Chattering Trajectories in Stabilization Problems for Nonlinear Control-Affine Systems

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.