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Reachability Analysis of Nonlinear ODEs Using Polytopic Based Validated Runge-Kutta

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Reachability Problems (RP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11123))

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Abstract

Ordinary Differential Equations (ODEs) are a general form of differential equations. This mathematical format is often used to represent the dynamic behavior of physical systems such as control systems and chemical processes. Linear ODEs can usually be solved analytically while nonlinear ODEs may need numerical methods to obtain approximate solutions. There are also various developments for validated simulation of nonlinear ODEs such as explicit and implicit guaranteed Runge-Kutta integration schemes. The implicit ones are mainly based on zonotopic computations using affine arithmetics. It allows to compute the reachability of a nonlinear ODE with a zonotopic set as its initial value. In this paper, we propose a new validated approach to solve nonlinear ODEs with a polytopic set as the initial value using an indirectly implemented polytopic set computation technique.

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Acknowledgement

The second author was grateful for the financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant EP/R005532/1.

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Correspondence to Julien Alexandre dit Sandretto .

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Alexandre dit Sandretto, J., Wan, J. (2018). Reachability Analysis of Nonlinear ODEs Using Polytopic Based Validated Runge-Kutta. In: Potapov, I., Reynier, PA. (eds) Reachability Problems. RP 2018. Lecture Notes in Computer Science(), vol 11123. Springer, Cham. https://doi.org/10.1007/978-3-030-00250-3_1

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  • DOI: https://doi.org/10.1007/978-3-030-00250-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00249-7

  • Online ISBN: 978-3-030-00250-3

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