Chattering trajectories in stabilization problems for nonlinear control-affine systems.

N. B. Melnikov^a, M. I. Ronzhina<sup>b

a</sup> Lomonosov Moscow State University
^b Gubkin Russian State University of Oil and Gas (National Research University), Moscow

Abstract: 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.

UDC: 517.977

MSC: 65K10, 37N40, 93C95

Received: 12.10.2024
Revised: 27.11.2024
Accepted: 02.12.2024

DOI: 10.21538/0134-4889-2025-31-1-138-153

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