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

Riccardo Trinchero, Paolo Manfredi and Igor S. Stievano

Mathematical Problems in Engineering, 2017, vol. 2017, 1-12

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6739857

DOI: 10.1155/2017/6739857

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