Keywords: Optimal Control, Real-Time Control Problems
Abstract: Locomotion of robots in a resistive medium can be based on special motions of auxiliary internal masses inside the main body of the robot. This locomotion principle is used in micro-robots and vibro-robots moving in tubes. In the paper, optimal motions of systems controlled by internal moving masses are considered. One-dimensional optimal motions are examined for systems moving in the presence of dry friction forces. Two-dimensional motions are considered for bodies subject to dry friction and containing internal moving masses. Optimal motions of a two-body system are obtained for the case where external forces are negligible. This situation is a model for the re-orientation of a spacecraft containing a moving internal mass.

Keywords: Differential Games, Stochastic Optimization
Abstract: In classical optimal control and in differential games, the controllers are supposed to a have a perfect knowledge of the dynamics, of the payoffs and of the initial conditions of the system. However in several practical situations only partial informations on these data are available. The most simple example is a control system with a given terminal payoff where the initial condition is not perfectly known: only a probabilistic information is known (for instance, the initial condition lies in a given ball with a uniform probability measure). The initial condition is then replaced by a probability measure which «propagates» according to the control system. One can be interested to characterize the optimal mean value of the cost. We will show that this value function – which depends on the initial probability measure – could be characterized as the unique solution – in a suitable sense – of a Hamilton Jacobi Bellmann equation stated on the space of probability measures. This brings some technical difficulties where the optimal transport theory is an important tool.

Keywords: Optimal Control, Robust Control and Stabilization, Applications in Economics, Management and Environmental Science
Abstract: The paper discusses the existence of a linear manifold in a vicinity of a steady state for stabilization of the Hamiltonian systems arising in optimal control problems for economic growth models. It is shown that such stable manifold exists for almost all possible values of model parameters guaranteeing the existence of a steady state. Research is based on the qualitative analysis of the Hamiltonian dynamics, which plays a key role for investigating the asymptotic behaviour of optimal trajectories. A procedure is proposed for stabilization of the Hamiltonian system, whose trajectories converge to equilibrium and approximate the optimal solution with the quadratic accuracy at a vicinity of the steady state. Basing on properties of the Hamiltonian matrices, the classification of steady states is provided and the sensitivity analysis for identification of their character is implemented with respect to model parameters. The proposed approach is applied to the model dealing with dynamic optimization of the resource productivity.

Keywords: Differential Games, Optimal Control
Abstract: We obtain sufficient conditions for the values of the Minkowski operators to be weakly convex and smooth. These operators play the same role in nonlinear differential games as the Minkowski sum and the Minkowski difference do in linear differential games: they are basic operators in algorithms of computing reachable sets and optimal strategies. We also prove that the signed distance to convex sets is a Lipschitz continuous function of the set with respect to the Hausdorff distance.

Keywords: Optimal Control, Optimization Methods, Applications in Economics, Management and Environmental Science
Abstract: The optimal control problem is studied, which was described by a dynamical system with a nonsmooth right-hand side, using the example of the problem of managing the development of individual human capital. Specialized methods of searching for optimal control are developed, focused on accounting for the violation of the smoothness of the right-hand side of the dynamical system under consideration. Necessary optimality conditions are obtained in the form of Pontryagin’s maximum principle with additional jump conditions for conjugate functions. Numerical methods have been developed to solve the nonsmooth task of managing the development of human capital, making it possible to find optimal control and give it a meaningful interpretation.

Keywords: Optimal Control
Abstract: An approach is proposed to determine the reachability region of the Psi_0 vector. It will significantly speed up the solution of optimal control problems using the maximum principle for multidimensional dynamic objects.

Keywords: Robust Control and Stabilization, Real-Time Control Problems
Abstract: In this paper a novel approach to the global trajectory tracking control problem for manipulators with flexible joints is presented. The dynamic model of such mechanical systems has a cascade structure that allows to decouple the links dynamics from the actuators ones. We propose a design procedure for nonlinear controller with computed feedforward of robot manipulators with revolute joints in a cylindrical phase space. Stability proof of the closed-loop system is given by constructing a Lyapunov function which is periodic on angular coordinates. We illustrate the implementation of the controller using simulation example.

Keywords: Robust Control and Stabilization
Abstract: This paper develops sufficient conditions for the constrained robust stabilization of continuous-time polytopic linear systems with unknown but bounded perturbations. The attractive ellipsoid method (AEM) is employed to determine a robustly controllable invariant set, known as attractive ellipsoid, such that the state trajectories of the system asymptotically converge to a small neighborhood of the origin despite the presence of non-vanishing perturbations. To solve the stabilization problem, we employ the Finsler's lemma and derive new linear matrix inequality (LMI) conditions for robust state-feedback control design, ensuring convergence of state trajectories of the system to a minimal size ellipsoidal set. We also consider the state and control constrained problem and derive extended LMI conditions. Under certain conditions, the obtained LMIs guarantee that the attractive ellipsoid is nested inside the bigger ellipsoids imposed by the control and state constraints. Finally, we extend our AEM approach to the gain-scheduled state-feedback control problem, where the scheduling parameters governing the time-variant system are unknown in advance but can be measured in real-time. Two examples demonstrate the feasibility of the proposed AEM and its improvements over previous works.

Keywords: Robust Control and Stabilization
Abstract: We prove that the property of uniform complete controllability is sufficient for the simultaneous proportional local assignability of the Lyapunov spectrum and the Lyapunov irregularity coefficient for linear control systems with discrete time.

Keywords: Robust Control and Stabilization
Abstract: The problem of constructing asymptotically stable program motions of the double pendulum with variable length and movable pivot is solved. This program motions are given arbitrarily. The solution is obtained by synthesis of the active program control applied to the system of bodies. Also, it’s obtained by the synthesis of the stabilizing control based on the feedback principle. The control is constructed in the form of an exact analytic solution in the class of continuous functions. The problem is solved based on the direct Lyapunov method of stability theory. The Lyapunov’s function with sign-constant derivative is used.

Keywords: Applications in Economics, Management and Environmental Science, Large Scale Optimization Problems
Abstract: One of the key issues of the selective statistical investigations (monitoring) analysis problem in case of small samples is insufficient representativeness of the monitoring parameters, especially in the context of selective statistical data generation. In the paper, the structural-classification correction method of monitoring parameter estimation is proposed. The new method allows increasing the reliability of indices estimates, which is critical for largescale socio-economic system analysis and control problems. Developed method applied for economic activity rates analysis problem.

Keywords: Applications in Economics, Management and Environmental Science, Optimization Methods
Abstract: A method of sentiment analysis of the text and its approbation in solving the problem of analysis of text comments left by the Bank's customers are performed. The proposed method consists in a combination of three approaches: rules-based, dictionaries and machine learning with a teacher. New method of text vectorization-tonal vectorization instead of classical ones, such as " bag-of-words " and TF-IDF, is proposed. The text was classified by logistic regression with regularization. A series of experiments were carried out and the optimal value of the regularization parameter was found in terms of classification accuracy.

Keywords: Applications in Economics, Management and Environmental Science, Optimization Methods, Optimal Control
Abstract: The objective of this research is a development of the municipality entrepreneurial network functioning system-dynamic simulation model. Model has been implemented in Powersim Studio 7 simulation modeling environment on experimental level. It allows monitoring the state of communications and exchange for various periods of time on the one hand, as well as establishing the architecture of links, levels and exchange flows between members of the network with the most effective conditions for the realization of commodity and money relations inside and outside the network on the other. Inject of inside money in entrepreneurial network is considered to be a method of increasing exchange effectiveness. Parameter that reflects its usage is a main regulator for exchange and a control model parameter. Simulation experiments result, expressed in resulting coefficients (liquidity, cooperation, exchange synchronization), allows to numerically assess the system state at different control parameter values. It makes the designed model an effective support tool for optimization decisions and administrating of a complicate economic system, like municipality entrepreneurial network.

Keywords: Applications in Economics, Management and Environmental Science, Optimization Methods
Abstract: An important task in business of any enterprise and, in particular, enterprises working in the industrial ecology is the timely transmission of data and relevant information. The article provides an overview and analysis of technologies of employee notification about any type of events. The model of optimization of data transmission over messengers is given. Today, there are a huge number of different applications for instant messaging: from ordinary messengers to social networks with built-in messaging modules. Among the usual messengers can be identified such as WhatsApp, Viber, Skype, Snapchat, KakaoTalk and others. Social network messengers include such examples as Vkontakte, Facebook, Instagram, etc. The special optimization model has been developed for enterprises operating in the industrial ecology which allows to manage the notifications and alerts of employees involved in specific business processes.

Keywords: Control of Partial Differential Equations, Optimal Control, Optimization under Uncertainties Including the Theory of Noise Measurements
Abstract: Boundary control of oxidizing species at the cathode surface is considered in an electrochemical system, which is the plant of two electrodes and plant of three electrodes submerged in the stirred and unstirred electrolytes. The exact feedforward controls are found using ideas of motion planning, Laplace transform and other techniques that in the end solve the inverse problem for the given time-variable reference of species at the cathode surface. The uncertainty of surface reaction existing in the system is suppressed with two modifications of controls. In the first case, the feedforward control is extended with a PI feedback that uses measured in the process electric current passing through the system. In the second case, an adaptive feedforward control is established for the case when the exchange current density is unknown drifting parameter and is estimated as it changes using a conditionally Gaussian filter. In both cases, the process control is simulated and revealed to be effective.

Keywords: Applications in Economics, Management and Environmental Science, Differential Games, Optimal Control
Abstract: Output is produced from labor and capital by technologies that differ in their emission intensity and relative capital intensity. Aggregate emissions decrease every individual's health, but each individual can invest its own health. Population grows by the difference of fertility and exogenous mortality. Labor is used in production or child rearing. I construct a differential game where the benevolent government is a leader that determines taxes and subsidies, while the representative family is a follower that saves in capital and decides on its number of children. The main results are as follows. Without government intervention, population increases or decreases indefinitely. Capital should be taxed, if dirty technology, and subsidized, if clean technology is relatively capital intensive. Child rearing should be taxed, if dirty technology is relatively capital intensive or mildly labor intensive.

Keywords: Optimal Control
Abstract: We considered a mechanical system consisting from a massive rigid body and a small point mass. This system can move only under the influence of the internal forces. Only plane movements are allowed. The problem is to rotate the rigid body to the specific angle in the shortest time changing the position of the point mass. We found both suboptimal and exact analytical solutions. When the mass of the point is much smaller in comparison with the mass of the body the optimal point trajectory in the coordinates system moving with the body is close to the arc of a circle. We obtained the analytical expressions for the accuracy of such an approximation.

Keywords: Optimal Control, Real-Time Control Problems
Abstract: In the present work, we develop an asymptotical control theory for a closed string under a bounded load applied to a single distinguished point. We find and describe exact classes of the string states that allows complete damping, and asymptotically exact value of the required time. We design a dry-friction like feedback control, which turns out to be asymptotically optimal. We also explicitly describe the singular arcs of the control. The central result is a proof of asymptotic optimality of the control thus constructed.

Keywords: Robust Control and Stabilization
Abstract: This paper presents sufficient conditions for the robust stabilization of discrete-time polytopic systems subject to control constraints and unknown but bounded perturbations. The attractive ellipsoid method (AEM) is extended and applied to cope with this problem. To tackle the stabilization problem, new linear matrix inequality (LMI) conditions for robust state-feedback control are developed. These conditions ensure the convergence of state trajectories of the system to a minimal size ellipsoidal set despite the presence of non-vanishing disturbances. The developed LMI conditions for the AEM are extended to deal with the problem of gain-scheduled state-feedback control, where the scheduling parameters governing the time-variant dynamical system are unknown in advance but can be measured in real-time. A feature of the obtained conditions is that the state-space matrices and Lyapunov matrix are separated. The desired robust control laws are obtained by convex optimization. Numerical simulations are given to illustrate the feasibility of the proposed AEM for robust disturbance rejection.

Keywords: Evolutionary Algorithms, Multi-Objective Control and Optimization, Robust Control and Stabilization
Abstract: At present, statistical process control in process industry is mainly off-line, which is incompetence in handling problems such as process control deviations and quality instability. In this work, an intelligent process control methodology is proposed for the on-line quality evaluation, by using GA-BP hybrid algorithm. Given that fact that the practical applications in industries are usually muti-objective, the multi-output neural network model is studied in order to compensate the deficiency of the single-output GA-BP algorithm. The proposed methodology was applied to a real operation unit to illustrate its effectiveness and feasibility. In the case study, two quality indicators were chosen as online evaluation objectives of the chosen operation unit. The algorithm was constructed, with 12 nodes in the input layer and 2 nodes in the output layer, which is then trained by 800 groups of real-time data and validated by 200 groups of test data.

Keywords: Robust Control and Stabilization
Abstract: An algorithm for stabilization of a class of systems with constant delay is proposed.

Keywords: Robust Control and Stabilization
Abstract: For linear time-varying discrete-time systems with incomplete feedback, the notion of uniform consistency is introduced and studied. Necessary and sufficient conditions for uniform consistency are obtained. This property is used for obtaining sufficient conditions of local assignability of Lyapunov spectrum for time-varying discrete-time systems with linear static output feedback.

Keywords: Applications in Economics, Management and Environmental Science
Abstract: In the era of globalization, local economic structures have not lost their significance and must be in the focus of a scientific research. Optimization problem solution could become a solid theoretical foundation for a local economic system effective functioning. To express an objective function in the analytical form in order to implement precise mathematical methods is impossible for a complex system, an economic system has proved to be such type system. Methods based on simulation are believed to be effective for finding solutions of a wide range of optimization problems. This paper details findings of the research aimed at solving optimization problem in terms of revealing optimal agent behavior in the course of exchanges in a local economic system on the basis of agent-based modeling usage. Pursuing this goal, a set of agent-based program models was engineered in Netlogo modelling framework to simulate communication process in a local economic system, and one model from the set, the Strategy Model, is oriented towards optimization problem solution. This problem was solved in terms of the minimum time for completion of exchanges in the whole system, the minimum time necessary for a single agent to complete his exchange operations in order to meet its demands, and the minimum time required for commencement of the manufacturing process. Moreover, as in many researches based on agent-based simulation, a specific and unpredicted phenomenon was revealed, the “selfish” phenomenon.

Keywords: Optimization Methods, Applications in Economics, Management and Environmental Science
Abstract: The problems of teaching students the synergistic basis of economy is considered. The scheme of presenting the subject is provided, which is adapted to the aspects of modern students teaching.

Keywords: Applications in Economics, Management and Environmental Science, Optimization Methods
Abstract: This paper suggests a methodological approach to the problem of waste management. Scenarios evaluation of waste disposal landfills is proposed. Integral index of ecological hazard based on the number of initial landfill indicators is used for decision-making. So one can calculate the value of integral index due to different waste disposal scenarios and choose the most optimal one. Our approach is illustrated by calculation of scenarios for three landfills of one city in the Russia Arctic Zone for 4 years.

Keywords: Optimal Control, Singularities in Optimization, Numerical Methods for Optimization
Abstract: In this paper, focus is on identifying the feedforward structure for the emergence of input periodicity at the optimal situation, and the fed-batch penicillin fermentation process is applied for case study. Through information of optimal control, the reversed system analysis methods are constructed, and the criterion for the emergency of optimal periodic control (OPC) is built, and possibly, analytical method to compute out the OPC problem would be proposed.