Stabilization for a class of nonholonomic perturbed systems via robust adaptive sliding mode control

This paper considers stabilization of a class of nonholonomic perturbed systems, which can be described as a perturbed chained form according to geometric conditions on the perturbation vector field. The resulted system is stabilized in two separate stages. Firstly one-dimensional subsystem is realized by state feedback with an adaption law. Then discontinuous coordinate transformation is applied into the other subsystem. Based on quadratic stability, a robust sliding surface is developed through Linear Matrix Inequalities (LMI) techniques, and then adaptive sliding mode control is applied to ensure the subsystem finite-time hitting the prescribed manifold thus realizing the stabilization with high robustness. In the singular case z₁(t₀) = 0, the designed switching law guarantees the settlement of the caused uncontrollability problem. The proposed control strategy steers the whole system globally to the origin, and meanwhile the estimated parameters are bounded. Finally numerical simulation on the perturbed unicycle-like vehicle demonstrates the effectiveness of the control scheme.