Semantics and computation of the evolution of hybrid systems with ariadne

Pieter Collins, Davide Bresolin, Sanja Živanovic Gonzalez, Luca Geretti, Tiziano Villa

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Abstract

In this talk we will present material on the semantics, computability, and algorithms for the evolution of hybrid dynamical systems, and an overview of the tool Ariadne for verification of hybrid systems [1]. Hybrid systems are characterised by undergoing continuous evolution interspersed by discrete jumps. They exhibit all the complexities of finite automata, nonlinear dynamic systems and differential equations, and are extremely difficult to analyze. We will consider hybrid systems in which the continuous dynamics is given by a differential equation x = f(x), with discrete jumps x' = ri(x) which occur as soon as a guard condition gi(x) = 0 is activated. It is clear that the evolution of a hybrid system undergoes discontinuities, but since only continuous functions are computable, it is not clear to what extent, if any, it is possible to perform a rigorous analysis of a hybrid system. We will first show that we can define lower and upper semantics of evolution under which it is possible to compute reachable sets, and that away from discontinuity points (such as grazing or corner collision points), these semantics agree [2]. In order to perform reachability analysis, it is necessary to define the evolution over bounded initial sets of states. We show that this can be done using the operations of range, compose, flow and solve operations on functions. We will see that constrained image sets of the form {f(x) | x ? D | g(x) ? C}, are sufficient to express the evolution exactly, except for the case of degenerate (non-transverse) cross- ings [3]. The flow operation is the most computationally demanding, and we will give some details of the implementation and efficiency considerations [4]. We will give examples of reachability analysis in Ariadne, including electrical power converters and heating systems. Finally, we will outline some areas of active research, including differential inclusions [5] and modular reasoning.
Original languageEnglish
Title of host publication14th International Conference on Computability and Complexity in Analysis, CCA 2017 - Proceedings
PublisherKAIST School of Computing
Pages22-23
Number of pages2
Publication statusPublished - 1 Jan 2017
Event14th International Conference on Computability and Complexity in Analysis - Daejeon, Korea, Republic of
Duration: 24 Jul 201727 Jul 2017
Conference number: 14

Conference

Conference14th International Conference on Computability and Complexity in Analysis
Abbreviated titleCCA 2017
Country/TerritoryKorea, Republic of
CityDaejeon
Period24/07/1727/07/17

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