Mathematical models with analytical properties are needed to create modern stabilization systems for various objects and technical systems. This is due to the fact that most of the existing methods for the synthesis of automatic systems are based on mathematical transformations of models of control objects. However, for complex objects and systems, these models are obtained experimentally. Moreover, the experimental data are approximated by various well-known methods. If the dependences are essentially nonlinear in nature, they are approximated by sections. Such a fragmented model as a whole is not analytical, which excludes the use of many well-known methods for the synthesis of nonlinear stabilization systems. In these cases, it is advisable to use the new Cut-Glue approximation method developed at DSTU, which allows one to obtain an analytical model of an object from piecewise approximations. This analytical model allows you to apply the analytical method for the design of quasilinear control systems for nonlinear objects. In this paper the propoused approach is illustrated by example of the design of a nonlinear system for stabilizing the flight altitude of an airship.

Keywords: stabilization system, analytical synthesis, nonlinear control object, mathematical model, quasilinear form, experimental data, fragmentary model, multiplicatively additive approximation

The construction of mathematical models of technical objects is most often associated with the mathematical processing of experimental data. Due to significant non-linearities, approximation of such dependencies using known methods (polynomial expansions, spline approximation, etc.) is, firstly, difficult, and, secondly, is associated with large errors. Studies have been conducted to create and substantiate an alternative to the existing “Cut-Glue” method of approximation (CGA).In the CGA problem, there are three subtasks: fragmentation, approximation, and multiplicatively additive processing of the results of the first two subtasks. The initial subtask is data fragmentation. It is a preparatory stage for the subsequent stages of the implementation of the Cut-Glue approximation method.The method of its solution is based on logical-combinatorial features and conditions for partitioning multidimensional data. It allows you to consider the maximum possible number of various solutions when searching for the best.The CGA method implements a fundamentally new approach and is designed to solve the problems of experimental description of nonlinear dependencies. To implement the CGA method, the software package ""Algorithmic structure and functionality of the"" CutGlueApproximation ""software complex was developed. The article describes the nature and capabilities of the functional implemented in software tool ST. ST can be used as part of the entire software package (SP) or independently to perform intermediate tasks in isolation from the entire complex. The connection between the parts is realized with the help of auxiliary libraries, which allow both to use input data and to present the resulting data in various forms, which makes the SP more flexible. A convenient user interface contains many variable parameters for flexible configuration and convenient structured information output at all stages. With the help of the developed ST, many demonstration experiments have been carried out.

Keywords: Approximation, optimization, mathematical model, combinatorics, heuristic algorithms, modeling, software complex, fragmentation

The construction of mathematical models of objects of experimental or computer simulation is associated with the mathematical processing of experimental data. The point dependences of the output variables for the input variables obtained for them are essentially nonlinear, piecewise, sometimes discontinuous. Approximation of such dependencies using polynomial expansions or spline functions is both difficult and involves large errors. A fundamentally new solution to this problem was proposed in the article. This method, called the "Cut-Glue" approximation method, is based on the partitioning of the modeled dependence into sections, the approximation of each section by polynomial dependencies, the multiplicative "excision" from each dependence of the fragments along the boundaries of the plot and the additive "gluing" them together into a single function - the model of the approximated dependence . The analyticity property of the resulting function allows to study the model and use it in models of vehicle dynamics. One of the stages of the "Cut-Glue" method is the "Glue" process - the additive "gluing" of fragments into a single function. For this, an auxiliary multiplicative function is used. The function of this function includes the steepness of the pulse fronts. In this paper, a developed modification of the method of burrowing particles is used in the problem of research and suboptimization of this parameter. As a test bench of the developed algorithm developed a special software tool.

Keywords: optimization, approximation, mathematical model, experimental data, heuristic methods, the method of burrowing particles

The methodology of regression mathematical description of fragments of experimental data of arbitrary dimension by polynomials necessary for a given accuracy of order and structure is considered with the help of a hybrid of classical regression analysis and a modified evolutionary genetic algorithm through which the polynomial structure is varied and optimized.

Keywords: optimization, approximation, regression analysis, mathematical model, experimental data, heuristic methods, evolutionary-genetic algorithm

The purpose of this paper is to develop a methodology of automation of production processes for which performance is a factor of efficiency. Solves the problem of developing a method of synthesis of high-speed automated control implemented with technological limitations. Parallel to solve the problem of ensuring asymptotic stability of systems controlled by these laws, which provides the reliability of the implementation technological process. The problem is complicated, so problems are solved for the simplest objects of the first order. The essence of the approach consists in the organization of such effect on the behavior of the derivative of the output variable of the object, which provides fast-acting, but asymptotically stable transition process of its change. This property formed a special non-linear function, leading to rapid change in a variable away from equilibrium, and the asymptotic approximation to the equilibrium point. The structure of the function, forming a mathematical model of the control system of the first order. Function parametrically depends on two factors that gives it the desired properties. It introduced the option of limiting the derivative of the output variable, and the parameter the degree of quasioptimality her performance. The control action generated by the function that meets the properties close to optimal performance, the limitations of the derivative and asymptoticity attenuation of transient processes of the controlled system. Asymptotic stability is a basic requirement of robustness of a dynamical system. The obtained results are important for practical problems of automation of technological processes of most industries. For a number of objects the performance is the performance, stability and robustness - a crucial factor in the reliability of the automatic control system. Robustness necessary process control systems, technology management, especially chemical processes taking place in the critical catalytic modes, as well as technological lines for the production of films, paper tapes, etc., in which even temporary disruption of synchrony leads to significant and irreversible losses. Obtained results have theoretical significance, and practical application that makes the publication relevant.  

Keywords: Production, Technology, Process, Object, Pronunciation, Productivity, speed, limitation, stability, asymptoticity, quasioptimality, parametric tuning