Adaptive sliding mode control using slack variables for affine underactuated systems

This paper presents an adaptive sliding mode control scheme using slack variables for affine and underactuated nonlinear systems. Slack variables are introduced to overcome the underactuated properties. A proper slack variable generating method is proposed to guarantee the stability of the proposed controller. Lyapunov stability theorem and LaSalle´s invariance theorem are used to analyze the stability of the proposed nonlinear control scheme. Numerical simulations are performed for a quadrotor Unmanned Aerial Vehicle, one of the affine underactuated systems, to verify the proposed control scheme.