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.

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.

On an optimal control problem with an integral functional of a rational control function

2009 ◽  
Vol 45 (11) ◽  
pp. 1621-1635 ◽  
Author(s):  
N. L. Grigorenko ◽  
D. V. Kamzolkin ◽  
L. N. Luk’yanova ◽  
D. G. Pivovarchuk
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Integral Functional ◽  
Rational Control

Solving the Problem of the Optimal Control System General Synthesis Based on Approximation of a Set of Extremals using the Symbol Regression Method

2020 ◽  
pp. 59-74
Author(s):  
S.V. Konstantinov ◽  
A.I. Diveev
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Symbolic Regression ◽  
Regression Method ◽  
Synthesis Problem ◽  
Optimal Control System ◽  
Initial States

A new approach is considered to solving the problem of synthesizing an optimal control system based on the extremals' set approximation. At the first stage, the optimal control problem for various initial states out of a given domain is being numerically sold. Evolutionary algorithms are used to solve the optimal control problem numerically. At the second stage, the problem of approximating the found set of extremals by the method of symbolic regression is solved. Approach considered in the work makes it possible to eliminate the main drawback of the known approach to solving the control synthesis problem using the symbolic regression method, which consists in the fact that the genetic algorithm used in solving the synthesis problem does not provide information about proximity of the found solution to the optimal one. Here, control function is built on the basis of a set of extremals; therefore, any particular solution should be close to the optimal trajectory. Computational experiment is presented for solving the applied problem of synthesizing the four-wheel robot optimal control system in the presence of phase constraints. It is experimentally demonstrated that the synthesized control function makes it possible for any initial state from a given domain to obtain trajectories close to optimal in the quality functional. Initial states were considered during the experiment, both included in the approximating set of optimal trajectories and others from the same given domain. Approximation of the extremals set was carried out by the network operator method

Optimal Control Problem with an Integral Functional of an Exponential Control Function

2014 ◽  
Vol 26 (1) ◽  
pp. 1-13 ◽  
Author(s):  
N. L. Grigorenko ◽  
D. V. Kamzolkin ◽  
L. N. Luk’yanova ◽  
D. G. Pivovarchuk
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Integral Functional

scholarly journals The properties of the solution for a class of switched systems with internally forced switching

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Huanting Li ◽  
Xiankang Chen
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Switched Systems ◽  
Special Class ◽  
Continuous Dependence ◽  
Control Function ◽  
The Past ◽  
Controlled Systems ◽  
Affine System

AbstractIn this paper, the dynamic behavior of a class of switched systems with internally forced switching (IFS) is investigated. By introducing the definitions of continuous dependence and differentiability, the continuous dependence and differentiability of the solution relative to the control function are obtained. In the past studies, the optimal control problem given by IFS mainly focused on a special class of controlled systems (the piece affine system). Our results lay a good foundation for studying the more general internally forced switching problem.

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>

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 Optimal Control of HIV Dynamic Using Embedding Method

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
H. Zarei ◽  
A. V. Kamyad ◽  
M. H. Farahi
Keyword(s):  
Optimal Control ◽  
Immune System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Treatment Protocol ◽  
Optimal Solution ◽  
Embedding Method ◽  
Piecewise Constant Control ◽  
The Cost

This present study proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the survival time of patients and minimize the cost of drug utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus (HIV). Optimal control problem transfers into a modified problem in measure space using an embedding method in which the existence of optimal solution is guaranteed by compactness of the space. Then the metamorphosed problem is approximated by a linear programming (LP) problem, and by solving this LP problem a suboptimal piecewise constant control function, which is more practical from the clinical viewpoint, is achieved. The comparison between the immune system dynamics in treated and untreated patients is introduced. Finally, the relationships between the healthy cells and virus are shown.

Optimal control problem for the equation of vibrations of an elastic plate

2018 ◽  
Vol 25 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Hamlet F. Guliyev ◽  
Khayala I. Seyfullaeva
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Elastic Plate ◽  
Control Function ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Necessary Condition ◽  
Necessary Condition Of Optimality ◽  
Initial Boundary Value

AbstractAn optimal control problem for the vibration equation of an elastic plate is considered when the control function is included in the coefficient of the highest order derivative and the right-hand side of the equation. The solvability of the initial boundary value problem is shown, the theorem on the existence of an optimal control is proved and a necessary condition of optimality in the form of an integral equation is obtained.

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