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 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.

Quadrocopter Control by Network Operator Method Based on Multi-Point Stabilization

2020 ◽  
Vol 21 (7) ◽  
pp. 428-438
Author(s):  
A. I. Diveev ◽  
E. Yu. Shmalko ◽  
O. Hussein
Keyword(s):  
Optimal Control ◽  
Control System ◽  
State Space ◽  
Operator Method ◽  
The State ◽  
Angular Motion ◽  
Stabilization System ◽  
Network Operator ◽  
System Synthesis ◽  
Phase Constraints

The paper presents a solution to the problem of optimal control of a quadrocopter under phase constraints by the numerical method of a network operator based on multi-point stabilization. According to this approach, the task of control system synthesis is initially solved. As a result, the quadrocopter is stabilized with respect to a certain point in the state space. At the second stage, a sequence of stabilization points is searched in the state space such that switching the stabilization points at fixed times ensures the movement of the quadrocopter from the initial state to the terminal state with an optimal value of the quality criterion taking into account phase constraints. To solve the problem of stabilization system synthesis, the network operator method is used. The method is numerical and, unlike the well-known analytical methods, allows to synthesize a control system automatically without a specific analysis of the right parts of the model. The method allows to find the structure and parameters of a mathematical expression in the encoded form using the genetic algorithm. The network operator code is an integer upper-triangular matrix. At the stage of solving the synthesis problem, the mathematical model of quadrocopter motion is decomposed into angular and spatial motions in order to separate control components for angular and spatial motions, respectively. The synthesized stabilization system consists of two subsystems connected in series for spatial and angular motion. As controls for spatial motion, moments around the axes and the total thrust of all quadcopter propellers were used. And the inputs for the angular motion stabilization system are the desired angles of inclination of the quadrocopter. The stabilization problem is considered as a general synthesis task for a control system. Using the network operator method, one control function is searched that provides stabilization of the object at a given point in the considered state space from the set of initial conditions. At the stage of the search for equilibrium points, the evolutionary particle swarm algorithm is used. A numerical example of solving the problem of optimal control of a quadrocopter with four phase constraints is given.

scholarly journals Optimal control of a rocket projectile according to the "minimum force" criterion

2021 ◽  
pp. 42-51
Author(s):  
Sergey Lutmanov ◽  
Keyword(s):  
Optimal Control ◽  
Quality Criterion ◽  
Initial Position ◽  
Resistance Force ◽  
Control Force ◽  
Force Vector ◽  
Force Criterion ◽  
Air Resistance ◽  
Vector Differential Equation ◽  
Minimum Force

The article solves the problem of optimal control of a rocket projectile by its delivery from a given initial position to a given final position, taking into account the air resistance force. The motion of the projectile is described by the vector differential equation of I.V. Meshchersky. The control quality criterion is taken in the form of "minimum force", the minimization of which ensures minimal overloads for the projectile. Three types of the norm of the control force vector are considered. For each of them, an optimal control is obtained that solves the task. The analysis of the results of the numerical experiment is carried out, confirming the general theoretical provisions.

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.

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.

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 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.

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