Global Exponential Regulation of Nonholonomic Chained Systems via Nonregular Feedback

This paper proposes a new nonsmooth nonregular feedback control to stabilize nonholonomic chained systems. Firstly, a discontinuous nonlinear coordinate transformation and a discontinuous input transformation are constructed to change nonholonomic chained systems into controllable linear systems. Secondly, an invariant set and a switching logic are explicitly constructed to process with the singular problems caused by the singular manifold. The obtained discontinuous control guarantees the global exponential convergence of the close-loop system and guarantees the global boundedness of the control inputs. Finally, simulation on the 4-dimension chained system justifies the effectiveness of the approach.