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Abstract domains for constraint programming with differential equations

Ziat, Ghiles and Mullier, Olivier and Sandretto, Julien Alexandre dit and Garion, Christophe and Chapoutot, Alexandre and Thirioux, Xavier Abstract domains for constraint programming with differential equations. (2020) In: Proceedings of the 9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains, 17 November 2020 - 17 November 2020 (United States).

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Official URL: https://doi.org/10.1145/3427762.3429453


Cyber-physical systems (CPSs), as cruise control systems, involve life-critical or mission critical functions that must be validated. Formal verification techniques can bring high assurance level but have to be extended to embrace all the components of CPSs. Physical part models of CPSs are usually defined from ordinary differential equations (ODEs) and reachability methods can be used to compute safe over-approximation of the solution set of ODEs. However, additional constraints, as obstacle avoidance have also to be considered to validate CPSs. To meet this need, we propose in this paper a framework, based on abstract domains, for solving constraint satisfaction problems where the objects manipulated are described by ODEs. We use a form of disjunctive completion for which we provide a split operator and an efficient constraint filtering mechanism that takes advantage of the continuity aspect of ODEs. We illustrate the benefits of our method on a real-world application of trajectory validation of a swarm of drones, for which the main property we aim to prove is the absence of collisions between drone trajectories. Our work has been concretized in the form of a cooperation between the DynIbex library, used for the abstraction of ODEs, and the AbSolute constraint solver, used for the constraint resolution. Experiments show promising results.

Item Type:Conference or Workshop Item (Paper)
Audience (conference):International conference proceedings
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Institution:Other partners > Ecole Nationale Supérieure de Techniques Avancées - ENSTA (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited On:06 Jan 2021 15:32

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