A computable and compositional semantics for hybrid automata

Abstract

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Categorical Semantics of Cyber-Physical Systems Theory

“…Hybrid systems is a well-established version of computational dynamical systems theory [3] (another being timed process algebras [16] or more recently model interfaces [57]). Ames (as well as Tabuada et al to some extent [69]) did develop a categorical theory of hybrid systems [5], which could be used to relate or otherwise use results from the wellestablished formalism of hybrid systems in our proposed framework as future work, but also the opposite; potentially strengthening notions of composition [4,15] in hybrid systems from category theory.…”

“…Recall that the image of a function is the subset of its codomain where all elements of the domain get mapped to, namely for an arbitrary : → , ( ) = { ∈ | ∃ ∈ such that ( ) = }. In the end, using the above constructions of the twostep process exhibited in (15), the explicit description of the resulting contract is precisely equation (8).…”

Monte Carlo Based Statistical Model Checking of Cyber-Physical Systems: A Review

“…In this section, we describe some of the existing Monte Carlo based SMC tools, focusing on those that are directly available to the academic community. There exist tools using simulation-based techniques, but whose output is not a statistical confidence interval, which are not included in our review, like: SyLVaaS [57], a Web-based software-as-a-service tool for System Level Formal Verification of CPSs; S-TaLiRo [58], which is a tool performing temporal logic falsification of properties over non-linear hybrid systems; Ariadne [59], which is a tool for the formal verification of CPSs, using reachability analysis for nonlinear hybrid automata; SpaceEx, a tool platform for reachability and safety verification of continuous and hybrid systems [60]; Symbolic PathFinder [61], a SMC tool implementing approximate algorithms for MDP.…”

Automating Numerical Parameters Along the Evolution of a Nonlinear System

“…The formalism of hybrid automata is commonly used to define the composition of controller and environment along with the semantics for its behavior (see [3,6]). Reachability analysis in particular is concerned with the computation of the reachable set, i.e., the set of points reached from an initial set that evolves under the system's dynamics.…”