Robust Interval Observer Design for Fractional-Order Models with Applications to State Estimation of Batteries

Abstract

Abstract Interval observers have been investigated by many researchers during the last decade, especially for those classes of systems that can be described by finite-dimensional continuous-time ordinary differential equations, discrete-time difference equations, and sets of partial differential equations in which both, system parameters and external disturbances, may be subject to bounded uncertainty. In contrast to this, only preliminary investigations were performed for fractional-order models. Due to the fact that many electro-chemical processes such as the charging and discharging dynamics of batteries can be described in good accuracy by using fractional-order models, this paper focuses on the design and numerical validation of interval observers for such systems. Here, we present a cooperativity-enforcing observer structure leading directly to decoupled lower and upper bounding systems for the sets of reachable states. This is visualized by a battery model with interval uncertainty in the output equation.