The stabilization problem is considered for systems that are affine in control and nonlinear in phase variables. The Hamiltonian system of Pontryagin’s maximum principle is studied in a neighborhood of a second-order singular extremal. An existence theorem is proved for chattering extremals reaching the singular extremal in a finite time. The theorem is illustrated by the example of feedback stabilization for the ball and beam system.
Keywords: feedback stabilization, singular extremals of the second order, chattering control, ball–beam system
Received October 12, 2024
Revised November 27, 2024
Accepted December 2, 2024
Nikolai B. Melnikov, Dr. Phys.-Math. Sci., Prof., Lomonosov Moscow State University, Moscow, 119899 Russia, e-mail: melnikov@cs.msu.ru
Mariya I. Ronzhina, Cand. Sci. (Phys.-Math.), National University of Oil and Gas “Gubkin University”, Moscow, 119991 Russia, e-mail: ronzhina.m@gubkin.ru
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Cite this article as: N.B. Melnikov, M.I. Ronzhina. Chattering trajectories in stabilization problems for nonlinear control-affine systems. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2025, vol. 31, no. 1, pp. 138–153.
