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Abstract <p> 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–beam system. </p>

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Chattering Trajectories in Stabilization Problems for Nonlinear Control-Affine Systems

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • N. B. Melnikov,
  • M. I. Ronzhina

摘要

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–beam system.