Compositional abstraction and safety synthesis using overlapping symbolic models

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

Symbolic Abstractions with Guarantees: A Data-Driven Divide-and-Conquer Strategy

This article is concerned with a data-driven divide-and-conquer strategy to construct symbolic abstractions for interconnected control networks with unknown mathematical models. We employ a notion of alternating bisimulation functions (ABF) to quantify the closeness between state trajectories of an interconnected network and its symbolic abstraction. Consequently, the constructed symbolic abstraction can be leveraged as a beneficial substitute for the formal verification and controller synthesis over the interconnected network. In our data-driven framework, we first establish a relation between each unknown subsystem and its data-driven symbolic abstraction, so-called alternating pseudo-bisimulation function (APBF), with a guaranteed probabilistic confidence. We then provide compositional conditions based on max-type small-gain techniques to construct an ABF for an unknown interconnected network using APBF of its individual subsystems, constructed from data. We demonstrate the efficacy of our data-driven approach over a room temperature network composing 100 rooms with unknown models. We construct a symbolic abstraction from data for each room as an appropriate substitute of original system and compositionally synthesize controllers regulating the temperature of each room within a safe zone with some guaranteed probabilistic confidence