research-article

Compositional construction of approximate abstractions

Authors:

Matthias Rungger,

Majid ZamaniAuthors Info & Claims

HSCC '15: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control

Pages 68 - 77

https://doi.org/10.1145/2728606.2728615

Published: 14 April 2015 Publication History

Abstract

In this paper we propose a compositional construction of approximate abstractions of interconnected control systems. Our notion of approximate abstraction is based on so-called simulation functions. The abstraction acts as substitute in the controller design process and is equipped with an interface that is used in lifting a controller, found for the abstraction, to a controller for the concrete system. The error between the abstraction and the concrete system is quantitatively bounded via the simulation function. In the first part of the paper, we provide conditions which facilitate the compositional construction of abstractions together with simulation functions and the associated interfaces of general interconnected control systems, given the abstractions and the simulation functions with the associated interfaces of the subsystems. In the second part of the paper, we characterize a general simulation function with the associated interface for the subclass of linear control systems. This characterization yields algorithmic procedures for the construction of approximate abstractions. Finally, we illustrate our findings with a simple example consisting of three linear subsystems.

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Cited By

Jagtap PDimarogonas D(2024)Controller synthesis against omega‐regular specifications: A funnel‐based control approachInternational Journal of Robust and Nonlinear Control10.1002/rnc.733934:11(7161-7173)Online publication date: 25-Mar-2024
https://doi.org/10.1002/rnc.7339
Sharifi MSwikir ANoroozi NZamani M(2022)Compositional construction of abstractions for infinite networks of discrete-time switched systemsNonlinear Analysis: Hybrid Systems10.1016/j.nahs.2022.10117344(101173)Online publication date: May-2022
https://doi.org/10.1016/j.nahs.2022.101173
Sharifi MSwikir ANoroozi NZamani M(2020)Compositional Construction of Abstractions for Infinite Networks of Switched Systems2020 59th IEEE Conference on Decision and Control (CDC)10.1109/CDC42340.2020.9304074(476-481)Online publication date: 14-Dec-2020
https://doi.org/10.1109/CDC42340.2020.9304074
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Index Terms

Compositional construction of approximate abstractions
1. Computing methodologies
  1. Artificial intelligence
    1. Control methods
      1. Computational control theory

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cover image ACM Conferences

HSCC '15: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control

April 2015

321 pages

ISBN:9781450334334

DOI:10.1145/2728606

Program Chairs:
Antoine Girard
Université Joseph Fourier, Grenoble, France
,
Sriram Sankaranarayanan
University of Colorado at Boulder

Copyright © 2015 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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IEEE-CSS: Control Systems Society
SIGBED: ACM Special Interest Group on Embedded Systems

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 April 2015

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HSCC '15: 18th International Conference on Hybrid Systems: Computation and Control

April 14 - 16, 2015

Washington, Seattle

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Overall Acceptance Rate 153 of 373 submissions, 41%

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Cited By

Jagtap PDimarogonas D(2024)Controller synthesis against omega‐regular specifications: A funnel‐based control approachInternational Journal of Robust and Nonlinear Control10.1002/rnc.733934:11(7161-7173)Online publication date: 25-Mar-2024
https://doi.org/10.1002/rnc.7339
Sharifi MSwikir ANoroozi NZamani M(2022)Compositional construction of abstractions for infinite networks of discrete-time switched systemsNonlinear Analysis: Hybrid Systems10.1016/j.nahs.2022.10117344(101173)Online publication date: May-2022
https://doi.org/10.1016/j.nahs.2022.101173
Sharifi MSwikir ANoroozi NZamani M(2020)Compositional Construction of Abstractions for Infinite Networks of Switched Systems2020 59th IEEE Conference on Decision and Control (CDC)10.1109/CDC42340.2020.9304074(476-481)Online publication date: 14-Dec-2020
https://doi.org/10.1109/CDC42340.2020.9304074
Apaza-Perez WCombastel CZolghadri A(2019)Abstraction-based low complexity controller synthesis for interconnected non-deterministic systems2019 18th European Control Conference (ECC)10.23919/ECC.2019.8795653(4174-4179)Online publication date: Jun-2019
https://doi.org/10.23919/ECC.2019.8795653
Lal RPrabhakar PRoop PZhan NGao SNuzzo P(2019)Compositional construction of bounded error over-approximations of acyclic interconnected continuous dynamical systemsProceedings of the 17th ACM-IEEE International Conference on Formal Methods and Models for System Design10.1145/3359986.3361210(1-5)Online publication date: 9-Oct-2019
https://dl.acm.org/doi/10.1145/3359986.3361210
Rungger MZamani M(2018)Compositional Construction of Approximate Abstractions of Interconnected Control SystemsIEEE Transactions on Control of Network Systems10.1109/TCNS.2016.25830635:1(116-127)Online publication date: Mar-2018
https://doi.org/10.1109/TCNS.2016.2583063
Guo MBoskos DTumova JDimarogonas D(2018)Distributed Hybrid Control Synthesis for Multi-Agent Systems from High-Level SpecificationsControl Subject to Computational and Communication Constraints10.1007/978-3-319-78449-6_12(241-260)Online publication date: 2-Jun-2018
https://doi.org/10.1007/978-3-319-78449-6_12
Chen XMover SSankaranarayanan S(2017)Compositional Relational Abstraction for Nonlinear Hybrid SystemsACM Transactions on Embedded Computing Systems10.1145/312652216:5s(1-19)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126522
Lesi VJovanov IPajic M(2017)Security-Aware Scheduling of Embedded Control TasksACM Transactions on Embedded Computing Systems10.1145/312651816:5s(1-21)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126518
Sadraddini SRudan JBelta CMartinez STovar EGill CSinopoli B(2017)Formal synthesis of distributed optimal traffic control policiesProceedings of the 8th International Conference on Cyber-Physical Systems10.1145/3055004.3055011(15-24)Online publication date: 18-Apr-2017
https://dl.acm.org/doi/10.1145/3055004.3055011
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