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Fractional-Order System Models and Their Verified Numerical Analysis Using Interval Methods
Verified integration of initial value problems for sets of ordinary differential equations were investigated in many research projects and resulted in numerous software implementations over the last decades. However, ordinary differential equations with integer orders of the derivatives are not the only relevant dynamic system models in modeling dynamic systems in engineering as well as computational physics, biology and other disciplines. One of the emerging modeling assumptions studied over the recent years is the use of fractional-order models that are characterized by non-integer order temporal derivatives. This presentation briefly touches upon their use in modeling applications from the areas of robotics and energy systems as well as for describing dynamic elements that are useful for so-called loop shaping techniques in control design. Novel, interval-based simulation routines for fractional-order systems are presented with an illustrating example from the field of modeling Lithium-ion batteries.
Andreas Rauh received his diploma degree in electrical engineering and information technology from the Technische Universität München, Munich, Germany, in 2001, his PhD degree (Dr.-Ing.) from the University of Ulm, Germany, in 2008. He got his habilitation (venia legendi) at the Faculty of Mechanical Engineering and Marine Technology at the University of Rostock, Germany, in 2017. His research interests include modeling, control, as well as state and parameter estimation for systems with stochastic and set-valued uncertainty.