Adaptive-Robust Stabilization of the Furuta's Pendulum Via Attractive Ellipsoid Method

This paper focuses on the issue of adaptive-robust stabilization of the Furuta's pendulum around unstable equilibrium where the dynamical model is unknown. The control scheme lies at the lack of the dynamical model as well as external disturbances. The stabilization analysis is based on the attractive ellipsoid method (AEM) for a class of uncertain nonlinear systems having “quasi-Lipschitz” nonlinearities. Even more, a modification of the AEM concept that permits to use online information obtained during the process is suggested here. This adjustment (or adaptation) is made only in some fixed sample times, so that the corresponding gain matrix of the robust controller is given on time interval too. Furthermore, under a specific “regularized persistent excitation condition,” the proposed method guarantees that the controlled system trajectories remain inside an ellipsoid of a minimal size (the minimal size is refereed to as the minimal trace of the corresponding inverse ellipsoidal matrix). Finally, the adaptive process describes a region of attraction (ROA) of the considered system under adaptive-robust nonlinear control law.