Interval-based sliding mode observer design for nonlinear systems with bounded measurement and parameter uncertainty

The estimation of non-measurable state variables as well as the reliable identification of unknown system parameters are important prerequisites for the design and implementation of controllers for nonlinear dynamic systems. However, these tasks are often impeded by the nonlinearity of dynamic system models as soon as observer techniques are sought for, which can be used for large operating ranges. Moreover, parameters and measured data are typically only known within given tolerance bounds. Such uncertainty makes the proof of the asymptotic stability of the error dynamics of classical state observers quite difficult. Therefore, a novel interval-based sliding mode observer providing point-valued estimates is presented in this paper which is designed in such a way that asymptotic stability can be guaranteed by means of an online evaluation of a suitable Lyapunov function. Furthermore, an efficient strategy for the adaptation of the switching amplitude of the observer´s variable structure part is presented to reduce the amplification of measurement noise as far as possible if time-varying state variables and time-invariant system parameters are estimated simultaneously. An illustrative example, describing the longitudinal dynamics of a vehicle, is presented to highlight the practical applicability of the observer.