Rigorous Continuous Evolution of Uncertain Systems

Luca Geretti; Sanja Zivanovic Gonzalez; Pieter Collins; Davide Bresolin; Tiziano Villa

doi:10.1007/978-3-030-28423-7_4

Rigorous Continuous Evolution of Uncertain Systems

Luca Geretti, Sanja Zivanovic Gonzalez^*, Pieter Collins, Davide Bresolin, Tiziano Villa

^*Corresponding author for this work

Advanced Computing Sciences

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

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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.

Original language	English
Title of host publication	Numerical Software Verification. NSV 2019
Subtitle of host publication	International Workshop on Numerical Software Verification
Editors	M. Zamani, D. Zufferey
Publisher	Springer
Pages	60-75
Number of pages	16
Volume	11652
ISBN (Electronic)	978-3-030-28423-7
ISBN (Print)	978-3-030-28422-0
DOIs	https://doi.org/10.1007/978-3-030-28423-7_4
Publication status	Published - 2019

Publication series

Series	Lecture Notes in Computer Science
Volume	11652
ISSN	0302-9743

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title = "Rigorous Continuous Evolution of Uncertain Systems",

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.",

author = "Luca Geretti and {Zivanovic Gonzalez}, Sanja and Pieter Collins and Davide Bresolin and Tiziano Villa",

note = "Funding Information: 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”. Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

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Geretti, L, Zivanovic Gonzalez, S, Collins, P, Bresolin, D & Villa, T 2019, Rigorous Continuous Evolution of Uncertain Systems. in M Zamani & D Zufferey (eds), Numerical Software Verification. NSV 2019: International Workshop on Numerical Software Verification. vol. 11652, Springer, Lecture Notes in Computer Science, vol. 11652, pp. 60-75. https://doi.org/10.1007/978-3-030-28423-7_4

Rigorous Continuous Evolution of Uncertain Systems. / Geretti, Luca; Zivanovic Gonzalez, Sanja; Collins, Pieter et al.
Numerical Software Verification. NSV 2019: International Workshop on Numerical Software Verification. ed. / M. Zamani; D. Zufferey. Vol. 11652 Springer, 2019. p. 60-75 (Lecture Notes in Computer Science, Vol. 11652).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

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T1 - Rigorous Continuous Evolution of Uncertain Systems

AU - Geretti, Luca

AU - Zivanovic Gonzalez, Sanja

AU - Collins, Pieter

AU - Bresolin, Davide

AU - Villa, Tiziano

N1 - Funding Information: 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”. Publisher Copyright: © 2019, Springer Nature Switzerland AG.

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N2 - 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.

AB - 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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Geretti L, Zivanovic Gonzalez S, Collins P, Bresolin D, Villa T. Rigorous Continuous Evolution of Uncertain Systems. In Zamani M, Zufferey D, editors, Numerical Software Verification. NSV 2019: International Workshop on Numerical Software Verification. Vol. 11652. Springer. 2019. p. 60-75. (Lecture Notes in Computer Science, Vol. 11652). doi: 10.1007/978-3-030-28423-7_4

Rigorous Continuous Evolution of Uncertain Systems

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