Dynamic surface control-based stabilization of an nth chained systems with application to a car-like robot

This work aims to design a Dynamic Surface Controller (DSC) in order to stabilize the n
^th
order chained systems able to express several kinds of nonholonomic, nonlinear and underactuated systems as unicycle, car-like, be-steerable car, car with trailer, etc. These latter are difficult to handle because of the complexity of their kinematic model. We purpose the use of the DSC in order to avoid the explosion of terms yielded by the backstepping algorithm and leading to compute the high order derivatives of variables. From the Lyapunov stability analysis, we prove that the designed controls render the closed loop system ultimately Uniformly Bounded (UUB). The applicability and the effectiveness of the control method are shown through simulation results when applying the control method on a car-like robot expressed by a fourth order chained system.