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Accurate Abstractions for Controller Synthesis with Non-uniform Disturbances

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 12531)

Abstract

Abstraction-Based Controller Synthesis (ABCS) is an emerging field for automatic synthesis of correct-by-design controllers for non-linear dynamical systems in the presence of bounded disturbances. Existing ABCS techniques assume a global (state-independent) and uniform upper bound on disturbances. This can be overly pessimistic, resulting in a failure to find a controller. In this paper, we extend ABCS to accurately compute abstractions for system models with state and input-dependent non-uniform disturbances. This requires a subtle assume-guarantee style computation of the state evolution and the estimation of the error. We empirically show the benefit of our approach with significantly smaller amount of non-determinism in the abstract transitions.

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Fig. 1.
Fig. 2.

Notes

  1. 1.

    We restrict our notation to piecewise constant control inputs as more general control inputs will be unnecessary for the later part.

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Bai, Y., Mallik, K. (2020). Accurate Abstractions for Controller Synthesis with Non-uniform Disturbances. In: Lin, SW., Hou, Z., Mahony, B. (eds) Formal Methods and Software Engineering. ICFEM 2020. Lecture Notes in Computer Science(), vol 12531. Springer, Cham. https://doi.org/10.1007/978-3-030-63406-3_18

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  • DOI: https://doi.org/10.1007/978-3-030-63406-3_18

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