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.

Synthesized Optimal Control of Group Interaction of Quadrocopters Based on Multi-Point Stabilization

2020 ◽  
pp. 114-133
Author(s):  
A.I. Diveev ◽  
E.Yu. Shmalko ◽  
O. Hussein
Keyword(s):  
Optimal Control ◽  
Group Interaction ◽  
Operator Method ◽  
Quality Criterion ◽  
Initial Position ◽  
Time Interval ◽  
Flexible Rods ◽  
Optimal Value ◽  
Phase Constraints ◽  
Point Stabilization

The study examines the problem of optimal control of group interaction of three quadrocopters. A group of three quadrocopters must move the load on flexible rods from one point in space to another one without hitting obstacles, one quadrocopter being not able to complete the task due to the weight of the load. To solve the problem, the method of synthesized optimal control based on multi-point stabilization was used. The method is called synthesized, since the problem of synthesizing the stabilization system for each robot is first solved. At the next stage, the problem of the optimal location of stabilization points in the state space is solved in such a way that when these points are switched from one to another, at a given time interval, the quadrocopters move the load from the initial position to the final one with the optimal value of the quality criterion. The network operator method is used to solve the synthesis problem. All phase constraints describing group interaction and obstacles are included in the quality criterion by the method of penalty functions. An evolutionary particle swarm optimization algorithm was used to find the positions of points

scholarly journals A Novel Optimal Control Method for Impulsive-Correction Projectile Based on Particle Swarm Optimization

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Ruisheng Sun ◽  
Qiao Hong ◽  
Gang Zhu
Keyword(s):  
Optimal Control ◽  
Particle Swarm Optimization ◽  
Control Algorithm ◽  
Reference Model ◽  
Particle Swarm ◽  
Suboptimal Control ◽  
Time Interval ◽  
Optimization Approach ◽  
Swarm Optimization ◽  
Model Linearization

This paper presents a new parametric optimization approach based on a modified particle swarm optimization (PSO) to design a class of impulsive-correction projectiles with discrete, flexible-time interval, and finite-energy control. In terms of optimal control theory, the task is described as the formulation of minimum working number of impulses and minimum control error, which involves reference model linearization, boundary conditions, and discontinuous objective function. These result in difficulties in finding the global optimum solution by directly utilizing any other optimization approaches, for example, Hp-adaptive pseudospectral method. Consequently, PSO mechanism is employed for optimal setting of impulsive control by considering the time intervals between two neighboring lateral impulses as design variables, which makes the briefness of the optimization process. A modification on basic PSO algorithm is developed to improve the convergence speed of this optimization through linearly decreasing the inertial weight. In addition, a suboptimal control and guidance law based on PSO technique are put forward for the real-time consideration of the online design in practice. Finally, a simulation case coupled with a nonlinear flight dynamic model is applied to validate the modified PSO control algorithm. The results of comparative study illustrate that the proposed optimal control algorithm has a good performance in obtaining the optimal control efficiently and accurately and provides a reference approach to handling such impulsive-correction problem.

MODELING AND OPTIMAL CONTROL FOR ANTIRETROVIRAL THERAPY

2014 ◽  
Vol 22 (02) ◽  
pp. 199-217 ◽  
Author(s):  
ELLINA V. GRIGORIEVA ◽  
EVGENII N. KHAILOV ◽  
NATALIA V. BONDARENKO ◽  
ANDREI KOROBEINIKOV
Keyword(s):  
Optimal Control ◽  
Control Function ◽  
Optimal Solution ◽  
Target Cells ◽  
Model Parameters ◽  
Time Interval ◽  
Intake Rate ◽  
Bounded Control ◽  
Infection Level ◽  
Hiv Model

We consider a three-dimensional nonlinear control model based on the Wodarz HIV model. The model phase variables are populations of the uninfected and infected target cells and the concentration of an antiretroviral drug. The drug intake rate is assumed to be a bounded control function. An optimal control problem of minimizing the cumulative infection level (the infected cells population) on a given time interval is stated and solved, and the types of the optimal control for different model parameters are found by analytical methods. We thereby reduce the two-point boundary value problem (TPBVP) for the Pontryagin maximum principle to a problem of the finite-dimensional optimization. Numerical results are presented to illustrate the optimal solution.

Phenomen by Fuller in the Problems of Analytical Design of Optimal Regulators

2021 ◽  
Vol 22 (7) ◽  
pp. 339-348
Author(s):  
B. V. Sukhinin ◽  
V. V. Surkov ◽  
N. B. Filimonov
Keyword(s):  
Optimal Control ◽  
Control Object ◽  
Quality Criterion ◽  
Analytical Form ◽  
Practical Implementation ◽  
Phase Variable ◽  
Controlled System ◽  
Optimal Value ◽  
Fast Acting ◽  
Error Coefficients

The problem of synthesis of an optimal controlled system with a quadratic quality criterion having an infinite number of switching points at a finite time inter val is discussed. In the theor y of optimal control, this phenomenon is called the "Fuller phenomenon". For more than 60 years, the Fuller problem has been very attractive, relevant, and still unsolved, especially for non-linear multidimensional dynamical systems of high order, and even more so, with obtaining a solution in an explicit analytical form for practical implementation in a control system.The purpose of this work is to demonstrate the theoretical aspects and practical features of the method of synthesis of optimal control systems by the fast acting criterion by the example of solving problems related to the Fuller phenomenon.When solving these problems, we use in the classical variations calculus and the Pontryagin maximum principle of the method of introducing a new additional phase variable into consideration, which is defined to the integral quality criterion and expands the original phase vector of the object. As a result, if the best optimal control in terms of fast acting for the control object is known then this technique makes it ver y easy to get a worse optimal control in terms of accuracy by including the Fuller accuracy criterion in the dynamics of the control object. It should be note that an important acquisition here is to increase the accuracy to the optimal value and reduce the established control error to zero, with all error coefficients (in position, speed, acceleration, jerk, etc.) equal to zeroin the presence of external and internal interference.Statements and solutions of the classical and modified Fuller problems are presented. As illustrative examples, we consider the traditional problems of the synthesis of optimal control in terms of speed, solved in well-known methods.

Sustainable approach towards the new EU-Sugar Market era

2016 ◽  
pp. 151-155 ◽  
Author(s):  
Arend Wittenberg ◽  
Menno Roukema ◽  
Jan L.M. Struijs ◽  
Olaf van Baal
Keyword(s):  
Production Capacity ◽  
Scaling Up ◽  
Production Costs ◽  
Production Chain ◽  
Northwest Europe ◽  
Market Situation ◽  
Sugar Market ◽  
Strong Market Position ◽  
Growth Scaling ◽  
The Given

Suiker Unie focuses on a strong market position in Northwest Europe at the lowest possible production costs for sugar. The company tries to achieve this by giving attention to the entire production chain. An important pillar of this mission is sustainability. During the recent years Suiker Unie developed a Masterplan to prepare its factories for the new market situation after 2017. In line with Cosun’s strategy of profitable growth, scaling up production capacity of beet factories was defined as goal of this Masterplan. The ambition of reduction of production costs and sustainability (e.g. carbon-footprint) was translated into the challenging constraint to increase the capacity growth within the given steam supply and the actual odour and noise emissions. Based on a thorough bottleneck study a portfolio of measures for each factory is defined, grouped into debottlenecking, energy saving, optimization and environmental projects.

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 Die zeitliche Änderung der radialen Elektronendichteverteilung beim Theta-Pinch

1963 ◽  
Vol 18 (8-9) ◽  
pp. 895-900
Author(s):  
Franz Peter Küpper
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Electron Distribution ◽  
Radial Symmetry ◽  
Zero Order ◽  
Time Interval ◽  
Interferometric Method ◽  
Density Distributions ◽  
Theta Pinch

In a θ-pinch the radial symmetry of the electron density distribution as a function of time has been measured by a MACH—ZEHNDER interferometer. In a time interval of 400 nsec during a discharge an image converter made three pictures (exposure times of 10 nsec each) . Up to 100 nsec after the first compression, the experimental results show different density distributions for the cases of trapped parallel and antiparallel magnetic fields. Complete radial symmetry of the electron density distribution was not found.Another interferometric method for measuring the radial symmetry of the electron distribution by observing “zero order” fringes is described.

Evaluation of Effect of Nd:YAG and Er:YAG Lasers on the Periodontal Pathogens: A Systematic Review

2020 ◽  
Author(s):  
Hosein Eslami
Keyword(s):  
Systematic Review ◽  
Chronic Periodontitis ◽  
Complementary Therapy ◽  
Root Surface ◽  
Laser Wavelength ◽  
Time Interval ◽  
Periodontal Pathogens ◽  
Probing Depth ◽  
Treatment Procedures ◽  
The Given

Introduction: By removing the periodontal pathogens and even the invasive bacteria attacking the tissues as well as the lack of normal periodontal treatment procedures, using a laser, as a complementary therapy, can have positive and useful impacts. The present study aims at investigating the impacts of Nd:YAG and Er:YAG laser on periodontal pathogens. Materials and Methods: In this systematic review, articles in the databases of Google Scholar, PubMed and Scopus were searched within 2000-2020. All information is classified into a table. Results: In searching the aforementioned databases and considering the given time interval, 78 articles were found in connection to the searched keywords and abstracts. Once the repeated titles and articles were deleted, 25 studies were selected which were decreased to 16 by the meticulous review by the assessment team. The full text of these 16 articles was reviewed. To make the final choice, 8 articles had the inclusion criteria which included the objectives of this study. Conclusion: To use the laser in treating the chronic periodontitis, an evidence-based study seems to be conducted. A few scientific pieces of evidence are indicating the advantage of a special laser wavelength in the common treatments.Based on most researches reviewed in this study, the results of the complementary application of Nd:YAG and Er:YAG lasers in treating the chronic periodontitis are the better than the ones obtained from the normal teeth scaling and planning the teeth root surface in terms of the reduced probing depth and subgingival bacteria population. The decision was made to use the laser in periodontal surgery based on the advantages such as hemostasis and less pain after the treatment. However, more studies are needed to apply the laser in periodontal treatments.

scholarly journals Quasilinearization of the Initial Value Problem for Difference Equations with “Maxima”

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
S. Hristova ◽  
A. Golev ◽  
K. Stefanova
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Initial Value Problem ◽  
Linear Difference Equation ◽  
Successive Approximations ◽  
Time Interval ◽  
Initial Value ◽  
Past Time ◽  
The Given ◽  
Unknown Solution

The object of investigation of the paper is a special type of difference equations containing the maximum value of the unknown function over a past time interval. These equations are adequate models of real processes which present state depends significantly on their maximal value over a past time interval. An algorithm based on the quasilinearization method is suggested to solve approximately the initial value problem for the given difference equation. Every successive approximation of the unknown solution is the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima,” and a formula for its explicit form is given. Also, each approximation is a lower/upper solution of the given mixed problem. It is proved the quadratic convergence of the successive approximations. The suggested algorithm is realized as a computer program, and it is applied to an example, illustrating the advantages of the suggested scheme.

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