Compositional synthesis of opacity-preserving finite abstractions for interconnected systems

Abstract

In this paper, we propose a compositional approach to construct opacity-preserving finite abstractions (a.k.a symbolic models) for networks of discrete-time nonlinear control systems. Particularly, we introduce new notions of simulation functions that characterize the distance between control systems while preserving opacity properties across them. Instead of treating large-scale systems in a monolithic manner, we develop a compositional scheme to construct the finite abstractions together with the overall opacity-preserving simulation functions based on those of the smaller subsystems. For a network of incrementally input-to-state stable control subsystems and under some small-gain type condition, an algorithm for designing local quantization parameters is presented to orderly build the local symbolic models of subsystems. We show that the network of those constructed symbolic models simulates the original network for an a-priori defined abstraction accuracy while preserving its opacity properties.