Data-Driven Backstepping Control of Underactuated Mechanical Systems

Abstract

This paper studies control problems of underactuated mechanical systems with model uncertainties. The control is designed with the method of backstepping. The first-order low-pass filters are used to estimate the unknown quantities and to avoid the “explosion of terms.” A novel method is also proposed to implement the control without the knowledge of the control coefficient, which makes the whole process of backstepping control data-driven. The stability of the proposed control in the Lyapunov sense is studied. It is numerically and experimentally validated, and compared with the well-known model-based linear quadratic regulator (LQR) control. The data-driven backstepping control is found to provide comparable performances to that of the LQR control with the advantage of being model-free and robust.

Backstepping control for a class of underactuated nonlinear mechanical systems with a novel coordinate transformation in the discrete-time setting

“…In the recent two decades, a lot of advanced control approaches are considered for stabilization problem of underactuated systems such as the backstepping control, 5–9 passivity based control, 10,11 adaptive control, 12–14 sliding-mode control, 15,16 and adaptive fuzzy sliding-mode control. 17 The backstepping control method among the above-mentioned nonlinear control methods is the one that comes into prominence since it is possible to bring the mathematical model of many underactuated mechanical systems into the strict-feedback form making use of several mathematical techniques; for example, partial feedback linearization 18 and state transformation.…”