To describe the true behavior of most real-world systems with sufficient accuracy, engineers have to overcome difficulties arising from their lack of knowledge about certain parts of a process or from the impossibility of characterizing it with absolute certainty. Depending on the application at hand, uncertainties in modeling and measurements can be represented in different ways. For example, bounded uncertainties can be described by intervals, affine forms or general polynomial enclosures such as Taylor models, whereas stochastic uncertainties can be characterized in the form of a distribution described, for example, by the mean value, the standard deviation and higher-order moments.

The goal of this Special Volume onModeling, Design, and Simulation of Systems with Uncertainties is to cover modern methods for dealing with the challenges presented by imprecise or unavailable information. All contributions tackle the topic from the point of view of control, state and parameter estimation, optimization and simulation.

Thematically, this volume can be divided into two parts. In the first we present works highlighting the theoretic background and current research on algorithmic approaches in the field of uncertainty handling, together with their reliable software implementation. The second part is concerned with real-life application scenarios from various areas including but not limited to mechatronics, robotics, and biomedical engineering.

Andreas Rauh

received his diploma degree in electrical engineering and information technology from the Technische Universität München, Munich, Germany, in 2001 and his PhD degree (Dr.-Ing.) from the University of Ulm, Germany, in 2008. His research interests are: State and parameter estimation for stochastic and set-valued uncertainties, verified simulation of nonlinear uncertain systems, nonlinear, robust, and optimal control, interval methods for ordinary differential equations as well as differential-algebraic systems. Currently, he is with the Chair of Mechatronics, University of Rostock, Germany, as post-doctoral researcher.

Ekaterina Auer

received her Diplomas in Mathematics and Computer Science from Ulyanovsk State University in 2001 and from the University of Duisburg-Essen in 2002. Since 2002, she has been working at the chair for computer graphics and scientific computing at the University of Duisburg-Essen as a research assistant, receiving her Ph.D. in 2006. Her main interests are scientific computing **and development of software for its application to problems in mechanics and engineering.

Part I Theoretic Background and Software Implementation

Implementing a Rigorous ODE Solver Through Literate Programming.- A New Method for Inner Estimation of Solution Sets to Interval Linear Systems.- Structural Analysis for the Design of Reliable Controllers and State Estimators for Continuous-Time Dynamical Systems with Uncertainties.- Analyzing Reachability of Linear Dynamic Systems with Parametric Uncertainties.- Robustness Comparison of Tracking Controllers Using Verified Integration.- Probabilistic Set-Membership State Estimator.- Verified Global Optimization for Estimating the Parameters of Nonlinear Models.-Optimal Control of Induction Heating: Theory and Application.- Coherent Upper and Lower Conditional Previsions Defined by Hausdorff Outer and Inner Measures.-

Part II Applications: Uncertainties in Engineering

Two Approaches for Guaranteed State Estimation of Nonlinear Continuous-Time Models.- Quantifying Spacecraft Failure in an Uncertain Environment: the Case of Jupiter Europa Orbiter.- Robust State and Parameter Estimation for Nonlinear Continuous-Time Systems in a Set-Membership Context.- Nonlinear Adaptive Control of a Bioprocess Model with Unknown Kinetics.- Verified Analysis of a Model for Stance Stabilization.- Adaptive Control Strategies in Heat Transfer Problems with Parameter Uncertainties Based on a Projective Approach.- State and Disturbance Estimation for Robust Control of Fast Flexible Rack Feeders.- Notation.