{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,19]],"date-time":"2026-08-19T20:15:20Z","timestamp":1787170520631,"version":"3.56.0"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T00:00:00Z","timestamp":1768348800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan","award":["AP25796073"],"award-info":[{"award-number":["AP25796073"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>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\u2013velocity method, which guarantees aperiodic robust stability under parametric uncertainty. The definiteness of the Lyapunov functions is established using Morse\u2019s 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.<\/jats:p>","DOI":"10.3390\/computation14010021","type":"journal-article","created":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T15:12:04Z","timestamp":1768403524000},"page":"21","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Solving the Synthesis Problem Self-Organizing Control System in the Class of Elliptical Accidents Optics for Objects with One Input and One Output"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9745-6925","authenticated-orcid":false,"given":"Maxot","family":"Rakhmetov","sequence":"first","affiliation":[{"name":"Department of Mathematics and Methods of Teaching Mathematics, Faculty of Physics, Mathematics and Information Technology, Kh. Dosmukhamedov Atyrau University, Atyrau 060000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5962-4561","authenticated-orcid":false,"given":"Ainagul","family":"Adiyeva","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Methods of Teaching Mathematics, Faculty of Physics, Mathematics and Information Technology, Kh. Dosmukhamedov Atyrau University, Atyrau 060000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9242-0920","authenticated-orcid":false,"given":"Balaussa","family":"Orazbayeva","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Faculty Information Technology, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9815-9594","authenticated-orcid":false,"given":"Shynar","family":"Yelezhanova","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Methods of Teaching Mathematics, Faculty of Physics, Mathematics and Information Technology, Kh. Dosmukhamedov Atyrau University, Atyrau 060000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2841-5166","authenticated-orcid":false,"given":"Raigul","family":"Tuleuova","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Methods of Teaching Mathematics, Faculty of Physics, Mathematics and Information Technology, Kh. Dosmukhamedov Atyrau University, Atyrau 060000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4570-0487","authenticated-orcid":false,"given":"Raushan","family":"Moldasheva","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Methods of Teaching Mathematics, Faculty of Physics, Mathematics and Information Technology, Kh. Dosmukhamedov Atyrau University, Atyrau 060000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ullah, K., Basit, A., Ullah, Z., Aslam, S., and Herodotou, H. (2021). Automatic generation control strategies in conventional and modern power systems: A comprehensive overview. Energies, 14.","DOI":"10.3390\/en14092376"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nijmeijer, H., and Van der Schaft, A. (1990). 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