Search

Differential inclusions have numerous applications in optimal control theory. The class of differential inclusions with control parameter are a convenient mathematical apparatus for studying problems of controlling a trajectories of a dynamic system under conditions of uncertainty. In the work considers a dynamical control system described by a linear differential inclusion with a delay argument. For this model of the control system, the optimization problem was studied according to the criterion of minimizing a non-smooth terminal functional of maximum type. The studied optimal control problem has the minimax form. Using methods from the theory of multivalued mappings and differential inclusions, necessary and sufficient conditions for optimality are obtained. The found optimality conditions are the theoretical basis of the method for constructing optimal control in the problem considered. As a substantiation of this conclusion, an algorithm for finding optimal control is proposed. [ABSTRACT FROM AUTHOR]

This paper deals with susceptible (S(t)), vaccinated (V(t)), exposed (E(t)), actively-infected (I(t)), and low-risk latent (L(t)), which describes the spread of tuberculosis with imperfect vaccine. We extend the model of Saputra et al. [1], an SVEIL model, by incorporating two control terms and applying optimal control theory to the resulting model. To control the disease spread, we introduce two measures, namely an education campaign to the public society, and screening and treatment for exposed individuals. Then we formulate the optimal control problem for those measures. The Pontragin's Minimum Principle is applied to obtain the optimal control characterization. The optimality system is solved numerically using the forward-backward method which is based on the fourth-order Runge-Kutta methods. Numerical simulations are presented to understand how the different optimal control strategies give effect in reducing the prevalence of tuberculosis disease. From the cost effectiveness analysis using ACER and ICER calculation, we find out that a single control of giving educational campaigns is the most effective strategy to reduce the spread of tuberculosis infection. [ABSTRACT FROM AUTHOR]

In this paper, an efficient analytical technique, namely the Optimal Homotopy Asymptotic Method (OHAM) is proposed to find an explicit and very accurate analytical solution to the motion of the center of mass of the human body. A numerical example is developed to prove the accuracy of the proposed approach, which is based on the presence of some convergence-control parameters whose optimal values ensure an excellent accuracy of the analytical solution constructed for particular cases. [ABSTRACT FROM AUTHOR]

In the present work, new analytical formula expressing the derivatives of Shifted Modified Chebyshev Polynomials (SMCPs) of any degree explicitly in terms of SMCPs themselves is contracted and proved. Then new scheme to obtain approximated solutions to optimal control problems is investigated. The obtained differentiation matrix is utilized in this scheme. The NSMCPs are used in the shifted case as a functional approximation in the shifted case. The presented project aims to transfer the original optimal control problem to optimization problems by approximating the state variable using NSMCPs with unknown coefficients. Then the constraints equation and the objective function are reduced to algebraic equations. As a result, an optimal control problem becomes an optimization problem. The proposed algorithm is designed to get both efficiency and accuracy simultaneously. The convergence of NSMCPs is also proved in this work. The high accuracy of the obtained results is illustrated with some numerical tests. [ABSTRACT FROM AUTHOR]

This study aims to explore a non-linear multi-agent with an optimal control theory approach are conducted, for an infinite system end time. This optimal control theory approach is known as an infinite horizon system. This research started with the latest studies, which are observed to be related to the multi-agents and infinite horizon time, as it aims to determine the methods, which are needed to control the movement of agents in an optimal path, without collision or moving away from each other. In this study, the non-linear model used was the Dubin model. Moreover, a functional model of costs, which describes the joint duties of agents, was also presented and used. Also, an infinite end time approach was specifically used, as there were initial and final requirements that should be attained by the agents. These initial and final requirements were the condition of the agents, at the beginning and infinite periods during the research. Another method used was the Pontryagin Maximum Principle, which was reported to have successfully resolved the problems associated with this research. The results of these agents being controlled were further presented at the end of this paper. [ABSTRACT FROM AUTHOR]

The article proposes the use of numerical optimization methods for solving the problems of researching the reliability of electric drives control. A review and analysis of existing numerical methods of the optimal control theory and the choice of a mathematical model is carried out. An algorithm, based on the optimal control theory methods, for calculating the optimal dynamic modes operation of a frequency-controlled high-inertia asynchronous electric drive has been developed. The application of the maximum principle and the Newton-Raphson method is given. The software has been improved to effectively solve the optimal control problems of the asynchronous electric drive frequency start. The operation modes from the maximum speed to the minimum-minimorum mode (the lower limit of possible diagrams) have been determined. The results obtained provide scientifically grounded recommendations to developers, designers and operators on the use of computational and graphical data and the optimal control algorithm. This will make it possible to determine the reserve possibilities for increasing the energy efficiency and operational reliability of a frequency-controlled asynchronous electric drive intended for various sectors of the national economy. [ABSTRACT FROM AUTHOR]

We investigate quantum control of isotope-selective molecular orientation using optimal control theory. The target in this study is to inversely orient two isotopologues, 7Li37Cl and 7Li35Cl, along the field polarization vector. The Hamiltonian includes dipole and polarization interactions and we prepare two laser sources, one of which is responsible for resonant transitions through the dipole interaction and the other is stronger and responsible for nonresonant transitions through the polarization interaction. Total time of the control pulse is set to twice the rotational period that is defined as the inverse of the J = 1 ← 0 transition frequency (J: the rotational quantum number). As a result of the calculation at 0 K, an optimal field leads to the expectation values of cosθ (θ: the angle between the field polarization vector and the molecular axis) for the two isotopologues, 0.76 and -0.78, indicating that the control is successful. It is found that in the optimal field the resonant and nonresonant pulses cooperatively interact with the molecules to enhance the control efficiency. [ABSTRACT FROM AUTHOR]

Two new variants of optimal controls (accelerations) of the object translational motion with the same motion goals are proposed and investigated. When designing controls, special conditions were used. Implementation of the conditions ensures a decrease in energy consumption for achieving the final state. Comparing the design results and the known solution (obtained by the variational method of the classical optimal control theory) it was revealed the advantages of the proposed controls of the "acceleration-deceleration" type, which make it possible to reduce energy consumption for the implementation. [ABSTRACT FROM AUTHOR]

The paper is devoted to analysis of the structure of approximation schemes for value functions in optimal control problems with the infinite time horizon. The problem peculiarity is a quality functional with an unbounded integrand, which is discounted by an exponential index. The main result is reduction of the optimal control problem to an equivalent problem with the value function that has the compact definition domain and the compact value range. This goal is reached by a series of nonlinear changes of variables and the transformations of the system dynamics and the Hamilton-Jacobi equations. The proposed method is resulted, first, in obtaining the strongly invariant calculation domains of approximation schemes and, second, in compactification of ranges for the value functions. The first property provides the opportunity to implement approximation schemes in the form of numerical finite difference schemes for the value functions in compact definition domains. The second property guarantees convergence of approximation schemes to the value functions. [ABSTRACT FROM AUTHOR]

We study the quantum control of isotope-selective rovibrational transitions for a binary mixture of diatomic alkali halides, 7Li37Cl and 7Li35Cl. Optimal control theory (OCT) calculations are carried out using the Hamiltonian including both the one-photon and two-photon field-molecule interaction terms. Time-dependent wave packet propagation is performed with both the radial and angular motions being treated quantum mechanically. The targeted processes are exciting one isotoplologue, 7Li37Cl, rotationally and vibrationally-rotationally, while suppressing any excitation of the other, 7Li35Cl. Total time of the control pulse is set to 2000000 atomic unit (48.4 ps). In each control excitation process weak and strong (two-photon absorption and Raman) optimal fields are obtained and total of six processes are investigated. It is found as a result of OCT calculations that every single process can be highly controlled with an appropriate control field. [ABSTRACT FROM AUTHOR]

The present paper studies a Bolza problem of optimal control theory with third-order polyhedral delay-differential inclusions and state constraints. We aim to establish well verifiable sufficient conditions of optimality for the polyhedral third- order delay-differential inclusions. Discrete-approximate inclusions are investigated using the method of discretization to ensure the transition to a continuous problem. The idea for obtaining sufficient conditions of the problem is based on passing the formal limit on the optimality conditions of the discrete-approximation problem. Thus, the sufficient conditions are formulated by using polyhedral Euler-Lagrange inclusions and the distinctive "transversality" conditions. [ABSTRACT FROM AUTHOR]

In this article the solvability of the problem of optimal control of oscillatory processes described by the integro- differential equation with the Fredholm operator, with given control limitation is investigated. It is established that the desired control is among the solutions of the nonlinear Fredholm integral equation of the first kind. Sufficient conditions for the existence of a solution of nonlinear optimization problem are found. [ABSTRACT FROM AUTHOR]

Formulation and approximated numerical solution of fixed final time and fixed final state optimal control problem (OCP) of fractional order singular system (FOSS) in the sense of Caputo derivative is presented in this paper. General form of performance index (PI) is considered. Singular systems (SSs) are complex in nature. Due to this, solution is difficult. Therefore, first we transform FOSS into the standard fractional order system (SFOS) using coordinate transformation and then obtain the optimal necessary conditions. Approximated numerical solution of necessary conditions is obtain by using Grünwald–Letnikov approximation (GLA) based numerical method. In order to demonstrate the applicability of the formulation and efficacy of solution method, an example is illustrated. [ABSTRACT FROM AUTHOR]

The problems to optimize the dynamic systems are complex and traditionally can be reduced to a two-point boundary value problem. Therefore, the problem to obtain the control laws close to optimal law and suitable for practical implementation is always relevant. Performed mathematical simulation shows that the controls synthesis based on the analysis of the variation of the extended functional on the set of functions of bounded variation leads to a constructive result. [ABSTRACT FROM AUTHOR]

In the class of problems in the optimal control theory for objects motion in a viscous medium, new formulations with advanced mathematical models, including additional parameters of the medium, are investigated. Such problems are degenerate and their solution requires the development of a special mathematical apparatus. In particular, the formulation of the problem of optimal energy consumption for overcoming the resistance of a viscous medium of variable density, the translational displacement of a variable form solid from one phase state to another (the displacement time is specified) is considered. An analysis of the nonlinear relationships of the physical characteristics of a viscous medium has been carried out and a mathematical model has been constructed taking into account these relationships. The features of the of optimal control problem of the movement of bodies with variable geometry in a viscous medium of variable density from the point of view of the theory of optimal control are revealed. The necessary optimality conditions are obtained. The construction of such a displacement is associated with the solution of some two–point boundary value problem for a system of Navier–Stokes equations and having a similar structure of the conjugate system. [ABSTRACT FROM AUTHOR]

Hydro-turbine governing system (HTGS) is a complicated nonlinear system that is directly related to the safety of the hydropower stations. In this paper, a simplified predictive control method is presented for the HTGS. Moreover, the system parameters of the predictive controllers are given. Simulated results are presented to evaluate the control performance of the predictive controller, which is compared with the conventional PID controller. [ABSTRACT FROM AUTHOR]

In this paper we consider a version of the Ramsey growth model in finite and continuous time, with the bounded consumption. This model of Ramsey leads to an optimal control problem. We prove an existence theorem of the optimal solution for this optimal control problem. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal shaping of the H section steel beam constituting part of an integral steel-concrete bridge girder. The problem is formulated as a control theory task. Consecutive work phases (construction and exploitation ) with different static schemes, cross-sectional characteristics and loadings are incorporated in the task formulation. The solution is compared to results obtained from the finite element software Abaqus. [ABSTRACT FROM AUTHOR]

In this paper we present a dynamic model of economic growth taking into account the ecological balance. This model is a problem of optimal control on feedback of the investments of a firm related to the production and the deterioration of the pollution generated by the industries, in order to maximize the profit of the firm. the containtes of this model, are two hyperbolic dynamic equations, correspond to the accumulation of physical and human capital [ABSTRACT FROM AUTHOR]

This paper aims to study optimal control of a nonlinear composite beam using classical PJD controller. The optimal PJD parameters are obtained through numerical simulations using fminsearch algorithm. For this purpose, a suitable objective function is constructed based on weighted mean of the different well-known performance criteria leading to obtain a tracking error from the error dynamics of the closed loop system of the beam. An arbitrary desired trajectory is chosen to confirm the efficacy of the proposed optimal control scheme as the actual trajectory is found to be closely matched with the desired. [ABSTRACT FROM AUTHOR]

In this paper we consider a network of micro grid systems including various distributed energy generation systems such as photo-voltaic with storage, diesel generators, wind turbines, combined heat and power system. The main objective is to satisfy heat and power for rural areas in Morocco. The maximum Pontryagin principal will be used to overcome technical constraints and track a reference load taking account the minimal cost. Simulations are given for the obtained result for a network of four micro grids with different generation and demand profiles. [ABSTRACT FROM AUTHOR]

We consider the problem of optimal control of a system consisting of two coupled cylinders. Such a system is a mathematical model of the nuclear fuel transfer mechanism at the nuclear power plant reactor. And also, such models are found in various robotic systems. We have obtained optimal control under certain assumptions on a controllable system. [ABSTRACT FROM AUTHOR]

The ballistic design of interplanetary missions consists of a choice of control programs and associated trajectories that ensure the achievement of the objective while meeting a variety of constraints. The use of solar-sails spacecraft for interplanetary missions imposes additional restrictions on mission parameters. These include limitations on the flight duration, the minimum distance from the Sun, the maximum angular velocity of spacecraft's rotation and many others. Obtaining an exact optimal solution to such complex problem is associated with significant theoretical and computational difficulties. In this paper, they describe a technique for designing interplanetary missions of a solar sail spacecraft, based on the use of locally optimal control laws. This method allows determining such a combination of these laws, which ensures all mission's requirements. An example of the application of the described technique to the calculation of the research mission associated with the exit from the Solar system is given. [ABSTRACT FROM AUTHOR]

This paper describes development and modeling of the spacecraft transfer schemes with low-thrust engines from a high-elliptical (with eccentricity up to 0.7 and more) to a geostationary orbit. The problem of orbital elements optimal control is formulated according to Pontryagin maximum principle. The problem of finding the optimal control law is solved using local optimization method. An algorithm and software are developed to solve the problem of flight optimization between non-coplanar orbits. The comparison of calculation results with local optimal control law and precise solutions showed that for a wide range of boundary conditions the results of calculations differ within a margin of no more than 1.5 – 2 %. Modeling examples of the developed control law for two cases of transfer from high-elliptical to a geostationary orbit are given. [ABSTRACT FROM AUTHOR]

The paper considers a three-dimension nonlinear motion of a spacecraft with frame-type solar sail. The mathematical model of a guided heliocentric motion is described within combined polar coordinate system. The locally optimal control laws of orbital element maintenance and correction are formulated. The solar sail spacecraft guided motion is analyzed. The flight trajectory, dependency graphs of flight parameters against duration are obtained. [ABSTRACT FROM AUTHOR]

The air of this research is obtaining of nominal control programs in problem of far rendezvous at geostationary orbit with low transversal thrust. The problem of control program designing in linear approximation divided to control in orbital plane and control in lateral direction. Motion in orbital plane is separate to secular and periodic. Using Pontriagins maximum principle, the structure of optimal control program with transversal thrust is determined. Base on optimal control program, the simple analytical control programs is obtained. Numeric simulation of rendezvous transfer with obtained control programs is carried out. [ABSTRACT FROM AUTHOR]

The problem of maximization of the horizontal coordinate of the intermediate vehicle model is considered. It is assumed, that vehicle is moving in the vertical plane driven by gravity, viscous drag, and thrust. Goal function is a horizontal coordinate of the vehicle. The slope angle and the thrust are considered as a control variables. Principle maximum procedure allows to reduce the optimal control problem to the boundary value problems for a system of two nonlinear differential equations. The extremal thrust is designed in feedback form depending on the slope angle and state variables. The qualitative analysis of the extremal trajectories is performed, and the characteristic features of the optimal solutions are determined. It is established that for the case of linear viscous drag the optimal thrust program does not contain any singular arcs. Besides, it is shown that optimal thrust program consists of either two arcs, maximum thrust at the beginning and zero thrust at the end, or three arcs: zero thrust at the beginning, then maximum thrust and again zero thrust at the end. [ABSTRACT FROM AUTHOR]

We consider a reachability problem for a nonlinear control-affine system with integral constraints on the state and control variables (isoperimetric constraints). The constraints supposed to be quadratic in control variables. Under controllability assumptions for the linearization of the system it is proved that any admissible control that steers the control system to the boundary of its reachable set is a local solution to some auxiliary optimal control problem with a vector-valued cost functional and terminal constraints on the trajectory. This leads to the Pontryagin maximum principle for boundary trajectories. We propose here a numerical algorithm for computing the reachable set boundary based on the maximum principle and provide some numerical examples of reachable sets for a linear systems with two convex quadratic isoperimetric constraints. [ABSTRACT FROM AUTHOR]

The translational movement in a viscous medium a homogeneous solid with a sufficiently smooth surface is considered. The center of mass moves along the curve connecting the origin of the coordinate system with a given point of space. Such motion is provided by a control force applied to the center of mass along the tangent to the curve of the trajectory. The problem is to determine the control force, under the action of which the mass center of the body at a given time reaches a predetermined point in space with minimum expenditure of energy to overcome the viscous resistance. To calculate the drag the Boussinesq approach is used. The problem does not involve any geometric restrictions on the control force. In such a situation, impulse components may appear in the composition of the optimal control force. Therefore, an attempt to solve this problem using known classical variational procedures is not correct. The original problem is reduced to an auxiliary problem that does not contain constraints on the phase coordinates and products of generalized functions. [ABSTRACT FROM AUTHOR]

The problems of reachability for control systems with integral constraints on the control variables have been studied in the literature on the optimal control theory. For a nonlinear control-affine system on a finite time interval it was shown that every admissible control that steers the control system to the boundary of its reachable set is a local solution of some auxiliary optimal control problem with an integral cost. In this paper we prove an analog of this result for an abstract control system defined by a differentiable mapping in Banach spaces with a constraint, given as a level set of some continuous functional. The proof is based on the covering mappings theorem for differentiable mappings of Banach spaces. We consider a nonlinear affine-control system with integral constraints on the state and the control variables given by the joint integral inequality with an integrant quadratic in the control variables. Assuming the controllability of the linearized system, we prove that any admissible control, that steers the control system to the boundary of its reachable set, is a local solution to an optimal control problem with integral cost functional. Necessary conditions are obtained for the optimality of controls taking the system to the boundary of the reachable set in the form of Pontryagin's maximum principle. An algorithm for computing the reachable sets based on the maximum principle is proposed. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) is one of the contagious and deadly disease in the world. TB can mutate into Multidrug Resistance Tuberculosis (MDR-TB) if the patient does not start with an appropriate treatments. These two diseases can be modeled using system of ten-dimensional ordinary differential equation which represents 10 groups of individuals. Analytic and numerical analysis are done to explain the existence of equilibrium points and the basic reproduction number (R0) of the model. The analytic and numerical analysis results show that the disease free equilibrium point is locally asymptotically stable if (R01 < 1) and unstable if (R > 1). The level set of (R0) respect to interventions parameters is discussed to understand the sensitivity of each parameters to control the spread of TB and MDR-TB. In this paper, the model is also constructed as an optimal control problem with involving three control variables, such as BCG vaccination, treatment with first-line anti-TB drug, and treatment with second-line anti-TB drug. The aim of this problem is to minimize the number of infected individuals and also minimize cost of the controls that given. Optimal control derived using Pontryagin Minimum Principle and then solved numerically using the gradient descent method.The effectiveness of optimal control is exhibited by comparing the number of total infected individuals with and without optimal control. It has been observed that the optimal control strategy gives better result in minimizing the number of total infected individuals. [ABSTRACT FROM AUTHOR]

Dengue fever is a disease caused by the bite of female Aedes aegypti mosquito which is infected by one of the four dengue viruses, namely DEN-1, DEN-2, DEN-3 or DEN-4. The disease has become a major priority of the WHO in recent years. Many efforts can be made to prevent dengue disease spreads. One of the efforts is to use fumigation to reduce the adult mosquito population. Unfortunately, fumigation intervention has many challenges. One of them is the budget limitation. To accomodate this problem, the optimal control theory will be implemented into the model of dengue disease spreads with fumigation intervention as the control variable. The purpose of this optimal control is to reduce the number of infected individuals and minimize the intervention cost. Characteristics of the optimal control is obtained by applying the Pontryagin principle. Furthermore, the optimal system is solved numerically by the Runge-Kutta method and the Gradient Descent method for the convergence criteria. It should be highlighted that the intervention (optimal control result) will be characterized as an impuls function to mimic the possibility of several strategies that might be implemented in the field. [ABSTRACT FROM AUTHOR]

This paper concerns the optimal control of a mathematical model of a growing tumor and its interaction with the immune system. This model consists of four populations-tumor cells, dendritic cells (as an innate immune system), cytotoxic T cells, and helper T cells (as a specific immune system)-in the form of a system of ordinary differential equations. Some tumors present dendritic cell and such cells have a potential role in regulating the immune system. In this model, we assume that dendritic cells can activate cytotoxic T cells and, in turn, can clear out tumor cells. Furthermore, by adding controls as a treatment to the model, we minimize both the tumor cell population and the cost of treatment. We do this by applying the optimal control for this problem. First, Pontryagin's Principle is used to characterize the optimal control. Then, the optimal system is solved numerically using the Forward-Backward Runge- Kutta method. Finally, the effect of each treatment is investigated. The numerical results show that these controls are effective in reducing the number of tumor cells. [ABSTRACT FROM AUTHOR]

A deterministic mathematical model with public health education campaigns and antiretroviral therapy as control variables are formulated and analyzed using sensitivity analysis and optimal control theory (Pontryagin's Maximum Principle). The sensitivity analysis shows that by increasing the public health education campaign for susceptible individuals and providing antiretroviral therapy to infected individuals in the symptomatic stage has an effect in reducing the spread of the HIV infection. The most sensitive parameter is the efficacy rate of the public health education campaign, followed by the contact rate of susceptibles with an infective in the asymptomatic stage, followed by the progression rate from the infected class into the pre-AIDS class. The least sensitive parameter is the natural death rate. The numerical simulation of both systems, i.e. with control and without control shows that the combination of the two strategies helps to make a significant reduction in the number of infectives in the asymptomatic stage, the number of individuals in the pre-AIDS stage, and the number of individuals with full-blown AIDS. [ABSTRACT FROM AUTHOR]

The effectiveness of an antiretroviral (ARV) treatment and a highly active antiretroviral therapy (HAART) on the epidemic model of HIV/AIDS is investigated. We apply the theory of optimal control where an antiretroviral (ARV) treatment and a highly active antiretroviral therapy (HAART) are used as control strategies in order to prevent the spread of HIV/AIDS. We apply Pontryagin's Maximum Principle to get the optimal system. Numerical simulations are conducted to support the analytical solution so that the effectiveness of an antiretroviral (ARV) treatment and a highly active antiretroviral therapy (HAART) can be shown. [ABSTRACT FROM AUTHOR]

In this article, we introduced an optimal control problem arising from differential equations for dengue which describe the spread of dengue in a region with a resistant mosquito population. The optimal control problem was constructed to handle a limited intervention budget, to reduce the number of infected humans and mosquitos. The Pontryagin Minimum Principle was used to formulate the optimal control problem, which was solved numerically with the forward-backward iterative method. The numerical simulation was performed with two scenarios, i.e., for different numbers of initially infected compartments (low and high) and for different numbers of initial basic reproduction (less than and greater than one). We find that fumigation intervention could be used to reduce the spread of dengue as long as the resistance of the mosquitos to the fumigant is low. We also found that fumigation intervention is much better in a prevention scenario since the cost function is much smaller than in a countermeasure scenario. Simulating the second scenario, we found that reducing the spread of dengue in a high risk area (basic reproduction number greater than one) is more costly than in a low risk area (basic reproduction number less than one). [ABSTRACT FROM AUTHOR]

Modern high-tech production with high innovation content, including petrochemical and oil and gas industry, is characterized by a flexible structural organization of technological processes, contributing to their versatility and multitasking, and the ability to quickly change the range of products, varying widely in its volume and quality characteristics. Optimal operation of such plants is often hampered or limited due to the lack of flexibility of existing automated technological processes control systems of (ATPCS). In this regard, the developments in the field of high performance flexible process control system are relevant, and are of considerable scientific and practical interest. The purpose of the research is to develop a methodological framework for building effective APCS capable of variation and modification within a wide range of optimal control tasks. The result of this research is to develop theoretical foundations of flexible, optimal control of complex technological systems using the principle of decentralized management and the method of situational decomposition. [ABSTRACT FROM AUTHOR]

The development of formalized decomposition methods of the complex and multidimensional problems of optimal control which are used as a tool of decentralization, is highly relevant and meets the requirements and challenges of scientific and technological progress in the field of industrial production automation. The rapid development of technology of petrochemical, oil and gas industry due to ever-increasing volumes of world consumption of petroleum products and the requirements for their quality characteristics, leads to a high complexity profile of industrial production and their enrichment with innovative content. All this significantly complicates the solution of problems concerning optimal computer-aided control of technological processes and build effective control systems. Despite, all aspects of the above issues are up-to date. The purpose of the research is to develop an effective methodological framework for building decentralized process control system with increased capacity to adapt to possible changes in the control objects structural organization. The result of this research is the development of a theoretical framework and recommendations for implementing the concept of flexible, decentralized management on the basis of the method of situational decomposition when solving optimal control problems. [ABSTRACT FROM AUTHOR]

The paper deals with linear-quadratic optimal control problems with a weak control and the fixed left point in a critical case, where a matrix standing in front of a state variable in the state equation is singular for any argument value if the small parameter is equal to zero. Using the direct scheme method, consisting in immediate substituting a postulated asymptotic solution into the problem condition and obtaining problems for finding asymptotics terms, the zero order asymptotic solution is constructed under some conditions. In contrast to the paper: N. T. Hoai, J. Optim. Theory Appl., vol. 175, 324-340 (2017), where the considered problem was studied, the projector approach is applied here. This approach allows us to make the algorithm of constructing asymptotic solution clearer and to correct some inaccuracies in the paper mentioned. [ABSTRACT FROM AUTHOR]

The study of multiobjective discrete fractional optimal control problems is introduced. The main results provide methods for identifying Pareto optimal solutions. A numerical example is given to illustrate the theory. [ABSTRACT FROM AUTHOR]

The analytic solutions for a nonlinear system on the Lie group S O(3) × R3 × R3 are presented. A comparison between the approximate solutions obtained with Optimal Homotopy Asymptotic Method and the corresponding numerical solutions is also attained. [ABSTRACT FROM AUTHOR]

This paper presents the algorithms for the solution of the optimal control problem of wide scale linear dynamic systems. These algorithms are based on the prediction concept. For the beginning, is considered the interaction prediction approach and afterwards, the cost prediction approach is used. The convergence behavior of the proposed algorithms is thoroughly investigated. In this paper is designed a multi-input, multi-output controller by shaping the gain of an openloop response across frequency. This technique is applied to controlling the pitch axis of an aircraft. Eventually, the paper successfully investigates and demonstrates how to choose a suitable target loop shape and to compute a multivariable controller that optimally matches the target loop shape. [ABSTRACT FROM AUTHOR]

In this paper we consider different methods for formulating boundary optimal control problems of either Dirichlet or Neumann type. On one hand, standard approaches typically have the drawback of searching for the optimal controls in proper subspaces of natural trace spaces. Therefore, we consider alternative formulations with lifting functions that have several advantages. First of all, boundary controls can be determined on natural trace spaces, without additional regularity as required by standard approaches. This also leads to numerical discretizations that have the same rate of convergence for the unknowns defined on the domain and for those on the boundary. A potential drawback of the method consists in the use of control functions defined over the problem domain instead of on its boundary, thus increasing the number of degrees of freedom of the problem. This drawback can be compensated by using lifting functions with restricted support, whose boundary contains the control boundary under interest. Numerical results solving the optimality systems in an all-at-once approach show that it is possible to use restricted functions which do not substantially change the minimum value of the target functional with respect to the case of lifting functions with non-restricted support. [ABSTRACT FROM AUTHOR]

This paper deals with validating of an assumption of the reforestation optimal control model. We focus on prices of different timber types. These serve as inputs for the simulation which gives the data for estimation of prescribed functions, whose parameters are used for the optimal control problem solution. As usual, parameters of such models are assumed as constants. Presence of trend in particular timber price development is tested. Rate of constancy violation is assessed also by testing equality of trend slopes. Rejected are both insignificance and equality of trend slopes. Using pairwise comparisons and cluster analysis it is possible to form sets with similar trend slopes. [ABSTRACT FROM AUTHOR]

The optimal controlled motion of a mechanical system, that is determined by the linear system ODE with constant coefficients and piecewise constant control components, is considered. The number of control switching points and the heights of control steps are considered as preset. The optimized functional is equal to the total area of all steps of all control components ("Expenditure criteria"). In the absence of control, the solution of the system is equal to the sum of the components (frequency components) corresponding to different eigenvalues of the matrix of the system. Admissible controls are those that turn to zero (at a non predetermined time moment) the previously chosen frequency components of the solution. An algorithm for the finding of control switching points, based on the necessary minimum conditions for Expenditure criteria, is proposed. [ABSTRACT FROM AUTHOR]

In this paper the analysis of the fuel optimal control of the plane oscillations of the satellite on the circular orbit subject to the aerodynamic moment variations has been done. On basis of necessary conditions of optimality the problem was reduced to the task of nonlinear programming. The numerical method of the sequential linearization of the boundary conditions for calculation of the switching moments has been proposed and its implementation has been presented. Examples for the different areas of the initial states have been calculated. [ABSTRACT FROM AUTHOR]

In this paper the guaranteeing approach is used to choose the measuring basis, which minimizes the maximal possible estimation error. If the optimal basis is found for some time, we have to know if it on the fixed time interval still the best is. The sufficient conditions for it are proved. The example of choosing the measuring basis to estimate coordinates of an object using the distance to some sputniks is considered. [ABSTRACT FROM AUTHOR]

The analytic solutions for a nonlinear system on the Lie group S O(3) × R3 × R3 are presented. A comparison between the approximate solutions obtained with Optimal Homotopy Asymptotic Method and the corresponding numerical solutions is also attained. [ABSTRACT FROM AUTHOR]

In this paper we are interested in the numerical solution of optimal control problems for non-linear hyperbolic conservation laws. To this aim, we consider relaxation approximations to the conservation laws coupled with the optimal control problem. Following a semi-Lagrangian interpretation of the hyperbolic relaxation system, and its adjoint counterpart, we solve efficiently the time discretization introducing a multi-step scheme in the class of BDF methods. Computational results illustrating the theoretical findings with applications to traffic flow models are presented. [ABSTRACT FROM AUTHOR]

This paper is concerning a mathematical model which describes the transmission dynamics of dengue. The optimal control representing insecticides spray and biological control for this model is investigated. The existence of optimal control is recognized analytically by the use of optimal control theory. Numerical simulations have shown that insecticides spray and biological control for the infected has a positive impact towards controlling dengue virus transmission. [ABSTRACT FROM AUTHOR]