research-article

Synthesis using approximately bisimilar abstractions: state-feedback controllers for safety specifications

Author:

Antoine GirardAuthors Info & Claims

HSCC '10: Proceedings of the 13th ACM international conference on Hybrid systems: computation and control

Pages 111 - 120

https://doi.org/10.1145/1755952.1755969

Published: 12 April 2010 Publication History

Abstract

This paper deals with the synthesis of state-feedback controllers using approximately bisimilar abstractions with an emphasis on safety problems.

Such problems consist in synthesizing a controller that restricts the behaviors of a system so that its outputs remain in some specified safe set.

One is usually interested in designing a controller that is as permissive as possible since this enables to ensure, a posteriori, secondary control objectives. Using the natural refinement technique for approximately bisimilar abstractions, a controller for a system can be synthesized from a controller for an abstraction. However, these controllers have some limitations in terms of performances, implementation cost and robustness.

The main contribution of this paper is a new procedure for the synthesis of controllers for safety specifications using approximately bisimilar abstractions. Given a controller for an abstraction, we describe an approach for synthesizing a controller for the system that does not suffer from the previous limitations.

Moreover, we show that if the controller of the abstraction is the maximal controller (i.e. the most permissive) then we can evaluate the distance between the synthesized controller and the maximal controller of the system. This distance can be made arbitrarily small by choosing sufficiently precise abstractions. We apply our results to synthesis problems for switched systems.

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Cited By

Weber AKreuzer MKnoll A(2020)A generalized Bellman-Ford Algorithm for Application in Symbolic Optimal Control2020 European Control Conference (ECC)10.23919/ECC51009.2020.9143743(2007-2014)Online publication date: May-2020
https://doi.org/10.23919/ECC51009.2020.9143743
Weber AKnoll A(2020)Approximately Optimal Controllers for Quantitative Two-Phase Reach-Avoid Problems on Nonlinear Systems2020 59th IEEE Conference on Decision and Control (CDC)10.1109/CDC42340.2020.9304048(430-437)Online publication date: 14-Dec-2020
https://doi.org/10.1109/CDC42340.2020.9304048
Girard A(2019)Brief paperAutomatica (Journal of IFAC)10.1016/j.automatica.2012.02.03748:5(947-953)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.automatica.2012.02.037
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Index Terms

Synthesis using approximately bisimilar abstractions: state-feedback controllers for safety specifications
1. Applied computing
  1. Computers in other domains
  2. Operations research
    1. Industry and manufacturing
      1. Command and control
2. Computing methodologies
  1. Artificial intelligence
    1. Control methods
      1. Computational control theory

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cover image ACM Conferences

HSCC '10: Proceedings of the 13th ACM international conference on Hybrid systems: computation and control

April 2010

308 pages

ISBN:9781605589558

DOI:10.1145/1755952

General Chairs:
Karl Henrik Johansson
KTH, Sweden
,
Wang Yi
Uppsala University, Sweden

Copyright © 2010 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 ACM 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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Published: 12 April 2010

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HSCC '10: The 13th ACM International Conference on Hybrid Systems: Computation and Control

April 12 - 15, 2010

Stockholm, Sweden

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Overall Acceptance Rate 153 of 373 submissions, 41%

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Cited By

Weber AKreuzer MKnoll A(2020)A generalized Bellman-Ford Algorithm for Application in Symbolic Optimal Control2020 European Control Conference (ECC)10.23919/ECC51009.2020.9143743(2007-2014)Online publication date: May-2020
https://doi.org/10.23919/ECC51009.2020.9143743
Weber AKnoll A(2020)Approximately Optimal Controllers for Quantitative Two-Phase Reach-Avoid Problems on Nonlinear Systems2020 59th IEEE Conference on Decision and Control (CDC)10.1109/CDC42340.2020.9304048(430-437)Online publication date: 14-Dec-2020
https://doi.org/10.1109/CDC42340.2020.9304048
Girard A(2019)Brief paperAutomatica (Journal of IFAC)10.1016/j.automatica.2012.02.03748:5(947-953)Online publication date: 2-Jan-2019
https://dl.acm.org/doi/10.1016/j.automatica.2012.02.037
Romero FEhlers R(2018)Steady Abstractions for CPS Controller Synthesis2018 Annual American Control Conference (ACC)10.23919/ACC.2018.8431809(778-785)Online publication date: Jun-2018
https://doi.org/10.23919/ACC.2018.8431809
Zamani MMazo MKhaled MAbate A(2018)Symbolic Abstractions of Networked Control SystemsIEEE Transactions on Control of Network Systems10.1109/TCNS.2017.27396455:4(1622-1634)Online publication date: Dec-2018
https://doi.org/10.1109/TCNS.2017.2739645
Kido KSedwards SHasuo I(2018)Bounding Errors Due to Switching Delays in Incrementally Stable Switched SystemsIFAC-PapersOnLine10.1016/j.ifacol.2018.08.04251:16(247-252)Online publication date: 2018
https://doi.org/10.1016/j.ifacol.2018.08.042
Yousefi Mvan Heusden KMitchell IDumont G(2017)Output-feedback safety-preserving control2017 American Control Conference (ACC)10.23919/ACC.2017.7963336(2550-2555)Online publication date: May-2017
https://doi.org/10.23919/ACC.2017.7963336
Svoreňová MKřetínský JChmelík MChatterjee KČerná IBelta C(2017)Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic gamesNonlinear Analysis: Hybrid Systems10.1016/j.nahs.2016.04.00623(230-253)Online publication date: Feb-2017
https://doi.org/10.1016/j.nahs.2016.04.006
Le Coënt ADe Vuyst FRey CChamoin LFribourg L(2016)Control of mechanical systems using set based methodsInternational Journal of Dynamics and Control10.1007/s40435-016-0245-y5:3(496-512)Online publication date: 2-May-2016
https://doi.org/10.1007/s40435-016-0245-y
Svoreňová MKřetínský JChmelík MChatterjee KČerná IBelta CGirard ASankaranarayanan S(2015)Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic gamesProceedings of the 18th International Conference on Hybrid Systems: Computation and Control10.1145/2728606.2728608(259-268)Online publication date: 14-Apr-2015
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