GD-aided IOL (input–output linearisation) controller for handling affine-form nonlinear system with loose condition on relative degree

Input–output linearisation (IOL) may encounter a singularity problem when applied to the tracking control of affine-form nonlinear system (AFNS), which may not have a well-defined relative degree. The singularity problem has occurred in the area of control for decades. In this paper, we incorporate the gradient dynamics (GD) into IOL, which leads to the GD-aided IOL method to solve the singularity problem, with the proposition of the loose condition on relative degree. Moreover, detailed theoretical analyses on tracking-error bound and convergence performance of the corresponding GD-aided IOL controller are presented. Simulations and comparisons substantiate that the proposed GD-aided IOL method is capable of completing the tracking-control task and conquering the singularity encountered in the AFNS.