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

الملخص EN

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.