The problem of approximate construction of the solvability set for a nonlinear controlled system with pointwise constraints on control parameters is considered. By linearizing the equations and using ellipsoidal calculus methods, formulas for internal ellipsoidal estimates of the solvability sets are derived. These estimates are guaranteed to be nondegenerate. This property is ensured by a special algorithm for matching the center and size of the linearization domain with the computed ellipsoidal estimates. The bounded linearization error is interpreted as uncertainty, and the original control problem for the nonlinear system is reduced to constructing minimax-type solvability sets for a linear system with uncertain parameters. The behavior of the eigenvalues of the matrices of the constructed ellipsoidal estimates is investigated. It is proved that the control synthesis obtained using the constructed solvability tube for the linearized system solves the target control problem for the original nonlinear system as well.
Keywords: nonlinear dynamics, solvability problem, ellipsoidal calculus, linearization, feedback control
Received May 11, 2026
Revised May 17, 2026
Accepted May 31, 2026
Funding Agency: The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation within the framework of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement no. 075-15-2025-345.
Pavel Aleksandrovich Tochilin, Cand. Sci. (Phis.-Math), Faculty of Computational Mathematics and Cybernetics of the Lomonosov Moscow State University, Moscow, 119991 Russia, e-mail: tochilin@cs.msu.ru
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Cite this article as: P.A. Tochilin. On the construction of nondegenerate internal ellipsoidal estimates for the solvability set of a nonlinear controlled system. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 3, pp. 236–251.
