Interval Methods for Reliable Modeling, Identification and Control of Dynamic Systems

European Control Conference 2015


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European Control Conference 2015


Andreas Rauh, Luise Senkel, Ekaterina Auer


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.



  1. Fundamentals of Interval Arithmetic
  2. Kinds of Uncertainty and Possibilities for Their Treatment during Modeling and Simulation in Engineering
  3. Verified Simulation of Dynamic Systems
  4. Current Possibilities for Simulating Uncertain Non-Smooth Dynamic Systems
  5. Control-Oriented Applications of Simulation Techniques for Non-Smooth Dynamic Systems
  6. Interval-Based Design of Sliding Mode Control and State Estimation Procedures
  7. Solid Oxide Fuel Cell Systems: Identification
  8. Solid Oxide Fuel Cell Systems: Interval-Based Sliding Mode Control


Software Demonstrations for Presentation 1

Software Demonstrations for Presentation 3

List of References

 Complete List


Hochschule Wismar
Lehrstuhl für Elektrotechnik und Informatik

Universität Rostock
Lehrstuhl für Mechatronik

Prof. Dr. rer. nat. habil. Ekaterina Auer

Phillip-Müller-Str. 14
23966 Wismar

Tel.: +49 3841 753-7322
Büro: Haus 17 Raum 305

PD Dr.-Ing. habil. Andreas Rauh

Justus-von-Liebig Weg 6
18059 Rostock

Tel.: +49 381 / 498 - 9216
Fax: +49 381 / 498 - 9092
Raum: 03

M.Sc. Luise Senkel