Slack Variables Generation via QR Decomposition for Adaptive Nonlinear Control of Affine Underactuated Systems

This paper presents a slack variable generation method utilizing QR decomposition for an adaptive nonlinear controller of affine underactuated systems. Slack variables are adopted to overcome nonsquare properties of underactuated systems. QR decomposition has an advantage of fast and accurate calculation to compute least square solution of underdetermined systems. In this paper, the slack variable generation using the QR decomposition is proposed to guarantee the stability of the closed-loop system with an adaptive nonlinear controller. Numerical simulations are performed to verify the performance of the adaptive nonlinear controller with the proposed slack variable generation method for a quadrotor unmanned aerial vehicle and an unmanned helicopter.