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.

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.

Simulation and optimization in marketing: Optimal control of consumer goodwill, price and investment

2014 ◽  
Vol 05 (03) ◽  
pp. 1450004
Author(s):  
Stanislaw Raczynski
Keyword(s):  
Optimal Control ◽  
Fixed Time ◽  
Static Model ◽  
Market Model ◽  
Time Interval ◽  
Total Revenue ◽  
Product Price ◽  
Simulation And Optimization ◽  
Fixed Time Interval ◽  
Seasonal Index

Dynamic market optimization with respect to price, advertisement and investment is presented. The market model is nonlinear. Its main parameters are the elasticities with respect to price, advertisement and consumer income. Dynamic elements has been added to the static model based on the market elasticities. The parameters like seasonal index and consumer income are functions of time, and the whole market can grow due to the investment. The tools of the optimal control theory are applied to calculate optimal policy for product price, advertisement and investment, controlled simultaneously. The total revenue at the end of a fixed time interval is maximized.

Optimal control of stochastic Ito differential systems by fixed terminal time

1975 ◽  
Vol 7 (1) ◽  
pp. 154-178 ◽  
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Systems ◽  
Fixed Time ◽  
Necessary Condition ◽  
Time Interval ◽  
Optimal Controls ◽  
Cauchy Problems ◽  
Terminal Time ◽  
Partially Observed

In this paper, the authors consider a class of stochastic systems described by Ito differential equations for which both controls and parameters are to be chosen optimally with respect to a certain performance index over a fixed time interval. The controls to be optimized depend only on partially observed current states as in a work of Fleming. However, he considered, instead, a problem of optimal control of systems governed by stochastic Ito differential equations with Markov terminal time. The fixed time problems usually give rise to the Cauchy problems (unbounded domain) whereas the Markov time problems give rise to the first boundary value problems (bounded domain). This fact makes the former problems relatively more involved than the latter. For the latter problems, Fleming has reported a necessary condition for optimality and an existence theorem of optimal controls. In this paper, a necessary condition for optimality for both controls and parameters combined together is presented for the former problems.

Optimal control of stochastic Ito differential systems by fixed terminal time

1975 ◽  
Vol 7 (01) ◽  
pp. 154-178
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Stochastic Systems ◽  
Fixed Time ◽  
Necessary Condition ◽  
Time Interval ◽  
Optimal Controls ◽  
Cauchy Problems ◽  
Terminal Time ◽  
Partially Observed

In this paper, the authors consider a class of stochastic systems described by Ito differential equations for which both controls and parameters are to be chosen optimally with respect to a certain performance index over a fixed time interval. The controls to be optimized depend only on partially observed current states as in a work of Fleming. However, he considered, instead, a problem of optimal control of systems governed by stochastic Ito differential equations with Markov terminal time. The fixed time problems usually give rise to the Cauchy problems (unbounded domain) whereas the Markov time problems give rise to the first boundary value problems (bounded domain). This fact makes the former problems relatively more involved than the latter. For the latter problems, Fleming has reported a necessary condition for optimality and an existence theorem of optimal controls. In this paper, a necessary condition for optimality for both controls and parameters combined together is presented for the former problems.

scholarly journals A minimum trapping time problem in optimal control theory

1990 ◽  
Vol 32 (1) ◽  
pp. 100-114 ◽  
Author(s):  
M. E. Fisher ◽  
J. L. Noakes ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Natural Extension ◽  
Computational Procedure ◽  
Fixed Time ◽  
Minimum Time ◽  
Time Interval ◽  
Trapping Time ◽  
Time Problem

AbstractIn this paper we consider a natural extension of the minimum time problem in optimal control theory which we refer to as the minimum trapping time problem. The minimum trapping time problem requires a fixed time interval [0, T], where T is finite. The aim is to determine a control for which the system trajectory not only reaches a specified target in minimum time but also remains trapped within the target until time T. Our aim is to devise a computational procedure for solving the minimum trapping time problem. The computational procedure we adopt uses control parametrisation in which the class of controls is approximated by a class of piecewise constant functions. The problem we are solving is therefore an approximation to the original minimum trapping time problem. Some properties for the approximate problem are then established. These lead to an extremely efficient iterative procedure for calculating the minimum trapping time.

Computational requirements for a discrete Kalman filter in robot dynamics algorithms

Robotica ◽  
1993 ◽  
Vol 11 (1) ◽  
pp. 27-36 ◽  
Author(s):  
Krzysztof Kozłowski
Keyword(s):  
Boundary Value Problem ◽  
Inverse Dynamics ◽  
Boundary Value ◽  
Equations Of Motion ◽  
Fixed Time ◽  
Time Interval ◽  
Robot Dynamics ◽  
Forward Dynamics ◽  
Point Boundary ◽  
Numerical Studies

SUMMARYIn standard classical kinematic and dynamic considerations the equations of motion for an n-link manipulator can be obtained as recursive Newton-Euler equations. Another approach to finding the inverse dynamics equations is to formulate the system dynamics and kinematics as a two-point boundary-value problem. The equivalence between these two approaches has been proved in this paper. Solution to the two-point boundary-value problem leads to the forward dynamics equations which are similar to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The extensive numerical studies conducted by the author on the new inverse and forward dynamics algorithms derived from the two-point boundary-value problem establish the same level of confidence as exists for current methods. In order to obtain the algorithms with the smallest coefficients of the polynomial of order O(n), the categorization procedure has been implemented in this work.

Utilization of remote sensing for estimation of scale of cutting and growing of forest zones

2017 ◽  
Vol 920 (2) ◽  
pp. 57-60
Author(s):  
F.E. Guliyeva
Keyword(s):  
Remote Sensing ◽  
Fixed Time ◽  
Time Interval ◽  
Time Points ◽  
Average Value ◽  
Time Period ◽  
Remote Estimation ◽  
The Given ◽  
Forest Cutting

The study of results of relevant works on remote sensing of forests has shown that the known methods of remote estimation of forest cuts and growth don’t allow to calculate the objective average value of forests cut volume during the fixed time period. The existing mathematical estimates are not monotonous and make it possible to estimate primitively the scale of cutting by computing the ratio of data in two fixed time points. In the article the extreme properties of the considered estimates for deforestation and reforestation models are researched. The extreme features of integrated averaged values of given estimates upon limitations applied on variables, characterizing the deforestation and reforestation processes are studied. The integrated parameter, making it possible to calculate the averaged value of estimates of forest cutting, computed for all fixed time period with a fixed step is suggested. It is shown mathematically that the given estimate has a monotonous feature in regard of value of given time interval and make it possible to evaluate objectively the scales of forest cutting.

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.

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