Development and implementation of a numerical approach for optimal control of oscillations in coupled systems with distributed and lumped parameters

Authors

DOI:

https://doi.org/10.15587/1729-4061.2025.322053

Keywords:

wave equations, oscillatory processes, method of successive approximations, controlled boundary effects

Abstract

This study focuses on numerical solutions to control problems in oscillatory systems consisting of two distinct objects. The primary issue addressed is the effective modeling and control of oscillations in these systems, particularly through the interaction of two objects. The research yields significant results by demonstrating a method to transform the complex boundary value problem into a more manageable system of ordinary differential equations using the method of straight lines. The findings reveal the influence of boundary conditions on the dynamics of an object characterized by distributed parameters. The results’ unique features include applying Pontryagin’s maximum principle to solve the associated variational problem, effectively integrating the behavior of both objects in the system. The numerical approach adopted in this research simplifies the problem and enhances the precision of the solutions obtained. Moreover, the study examines the convergence of numerical methods, improving their applicability to practical scenarios. The computational results demonstrate the convergence of the functional and show that the gradient projection method provides a convergent sequence in the control space, even for ill-posed optimal control problems. The conditions under which these results are most applicable include scenarios where boundary effects play a critical role in system dynamics, offering a robust framework for further investigation and application in real-world systems. This work significantly contributes to the understanding of oscillatory systems and provides a foundation for future research in optimal control strategies, thereby advancing the field of dynamic system control

Author Biographies

Kamil Mamtiyev, Azerbaijan State University of Economics (UNEC)

PhD, Associate Professor

Department of Digital Technologies and Applied Informatics

Ulviyya Rzayeva, Azerbaijan State University of Economics (UNEC)

PhD, Associate Professor, Head of the Research Center of Digital Economy

Department of Digital Technologies and Applied Informatics

Aygun Abdulova, Azerbaijan State University of Economics (UNEC)

PhD

Department of Economics and Technological Sciences

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Development and implementation of a numerical approach for optimal control of oscillations in coupled systems with distributed and lumped parameters

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Published

2025-02-24

How to Cite

Mamtiyev, K., Rzayeva, U., & Abdulova, A. (2025). Development and implementation of a numerical approach for optimal control of oscillations in coupled systems with distributed and lumped parameters. Eastern-European Journal of Enterprise Technologies, 1(4 (133), 22–29. https://doi.org/10.15587/1729-4061.2025.322053

Issue

Vol. 1 No. 4 (133) (2025): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2025 Kamil Mamtiyev, Ulviyya Rzayeva, Aygun Abdulova

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