Towards the Development of an Interval Arithmetic Environment for Validated Computer-Aided Design and Verification of Systems in Control Engineering

Authors:
Andreas Rauh;Johanna Minisini;Eberhard P. Hofer
Affiliations:
Chair of Mechatronics, University of Rostock, Rostock, Germany D-18059;Institute of Measurement, Control, and Microtechnology, University of Ulm, Ulm, Germany D-89069;Institute of Measurement, Control, and Microtechnology, University of Ulm, Ulm, Germany D-89069
Venue:
Numerical Validation in Current Hardware Architectures
Year:
2009

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Abstract

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 which constraints for both state and control variables are taken into account. For that purpose, the use of interval arithmetic routines for calculation of guaranteed enclosures of the solutions of sets of ordinary differential equations and for the calculation of validated sensitivity measures of state variables with respect to parameter variations are discussed. Simulation results as well as further steps towards the development of a general-purpose interval arithmetic framework for the design and verification of systems in control engineering are summarized.