Compositional Synthesis of Symbolic Models for Networks of Switched Systems

Abstract

In this paper, we provide a compositional methodology for constructing symbolic models for networks of discrete-time switched systems. We first define a notion of so-called augmented-storage functions to relate switched subsystems and their symbolic models. Then we show that if some dissipativity type conditions are satisfied, one can establish a notion of so-called alternating simulation function as a relation between a network of symbolic models and that of switched subsystems. The alternating simulation function provides an upper bound for the mismatch between the output behavior of the interconnection of switched subsystems and that of their symbolic models. Moreover, we provide an approach to construct symbolic models for discrete-time switched subsystems under some assumptions ensuring incremental passivity of each mode of switched subsystems. Finally, we illustrate the effectiveness of our results through two examples. * This works has been accepted for publication in the IEEE Control Systems Letters (L-CSS).

Compositional Verification of Initial-State Opacity for Switched Systems

“…switching is allowed but no switch occurs; -l = k d − 1, p + = p and l + = 0: switching is allowed and a switch occurs. The following proposition is borrowed from [12] showing that the output runs of a dt-SS Σ and its associated transition system T (Σ) are equivalent so that one can use Σ and T (Σ) interchangeably.…”

“…l < k d − 1, p + = p and l + = l + 1: switching is not allowed because the time elapsed since the latest switch is strictly smaller than the dwell time; -l = k d − 1, p + = p and l + = k d − 1: switching is allowed but no switch occurs; -l = k d − 1, p + = p and l + = 0: switching is allowed and a switch occurs. The following proposition is borrowed from [12] showing that the output runs of a dt-SS Σ and its associated transition system T (Σ) are equivalent so that one can use Σ and T (Σ) interchangeably.…”

“…Motivated by those abstraction-based techniques in [6], [7], [8] and their limitations, this work proposes an approach to analyze approximate initial-state opacity for networks of switched systems by constructing their opacity-preserving finite abstractions compositionally. There have been some recent results proposing compositional techniques for constructing finite abstractions for networks of systems (see the results in [9], [10], [11], [12] for more details). However, the aforementioned compositional schemes are proposed for the sake of controller synthesis for temporal logic properties, and none of them are applicable to deal with security properties.…”

Data-driven verification and synthesis of stochastic systems through barrier certificates

“…where parameters , , and H are the same as in Definition (3). Another advantage of choosing in the interval (0, 1) is that this new formulation can be utilized in the context of compositionality and interconnected systems [41,42].…”

“…In the next theorem, we present our solution to Problem 3 by proposing a new confidence bound which is always valid even for the non-convex scenario program in (42).…”