Solving the Synthesis Problem Self-Organizing Control System in the Class of Elliptical Accidents Optics for Objects with One Input and One Output
Rakhmetov M. Adiyeva A. Orazbayeva B. Yelezhanova S. Tuleuova R. Moldasheva R.
January 2026Multidisciplinary Digital Publishing Institute (MDPI)
Computation
2026#14Issue 1
Nonlinear single-input single-output (SISO) systems operating under parametric uncertainty often exhibit bifurcations, multistability, and deterministic chaos, which significantly limit the effectiveness of classical linear, adaptive, and switching control methods. This paper proposes a novel synthesis framework for self-organizing control systems based on catastrophe theory, specifically within the class of elliptic catastrophes. Unlike conventional approaches that stabilize a predefined system structure, the proposed method embeds the control law directly into a structurally stable catastrophe model, enabling autonomous bifurcation-driven transitions between stable equilibria. The synthesis procedure is formulated using a Lyapunov vector-function gradient–velocity method, which guarantees aperiodic robust stability under parametric uncertainty. The definiteness of the Lyapunov functions is established using Morse’s lemma, providing a rigorous stability foundation. To support practical implementation, a data-driven parameter tuning mechanism based on self-organizing maps (SOM) is integrated, allowing adaptive adjustment of controller coefficients while preserving Lyapunov stability conditions. Simulation results demonstrate suppression of chaotic regimes, smooth bifurcation-induced transitions between stable operating modes, and improved transient performance compared to benchmark adaptive control schemes. The proposed framework provides a structurally robust alternative for controlling nonlinear systems in uncertain and dynamically changing environments.
catastrophe , elliptical dynamics , nonlinear system , parametric uncertainty , self-organizing control system
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Department of Mathematics and Methods of Teaching Mathematics, Faculty of Physics, Mathematics and Information Technology, Kh. Dosmukhamedov Atyrau University, Atyrau, 060000, Kazakhstan
Department of Computer Science, Faculty Information Technology, L.N. Gumilyov Eurasian National University, Astana, 010000, Kazakhstan
Department of Mathematics and Methods of Teaching Mathematics
Department of Computer Science
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