Adaptive locally homogeneous control of input affine nonlinear systems and its application to magnetic levitation system control

We have recently proposed a locally homogeneous stabilizing controller that guarantees a convergence rate for input affine nonlinear control systems. However, adaptive control problem has not been discussed. In this research, we propose an adaptive homogeneous controller for homogeneous control systems. Consecutively, we propose an adaptive locally homogeneous controller with a convergence rate guarantee for input affine nonlinear systems. We apply our proposed controller to a stabilization problem of a magnetic levitation system. We confirm the effectiveness of the proposed method by an experiment.