Adaptive backstepping control of some uncertain nonlinear oscillators

Abstract

Abstract-A backstepping-based adaptive controller is designed for a class of uncertain second orded nonlinear systems under the strict-feedback form. It is shown that the closed loop is globally uniformly ultimately bounded and we give explicit bounds on both the asymptotic and transient performance. The control strategy is applied to a system typically found in base isolation schemes for seismic active protection of building structures. This system exhibits a hysteretic nonlinear behavior which is described analytically by the so-called Bouc-Wen model. Unlike other control schemes, the developed backstepping control does not require an exact knowledge of the model parameters. They are only defined within known intervals. The practical effectiveness of the controller is illustrated by numerical simulations.

Adaptive Sliding Mode Control of a Single Degree-of-Freedom Structure with Parameter Uncertainty

“…In [8] and [9] a multi-storey structure with parameter uncertainties is studied and a robust controller with relative stability is proposed. References [10] and [11] propose an adaptive backstepping controller for a one-storey nonlinear structure and suppose that the parameters of structure are not known exactly and lie in known intervals. In [7] a model-reference adaptive structural control algorithm is presented and the parameters of structure are estimated in real time together with the timevarying control gains.…”

Semiactive backstepping control for vibration attenuation in structures equipped with magnetorheological actuators

“…The following standard variables, typically adopted in the literature of backstepping control [9]- [10], are used for the controller design:…”