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In this paper, an overview of the potential use of validated techniques for the analysis and design of controllers for linear and nonlinear dynamical systems with uncertainties is given. In addition to robust pole assignment for linear dynamical systems with parameter uncertainties, mathematical system models and computational techniques are considered in… (More)

Interval arithmetic techniques such as VALENCIA-IVP allow calculating guaranteed enclosures of all reachable states of continuous-time dynamical systems with bounded uncertainties of both initial conditions and system parameters. Considering the fact that, in naive implementations of interval algorithms, overestimation might lead to unnecessarily… (More)

Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to… (More)

In this paper, interval arithmetic techniques for controller design of nonlinear dynamical systems with uncertainties are summarized. The main reason for the application of interval techniques in this context is the quantification of the influence of uncertainties and modeling errors. They result from neglecting nonlinear phenomena in the mathematical… (More)

In this paper, we introduce a general-purpose approach for the detection and reduction of overestimation in verified interval simulations of the dynamics of mechanical systems. For that purpose, we automatically derive constraints which eliminate physically meaningless parts of the state enclosures of the corresponding ordinary differential equations. The… (More)