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Abstract: A large variety of real-life dynamic systems in engineering, biology, biomechanics, and medicine are significantly influenced by uncertainty. In the field of uncertainty quantification, two main sources are discerned: aleatoric (due to randomness) and epistemic (due to the lack of knowledge). Both kinds have to be taken into consideration while designing a model for the given system to deal with such tasks as reliable simulation, online system and parameter identification, optimization and real-time (online) control, or state observation.

Although it is usually possible to reduce the epistemic uncertainty by performing further experiments during system identification, this is not the case for the aleatoric one. Hence, mathematical approaches for system modeling, simulation, and design should explicitly make use of suitable uncertainty descriptions. Here, set-valued or stochastic techniques offer appropriate solutions depending on the application at hand. The combination of both approaches, which constitutes a challenging subject of current research, is less explored but promising in certain real-life situations, for example, if probabilities are not known exactly.

This workshop is focused on set-valued uncertainty representations which are described in the form of scalar intervals and multi-dimensional interval boxes. Where necessary, we touch upon polytopes, affine forms, or more general descriptions such as Taylor models to improve accuracy or to reduce the computational load. The topic of interoperability of techniques is addressed both from the theoretical (e.g., the concept of imprecise probabilities) and from the practical point of view. In the latter case, generalizations of the Itô differential operator are employed for robust variable-structure control and state estimator design of systems where both bounded and stochastic uncertainty are present.

The workshop consists of two interconnected parts, the theoretical and the application-oriented one. The topics of the first part are methodological aspects of interval analysis along with the available software, a general framework for uncertainty modeling/assessment, and the solution of initial value problems for systems of ordinary differential equations with smooth and non-smooth right-hand sides. In the second part of the workshop, engineering, biological and biomedical applications are presented to highlight the use of the theoretical contributions in the context of robust parameter identification, reliable simulation, and guaranteed stabilizing control. Considered application scenarios include the simulation and control of mechanical systems with friction and hysteresis, biological system models in wastewater treatment and human blood cell growth, as well as modeling, identification, and control of high-temperature solid oxide fuel cells. Both simulation results and experimental validation are addressed for the above-mentioned benchmark applications.

Workshop goals: Presentation of methodological approaches for modeling and quantification of uncertainty as well as their application to real-life systems in engineering, biology, and medicine with a focus on an efficient usage of interval arithmetic techniques.

Synopsis of workshop content and major topics:

Part 1

Methods for modeling of uncertain dynamic systems, software demonstration, and mathematical background for verified simulation of dynamic systems with interval uncertainty

Part 2

Application of interval arithmetic and stochastic techniques in the framework of parameter identification, robust and nonlinear control, state estimation, and system optimization

Intended audience: Researchers and practitioners in robust and nonlinear simulation and control of dynamic systems with uncertainty

Workshop length and schedule: The workshop takes a full day and is splitted into two parts with a break in between.