Approximate Bisimulation: A Bridge Between Computer Science and Control Theory

Girard, Antoine; Pappas, George J.

doi:10.3166/ejc.17.568-578

Cited by 121 publications

(84 citation statements)

References 50 publications

(61 reference statements)

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“…Frehse et al [9] develop assume-guarantee reasoning for hybrid systems based on over-approximation by simulation to enable compositional reasoning. A similar approach is taken by Girard and Pappas [11] using bisimulation, simulation, and language inclusion to develop approximate system relationships. These approaches are focused on the intersection of control theory and computer science.…”

Section: Discussionmentioning

confidence: 99%

Contract-based integration of cyber-physical analyses

Ruchkin

Niz

Garlan

et al. 2014

Proceedings of the 14th International Conference on Embedded Software

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Developing cyber-physical systems involves creating systems with properties from multiple domains, e.g., timing, logical correctness, thermal resilience, aerodynamics, and mechanical stress. In today's industrial practice, multiple analyses are used to obtain and verify such properties. Unfortunately, given that these analyses originate from different scientific domains, they abstract away interactions among themselves, risking the invalidation of their results. Specifically, one challenge is to ensure that an analysis is never applied to a model that violates its assumptions. Since such violation can originate from the updating of the model by another analysis, analyses must be executed in the correct order. Another challenge is to do this soundly and scalably over models of realistic complexity and diverse set of analyses. To address these challenges, we develop an analysis integration approach that uses contracts to specify dependencies between analyses, determine their correct orders of application, and specify and verify applicability conditions across multiple domains. We present an implementation of our approach, and demonstrate its effectiveness, extensibility, and scalability.

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Section: Discussionmentioning

confidence: 99%

Contract-based integration of cyber-physical analyses

Ruchkin

Niz

Garlan

et al. 2014

Proceedings of the 14th International Conference on Embedded Software

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“…Girard and Pappas explored approximate bisimulation of continuous systems in [9], and Pappas earlier developed (exact) bisimulations between continuous linear systems [18]. However, these works employ a different notion of simulation and do not seek to make the structure of the simulation easier to analyze in the way that we do with decoupling, and are in practice limited to linear ODEs due to reliance on solving linear matrix inequalities (LMIs).…”

Section: Related Workmentioning

confidence: 99%

Decoupling Abstractions of Non-linear Ordinary Differential Equations

Sogokon

Ghorbal

Johnson

2016

FM 2016: Formal Methods

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Abstract. We investigate decoupling abstractions, by which we seek to simulate (i.e. abstract) a given system of ordinary differential equations (ODEs) by another system that features completely independent (i.e. uncoupled) sub-systems, which can be considered as separate systems in their own right. Beyond a purely mathematical interest as a tool for the qualitative analysis of ODEs, decoupling can be applied to verification problems arising in the fields of control and hybrid systems. Existing verification technology often scales poorly with dimension. Thus, reducing a verification problem to a number of independent verification problems for systems of smaller dimension may enable one to prove properties that are otherwise seen as too difficult. We show an interesting correspondence between Darboux polynomials and decoupling simulating abstractions of systems of polynomial ODEs and give a constructive procedure for automatically computing the latter.

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“…The finite-state abstraction can then be used for various purposes such as verification and controller synthesis (see, e.g. [34]). …”

Section: Simulation and Bisimulation Notionsmentioning

confidence: 99%

Metamathematics for Systems Design

Hasuo

2017

New Gener. Comput.

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This position paper describes the context, the goal, the strategy and the tactics of the ERATO MMSD project (2016-2022. The project aims at enhanced quality assurance measures for industry products like cars. In doing so, we follow a recent trend and exploit formal methods, a body of mathematical techniques originally developed for computer systems. However, there are fundamental gaps in application of formal methods to industry products: additional concerns in industry products such as continuous dynamics of physical components and quantitative measures such as probability, time, and cost make problems fundamentally different from those about software. Formal methods that accommodate these concerns is an active research area, which shows that it is a hard problem. There are several successful theoretical developments in this direction. They typically combine one individual technique with one specific concern, such as hybrid automata that extend automata with continuous dynamics. Our project aims to contribute to this hard problem in a unique way. In our project we will take a unique metamathematical strategy to bridging the gaps: instead of creating one technique for each concern, we want to find a meta-level theory that describes how to develop such techniques for many potential concerns in general. Through this strategy, together with our emphasis on real-world applications in industry, we expect a new prototype of applied mathematics will emerge. In this prototype, abstraction and genericitycharacteristics of modern mathematics that are not often associated with application-are turned into crucial advantages in applications.

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Approximate Bisimulation: A Bridge Between Computer Science and Control Theory

Cited by 121 publications

References 50 publications

Contract-based integration of cyber-physical analyses

Contract-based integration of cyber-physical analyses

Decoupling Abstractions of Non-linear Ordinary Differential Equations

Metamathematics for Systems Design

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