INVESTIGATION OF OPTIMAL CONTROL OF VARIABLE SYSTEMS IN THE DYNAMIC SPECTRUM

The article presents a study of systems of difference equations, their role and application in modeling and analysis of dynamical systems in various fields. The purpose of the work is to analyze and develop methods for solving difference equations with a special emphasis on their application in automation and mechanics. Difference equations are mathematical models describing the evolution of variables in a discrete time space. Their study allows for a deeper understanding of complex dynamic processes and effective modeling of systems of diverse nature. The paper presents an overview of various methods of analysis and solution of difference equations. Numerical integration methods, approximation methods and stabilization methods of systems of difference equations are considered. Special attention is paid to the properties of stability, convergence and controllability of such systems. The results of the study contribute to a deep understanding of the dynamics of systems of difference equations and the development of effective numerical methods for their solution. The solution of difference equations is widely used in automatic control, robotics, aviation, mechatronics and other industries. It plays an important role in modeling and controlling various systems, including electromechanical systems, robots, autopilots, automation processes, and others.