Robust asymptotic tracking control of a chain of integrator nonlinear systems with input constraint and hysteresis nonlinearity

Abstract

This paper focuses on the problem of tracking control of a chain of integrator nonlinear systems with input constraint and hysteresis nonlinearity. Input constraint, always existing in physical systems, has been proved a source of performance degradation. To handle this issue, an effective hyperbolic saturation function is employed, which is bounded no matter how the disturbances and error signals change. Furthermore, hysteresis nonlinearity, which may also limit the system performance, is modelled as a combination of a linear term with constant slope and a bounded disturbance term, which makes it possible to be integrated in the model based controller design. The robust integral of the sign of error (RISE) control is synthesized to guarantee the asymptotic tracking performance in the presence of parametric uncertainties and unmodelled nonlinearities such as external disturbances and unmodelled hysteresis nonlinearity. The closed-loop stability is proved via Lyapunov analysis. Some simulations are carried out to verify the effectiveness of the proposed controller.