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Mathematical Problems in Engineering
Volume 2017, Article ID 6739857, 12 pages
https://doi.org/10.1155/2017/6739857
Research Article

TMsim: An Algorithmic Tool for the Parametric and Worst-Case Simulation of Systems with Uncertainties

1Department of Electronics and Telecommunications, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2Department of Information Technology, IDLab, Ghent University-IMEC, iGent Tower, Technologiepark-Zwijnaarde 15, 9052 Ghent, Belgium

Correspondence should be addressed to Riccardo Trinchero; ti.otilop@orehcnirt.odraccir

Received 3 November 2016; Accepted 8 March 2017; Published 30 March 2017

Academic Editor: J.-C. Cortés

Copyright © 2017 Riccardo Trinchero et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters. The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors. This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous-time linear equalizer.