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• ## Analytical problem solution of synthesis of a nonlinear stabilization system based on a mathematical CGA model

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

• ## Mathematical modeling of a fuzzy decoder

The approach to construction a computer model of a functional information converter based on element-wise operations with multidimensional tables of numbers is investigated. A numerical decision-making algorithm based on infinite-valued logic was built and verified (in particular, fuzzification, implication, aggregation, defuzzification algorithms). The mathematical, algorithmic and software model of fuzzy decoder of the positional bipolar code in a single-unit one is investigated. The transition from the initial model given in terms of three-valued logic to a similar system having an infinite logical basis is shown. The numerical algorithm has been tested and debugged in the GNU Octave mathematical computation package environment with minimal use of functions from the fuzzy-logic toolkit.

Keywords: decoder, single-unit code, functional converter, infinite-valued logic, t-norm, fuzzification, defizzification, implication, aggregation, three-valued logic, bipolar code

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