Conditional Bisimilarity for Reactive Systems

Logical Methods in Computer Science ◽

10.46298/lmcs-18(1:6)2022 ◽

2022 ◽

Vol Volume 18, Issue 1 ◽

Author(s):

Mathias Hülsbusch ◽

Barbara König ◽

Sebastian Küpper ◽

Lars Stoltenow

Keyword(s):

Reactive Systems ◽

Compositional Semantics ◽

Graph Rewriting ◽

Categorical Framework ◽

System States ◽

Suitable Framework

Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to obtain a compositional semantics. We enrich the notion of reactive systems by conditions on two levels: first, as in earlier work, we consider rules enriched with application conditions and second, we investigate the notion of conditional bisimilarity. Conditional bisimilarity allows us to say that two system states are bisimilar provided that the environment satisfies a given condition. We present several equivalent definitions of conditional bisimilarity, including one that is useful for concrete proofs and that employs an up-to-context technique, and we compare with related behavioural equivalences. We consider examples based on DPO graph rewriting, an instantiation of reactive systems.

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Congruences for Contextual Graph-Rewriting

BRICS Report Series ◽

10.7146/brics.v11i11.21836 ◽

2004 ◽

Vol 11 (11) ◽

Cited By ~ 6

Author(s):

Vladimiro Sassone ◽

Pawel Sobocinski

Keyword(s):

General Theorem ◽

Reactive Systems ◽

Semantic Theory ◽

Central Idea ◽

Arbitrary Graph ◽

Graph Rewriting ◽

Rewriting Systems ◽

Bisimulation Equivalence ◽

Graph Rewriting Systems ◽

Shed Light

We introduce a comprehensive operational semantic theory of graph rewriting. The central idea is recasting rewriting frameworks as Leifer and Milner's reactive systems. Consequently, graph rewriting systems are associated with canonical labelled transition systems, on which bisimulation equivalence is a congruence with respect to arbitrary graph contexts (cospans of graphs). This construction is derived from a more general theorem of much wider applicability. Expressed in abstract categorical terms, the central technical contribution of the paper is the construction of groupoidal relative pushouts, introduced and developed by the authors in recent work, in suitable cospan categories over arbitrary adhesive categories. As a consequence, we both generalise and shed light on rewriting via borrowed contexts due to Ehrig and König.

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SOL: A Verifiable Synchronous Language for Reactive Systems

10.21236/ada465328 ◽

2002 ◽

Cited By ~ 2

Author(s):

Ramesh Bharadwaj

Keyword(s):

Reactive Systems ◽

Synchronous Language

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Lexical Meaning, Concepts, and the Metasemantics of Predicates

10.1093/oso/9780198739548.003.0007 ◽

2018 ◽

Author(s):

Michael Glanzberg

Keyword(s):

Mental Representations ◽

Compositional Semantics ◽

Lexical Meaning ◽

Standard Methods

This chapter examines how concepts relate to lexical meanings. It focuses on how we can appeal to concepts to give specific, cognitively rich contents to lexical entries, while at the same time using standard methods of compositional semantics. This is a problem, as those methods assume lexical meanings provide extensions, while concepts are mental representations that have very different structure from an extension. The chapter proposes a way to solve this problem which is by casting concepts in a metasemantic role for certain expressions, notably verbs, but more also generally, with expressions that function as content-giving predicates in a sentence.

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An Optimized Triggering Algorithm for Event-Triggered Control of Networked Control Systems

Mathematics ◽

10.3390/math9111262 ◽

2021 ◽

Vol 9 (11) ◽

pp. 1262

Author(s):

Sunil Kumar Mishra ◽

Amitkumar V. Jha ◽

Vijay Kumar Verma ◽

Bhargav Appasani ◽

Almoataz Y. Abdelaziz ◽

...

Keyword(s):

Control Systems ◽

Networked Control Systems ◽

Networked Control ◽

Pendulum System ◽

Uniform Sampling ◽

Inverted Pendulum System ◽

Event Triggering ◽

Non Uniform Sampling ◽

System States ◽

Event Triggered

This paper presents an optimized algorithm for event-triggered control (ETC) of networked control systems (NCS). Initially, the traditional backstepping controller is designed for a generalized nonlinear plant in strict-feedback form that is subsequently extended to the ETC. In the NCS, the controller and the plant communicate with each other using a communication network. In order to minimize the bandwidth required, the number of samples to be sent over the communication channel should be reduced. This can be achieved using the non-uniform sampling of data. However, the implementation of non-uniform sampling without a proper event triggering rule might lead the closed-loop system towards instability. Therefore, an optimized event triggering algorithm has been designed such that the system states are always forced to remain in stable trajectory. Additionally, the effect of ETC on the stability of backstepping control has been analyzed using the Lyapunov stability theory. Two case studies on an inverted pendulum system and single-link robot system have been carried out to demonstrate the effectiveness of the proposed ETC in terms of system states, control effort and inter-event execution time.

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Vibro-Acoustical Sensitivities of Stiffened Aircraft Structures Due to Attached Mass-Spring-Dampers with Uncertain Parameters

Aerospace ◽

10.3390/aerospace8070174 ◽

2021 ◽

Vol 8 (7) ◽

pp. 174

Author(s):

Johannes Seidel ◽

Stephan Lippert ◽

Otto von Estorff

Keyword(s):

System Response ◽

Fuzzy Arithmetic ◽

Parameter Uncertainties ◽

Excitation Spectra ◽

Radiated Noise ◽

Linking Elements ◽

Manufacturing Tolerances ◽

Suitable Framework ◽

Mass Spring ◽

The Impact

The slightest manufacturing tolerances and variances of material properties can indeed have a significant impact on structural modes. An unintentional shift of eigenfrequencies towards dominant excitation frequencies may lead to increased vibration amplitudes of the structure resulting in radiated noise, e.g., reducing passenger comfort inside an aircraft’s cabin. This paper focuses on so-called non-structural masses of an aircraft, also known as the secondary structure that are attached to the primary structure via clips, brackets, and shock mounts and constitute a significant part of the overall mass of an aircraft’s structure. Using the example of a simplified fuselage panel, the vibro-acoustical consequences of parameter uncertainties in linking elements are studied. Here, the fuzzy arithmetic provides a suitable framework to describe uncertainties, create combination matrices, and evaluate the simulation results regarding target quantities and the impact of each parameter on the overall system response. To assess the vibrations of the fuzzy structure and by taking into account the excitation spectra of engine noise, modal and frequency response analyses are conducted.

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