Compositional Abstraction and Safety Synthesis using Overlapping Symbolic Models

Pierre-Jean Meyer (1) , Antoine Girard (2) , Emmanuel Witrant (3)

1 Department of Electromagnetic Engineering [Stockholm]
2 L2S - Laboratoire des signaux et systèmes
3 GIPSA-SLR - GIPSA - Systèmes linéaires et robustesse

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems.

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique; Systèmes et contrôle [cs.SY]

Pierre-Jean Meyer, Antoine Girard, Emmanuel Witrant. Compositional Abstraction and Safety Synthesis using Overlapping Symbolic Models. IEEE Transactions on Automatic Control, 2018, 63 (6), pp.1835-1841. ⟨10.1109/TAC.2017.2753039⟩. ⟨hal-01620532⟩