Optimal Control on a Time Interval of Random Duration

1996 ◽  
pp. 435-466
Author(s):  
V. N. Afanas’ev ◽  
V. B. Kolmanovskii ◽  
V. R. Nosov
Keyword(s):  
Optimal Control ◽  
Time Interval

scholarly journals Optimal Control and Positional Controllability in a One-Sector Economy

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 11
Author(s):  
Nikolai Grigorenko ◽  
Lilia Luk’yanova
Keyword(s):  
Optimal Control ◽  
Production Capacity ◽  
Quality Criterion ◽  
Zero Order ◽  
Suboptimal Control ◽  
Time Interval ◽  
Bounded Control ◽  
Optimal Value ◽  
Current Production ◽  
The Given

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

A PROPOSED FORMULA FOR HORIZONTAL REVENUE ALLOCATION IN NIGERIA

2012 ◽  
Vol 29 (06) ◽  
pp. 1250033
Author(s):  
VIRTUE U. EKHOSUEHI ◽  
AUGUSTINE A. OSAGIEDE
Keyword(s):  
Optimal Control ◽  
Federal Government ◽  
Optimal Control Theory ◽  
Fixed Time ◽  
Tax Revenue ◽  
Time Interval ◽  
Fixed Time Interval ◽  
Hypothetical Data ◽  
Revenue Allocation ◽  
The Individual

In this study, we have applied optimal control theory to determine the optimum value of tax revenues accruing to a state given the range of budgeted expenditure on enforcing tax laws and awareness creation on the payment of the correct tax. This is achieved by maximizing the state's net tax revenue over a fixed time interval subject to certain constraints. By assuming that the satisfaction derived by the Federal Government of Nigeria on the ability of the individual states to generate tax revenue which is as near as the optimum tax revenue (via the state's control problem) is described by the logarithmic form of the Cobb–Douglas utility function, a formula for horizontal revenue allocation in Nigeria in its raw form is derived. Afterwards, we illustrate the use of the proposed horizontal revenue allocation formula using hypothetical data.

scholarly journals Optimal Control against the Human Papillomavirus: Protection versus Eradication of the Infection

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Fernando Saldaña ◽  
Andrei Korobeinikov ◽  
Ignacio Barradas
Keyword(s):  
Optimal Control ◽  
Human Papillomavirus ◽  
Control Problem ◽  
Initial Conditions ◽  
Fixed Time ◽  
Hpv Infection ◽  
Control Problems ◽  
Time Interval ◽  
Optimal Controls ◽  
Total Prevalence

We investigate the optimal vaccination and screening strategies to minimize human papillomavirus (HPV) associated morbidity and the interventions cost. We propose a two-sex compartmental model of HPV-infection with time-dependent controls (vaccination of adolescents, adults, and screening) which can act simultaneously. We formulate optimal control problems complementing our model with two different objective functionals. The first functional corresponds to the protection of the vulnerable group and the control problem consists of minimizing the cumulative level of infected females over a fixed time interval. The second functional aims to eliminate the infection, and, thus, the control problem consists of minimizing the total prevalence at the end of the time interval. We prove the existence of solutions for the control problems, characterize the optimal controls, and carry out numerical simulations using various initial conditions. The results and properties and drawbacks of the model are discussed.

Discrete Mechanics and Optimal Control of Walking Gaits

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
M. W. Koch ◽  
M. Ringkamp ◽  
S. Leyendecker
Keyword(s):  
Optimal Control ◽  
Time Span ◽  
Constrained Systems ◽  
Bipedal Walking ◽  
Interval Length ◽  
Time Interval ◽  
Discrete Mechanics ◽  
Flat Foot ◽  
Flat Feet ◽  
Heel Contact

In this work, we optimally control the upright gait of a three-dimensional symmetric bipedal walking model with flat feet. The whole walking cycle is assumed to occur during a fixed time span while the time span for each of the cycle phases is variable and part of the optimization. The implemented flat foot model allows to distinguish forefoot and heel contact such that a half walking cycle consists of five different phases. A fixed number of discrete time nodes in combination with a variable time interval length assure that the discretized problem is differentiable even though the particular time of establishing or releasing the contact between the foot and the ground is variable. Moreover, the perfectly plastic contact model prevents penetration of the ground. The optimal control problem is solved by our structure preserving discrete mechanics and optimal control for constrained systems (DMOCC) approach where the considered cost function is physiologically motivated and the obtained results are analyzed with regard to the gait of humans walking on a horizontal and an inclined plane.

DECISION-MAKING IN A HYBRID TWO-STEP PROBLEM OF DYNAMIC CONTROL

2018 ◽  
pp. 415-423
Author(s):  
Anatolii Fedorovich Kleimenov
Keyword(s):  
Optimal Control ◽  
Equations Of Motion ◽  
Dynamic Control ◽  
Control Process ◽  
Fixed Time ◽  
Time Interval ◽  
Initial Moment ◽  
Fixed Amount ◽  
Controlled System ◽  
Abnormal Behaviors

The equations of motion of the controlled system in the two-step problem under consideration at a fixed time interval contain the controls of either one player or two players. In the first step (stage) of the controlled process (from the initial moment to a certain predetermined moment), only the first player controls the system, which solves the problem of optimal control with a given terminal functional. In the second step (stage) of the process, the first player decides whether the second player will participate in the control process for the remainder of the time, or not. It is assumed that for participation the second player must pay the first side payment in a fixed amount. If «yes», then a non-antagonistic positional differential game is played out, in which the Nash equilibrium is taken as the solution. In addition, players can use «abnormal» behaviors, which can allow players to increase their winnings. If « no », then until the end of the process continues to solve the problem optimal control.

scholarly journals LQG Homing in a Finite Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-3 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Diffusion Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Fixed Constant

LetX(t)be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controllingX(t)until timeT(x)=min{T1(x),t1}, whereT1(x)is the first-passage time of the process to a given boundary andt1is a fixed constant. The optimal control is obtained explicitly in the particular case whenX(t)is a controlled Wiener process.

Sign in / Sign up

Export Citation Format

Share Document