Continuous Stabilizing Control for a Class Of Non-holonomic systems: Brockett System Example - Rehman, Fazal Ur; Satti, A Baseer; Saleem, A. Ahmed (Journal of Vibration Testing and System Dynamics, 2026)
A continuous adaptive controller is designed for a famous example of Brockett system which is an example of a class of non-holonomic systems. The controllability Lie Algebra of the Brockett’s system contains Lie brackets of depth one. It is shown that the closed loop system is globally uniformly asymptotically stable. The advantage of this method is that it does not require the conversion of the system model into a “chained form,” and thus does not rely on any special transformation techniques. The practical effectiveness of the controller is illustrated by numerical simulations.