Abstract
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide several theoretical improvements to the algorithm, including its extension to piecewise constant and sinusoidal approximations of uncertain inputs, updates on the affine approximation bounds and a generalized formula for the analytical error. In addition, we implemented the methodology in Ariadne, a library for the verification of continuous and hybrid systems. Then we evaluated ten systems with varying degrees of nonlinearity, number of variables and uncertain inputs. The results are hereby compared with two state-of-the-art approaches to time-varying uncertainties in nonlinear systems.
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Acknowledgments
This work was partially supported by MIUR, Project “Italian Outstanding Departments, 2018-2022” and by INDAM, GNCS 2019, “Formal Methods for Mixed Verification Techniques”.
The authors would like to thank Xin Chen and Matthias Althoff for the support on setting up their respective softwares and building the examples for the comparison.
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Geretti, L., Živanović Gonzalez, S., Collins, P., Bresolin, D., Villa, T. (2019). Rigorous Continuous Evolution of Uncertain Systems. In: Zamani, M., Zufferey, D. (eds) Numerical Software Verification. NSV 2019. Lecture Notes in Computer Science(), vol 11652. Springer, Cham. https://doi.org/10.1007/978-3-030-28423-7_4
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