UTOPIC: Under-Approximation Through Optimal Control

Abstract : We consider a class of nonlinear systems of differential equations with uncertainties, i.e., with lack of knowledge in some of the parameters that is represented by a time-varying unknown bounded functions. An under-approximation of such systems consists of a subset of its reachable set, for any value of the unknown parameters. By relying on optimal control theory through Pontryagin's principle, we provide an algorithm for the under-approximation of a linear combination of the state variables in terms of a fully automated tool-chain named UTOPIC. This allows to establish tight under-approximations of common benchmarks models with dimensions as large as sixty-five.
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Josu Doncel, Nicolas Gast, Mirco Tribastone, Max Tschaikowski, Andrea Vandin. UTOPIC: Under-Approximation Through Optimal Control. QEST 2019 - 16th International Conference on Quantitative Evaluation of SysTems, Sep 2019, Glasgow, United Kingdom. pp.277-291, ⟨10.1007/978-3-030-30281-8_16⟩. ⟨hal-02283189⟩

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