Adaptive backstepping control of nonlinear systems and application to base isolation schemes

In this paper, we present an adaptive backstepping control algorithm for a class of uncertain nonlinear systems under state-feedback form including hysteretic nonlinearity. The result is applied to a system found in base isolation schemes for seismic active protection of building structures. This system exhibits a hysteretic nonlinear behavior which is described by the so-called Bouc-Wen model. Unlike other control schemes, the developed backstepping control does not require the model parameters within known intervals. It is shown that not only global stability is guaranteed by the proposed controller, but also both transient and asymptotic performances are quantified as explicit functions of the design parameters so that designers can tune the design parameters in an explicit way to obtain the required closed loop behavior.