Compositional abstraction and safety synthesis using overlapping symbolic models
For control engineers working on safety-critical systems, this method reduces computational complexity in symbolic control synthesis while maintaining less conservative results.
The paper develops a compositional approach for abstraction and safety synthesis of discrete-time nonlinear systems using overlapping symbolic subsystems, achieving significant complexity reduction compared to centralized methods while reducing conservatism relative to non-overlapping compositional approaches.
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.