The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.

The aim of this article is to develop efficient methods of expressing multilevel structured information from various modalities (images, speech, and text) in order to naturally duplicate the structure as it occurs in the human brain. A number of theoretical and practical issues, including the creation of a mathematical model with a stability point, an algorithm, and software implementation for the processing of offline information; the representation of neural networks; and long-term synchronization of the various modalities, must be resolved in order to achieve the goal. An artificial neural network (ANN) of the Cohen–Grossberg type was used to accomplish the objectives. The research techniques reported herein are based on the theory of pattern recognition, as well as speech, text, and image processing algorithms.

This paper aims to identify efficient methods of mathematically modeling an automated physical system using a neural network. Based on the Levenberg-Marquardt method, we built a feed-forward neural network with the capabilities of a graphics accelerator. The model also sums up and suggests a new neural network training algorithm with Bayes regularization, Nguyen-Widrow initialization, and the early stopping and control method. This greatly expands the efficiency of solving problems where knowledge of an automation system is usable.

An analysis of the possibilities of using alternative energy to solve the problem of electricity shortages in developing countries shows that solar energy can potentially play an essential role in the fuel and energy complex. The geographical location, on the one hand, and the global development of solar energy technologies, on the other, create an opportunity for a fairly complete and rapid solution to problems of insufficient energy supply. An autonomous solar installation is expensive; 50% of the cost is solar modules, 45% of the cost consists of other elements (battery, inverter, charge controller), and 5% is for other materials. This work proposes the most efficient PV system, based on the technical characteristics of the SB and AB. It has a direct connection between the SB and AB and provides almost full use of the solar panel’s installed power with a variable orientation to the Sun. The development of a small solar photovoltaic (PV) installation, operating both in parallel with the grid and in autonomous mode, can improve the power supply of household consumers more efficiently and faster than the development of a large energy system. It is suggested that two minimized criteria be used to create a model for forecasting FOU. This model can be used with a genetic algorithm to make a prediction that fits a specific case, such as a time series representation based on discrete fuzzy sets of the second type. The goal is to make decisions that are more valid and useful by creating a forecast model and algorithms for analyzing small PV indicators whose current values are shown by short time series and automating the processes needed for forecasting and analysis.

In this paper, we discuss how to make electric street lighting systems more energy efficient by creating an algorithm and mathematical model for optimizing parameters, minimizing active power losses, and finding the best topology for the lighting network when it is being designed or updated. Scientific and technological progress has led to an increase in the complexity of every human being's daily life. Companies, institutions, and countries constantly need to find modern tools to help them make the best decisions. Graph theory has numerous applications to many everyday problems. It can resolve and simplify them. An algorithm was developed to determine the shortest length in the form of a modified Dijkstra graph, with nodes supporting the street lights and ribs being the wires connecting them.

This article investigates algorithmic approaches for analyzing and predicting the operating modes of small photovoltaic power plants. A multi-criteria genetic algorithm is analyzed and developed, applicable to short data series and variable operating modes typical of energy systems. Peak demand, which occurs during a limited number of hours, represents a significant challenge for the overall energy balance and grid stability. The task under consideration is formulated as a problem in which the forecast error and the model uncertainty measure are simultaneously minimized. For this purpose, an interval forecasting scheme based on fuzzy regression is used, with its parameters optimized by an evolutionary mechanism. The proposed multi-criteria genetic algorithm is an effective tool for the parametric adaptation of forecasting models. It lays the groundwork for implementation in monitoring and control systems for autonomous photovoltaic installations, thereby enhancing energy efficiency and optimizing performance through real-time data analysis and adaptive decision-making. The obtained results show improved robustness and reliability of the forecast compared to classical approaches for short time series.