Lie groups in tackling the various problems occurring in physics, mathematics, engineering and economic areas [1, 2, 3, 4, 5]. The stability results for the initial dynamics were inconclusive for a lot of equilibrium points (see [6]), so a linear control has been considered in order to stabilize the dynamics. The analytic approximate solutions of the resulting nonlinear system are established and a comparison with the numerical results obtained via the fourth-order Runge-Kutta method is achieved.

scholarly journals On Optimal Retirement

2014 ◽  
Vol 51 (2) ◽  
pp. 333-345 ◽  
Author(s):  
Philip A. Ernst ◽  
Dean P. Foster ◽  
Larry A. Shepp
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Time Interval ◽  
Investment Strategies ◽  
Net Worth ◽  
New Model ◽  
Ito Process

We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function f and our current net worth X(t) for any t, we invest an amount f(X(t)) in the market. We need a fortune of M ‘superdollars’ to retire and want to retire as early as possible. We model our change in net worth over each infinitesimal time interval by the Itô process dX(t) = (1 + f(X(t)))dt + f(X(t))dW(t). We show how to choose the optimal f = f0 and show that the choice of f0 is optimal among all nonanticipative investment strategies, not just among Markovian ones.

Optimal Feedback Production for a Supply Chain

2005 ◽  
pp. 50-66
Author(s):  
K. Wong ◽  
H. W.J. Lee ◽  
Chi Kin Chan
Keyword(s):  
Optimal Control ◽  
Supply Chain ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Objective Function ◽  
Production Rate ◽  
Infinite Horizon ◽  
Time Interval ◽  
Control Parameterization ◽  
Demand Rate

In this chapter, we modeled the dynamics of a supply chain considered by several authors. An infinite-horizon, time-delayed, optimal control problem was thus obtained. By approximating the time interval [0, ¥] by [0, Tf ], we obtained an approximated problem (P(Tf )) which could be easily solved by the control parameterization method. Moreover, we could show that the objective function of the approximated problem converged to that of the original problem as Tf ® ¥. Several examples have been solved to illustrate the efficiency of our method. In these examples, some important results relating the production rate to demand rate have been developed.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

Sign in / Sign up

Export Citation Format

Share Document