Composing Abstractions of Hybrid Systems

Abstract

Abstract. The analysis and design of hybrid systems must exploit their hierarchical and compositional nature of in order to tackle complexity. In previous work, we presented a hierarchical abstraction framework for hybrid control systems based on the notions of simulation and bisimulation. In this paper, we build upon our previous work and investigate the compositionality of our abstraction framework. We present a composition operator that allows synchronization on inputs and states of hybrid systems. We then show that the composition operator is compatible with our abstraction framework in the sense that abstracting subsystems will the result in an abstraction of the overall system.

Equivalence of Dynamical Systems by Bisimulation

“…For concurrent discrete processes the advantages of allowing nondeterminism are clear [15], [11], but for continuous dynamical systems such arguments have not been explicitated except in the context of abstraction. Indeed, in the area of verification of hybrid systems it is natural to look for notions of abstraction which allow to extend methods for verification of discrete processes to the hybrid case, see [10], [2], [13], [14], and [30]. This naturally leads to considering ways of abstracting continuous dynamical systems.…”

CASP solutions for planning in hybrid domains

“…Some examples include (Cimatti et al 2015;Cavada et al 2014;Tabuada et al 2002;Maly et al 2013;Bae et al 2016;Liu and Ozay 2014;Henzinger and Otop 2014), sampling-based planners (Karaman et al 2011;Lahijanian et al 2014). Similarly, falsification of hybrid systems tries to guide the search towards the error states, that can be easily cast as a planning problem, (Plaku et al 2013;Cimatti et al 1997).…”

Bisimulation theory for switching linear systems

“…Aim of this section is to characterize the notion of simulation and to introduce the notion of abstraction [1], [12], [14] for the class of SLSs. By specializing Theorem 3, the following result is obtained.…”

“…In fact, extensions of the notion of bisimulation to dynamical systems have been explored before in [2] and in a series of papers by Pappas and co-authors (e.g. [1], [11], [12], [14]). The common denominator of those works is to associate a transition system [7] to the process under consideration that preserves reachability properties.…”