On stabilizing of dynamics of the elastic structural element in supersonic flow

Title	On stabilizing of dynamics of the elastic structural element in supersonic flow
Authors	A. V. Gladun¹ ¹Ulyanovsk Civil Aviation Institute named after Chief Marshal of Aviation B.P. Bugaev
Annotation	The paper addresses the problem of nonlinear stabilization for the dynamics of an elastic structural element under supersonic flow conditions, in the case of its inherent instability. The nonlinear partial differential equation describing the dynamics of the elastic element under the action of a control input is reduced to a system of nonlinear ordinary differential equations using the Galerkin method. The resulting system is analyzed for controllability employing differential-geometric methods, and a control law is synthesized to ensure asymptotic stability of the zero solution.
Keywords	elastic element, supersonic flow, dynamics, controllability, stabilization, partial differential equations (PDEs), Galerkin method, differential-geometric methods, stabilization, nonlinear control, asymptotic stability.
Citation	Gladun A. V. ''On stabilizing of dynamics of the elastic structural element in supersonic flow'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 69-73. Available at: https://conf.svmo.ru/files/2025/papers/paper13.pdf. - Date of access: 30.08.2025.