Robust State Estimation for Underactuated Systems Using Sliding Modes and Attractive Ellipsoid Method

The control of underactuated systems is a challenging and interesting topic in applied engineering mainly due to their high-range of applicability. This condition arises because they have less independent control inputs than configuration variables. In real-time experimental environments, the presence of uncertainties, disturbances and the unavailability of the full state vector complicate the control objectives. Furthermore, when the number of passive joints is greater than the number of active ones, the stabilizability radius is too small, and the control techniques based on the linear approximation are not robust enough to perform stabilization in practice. Under these conditions, the control problem when the full state-vector is not available becomes challenging. State-estimation may lead to a well-know peaking phenomenon. In this paper, the Attractive Ellipsoid Method and Sliding Modes are used to estimate the unavailable states. These give the possibility to reach a stability-zone in finite time, while uncertain and the peaking phenomenon effects are reduced, in order to provide sufficient conditions for its applicability in observer-based control. Experimental results are presented for the electromechanical triple-link inverted pendulum.