research-article

An improved algorithm for robust safety analysis of sampled data systems

Authors:

Ian M. Mitchell,

Shahab KaynamaAuthors Info & Claims

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

Pages 21 - 30

https://doi.org/10.1145/2728606.2728619

Published: 14 April 2015 Publication History

Abstract

A sampled data model falls somewhere between continuous and discrete time models: The plant evolves in continuous time, but the controller receives feedback and can modify its control input(s) only at periodic points in time. In previous work we have demonstrated how to compute the discriminating kernel (also called the maximal robust control invariant set) for sampled data systems and how this kernel can be used to analyze and even synthesize safe feedback controllers for systems with state space safety constraints; however, the algorithm for computing the kernel was conservative. In this paper we provide an improved abstract algorithm whose computations are tight to the sampled data discriminating kernel. The improved algorithm can also take sample time jitter into account. A level set implementation is used to demonstrate that the new algorithm is tight and a conservative ellipsoidal implementation is used to demonstrate its practical benefits on a nonlinear quadrotor model.

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Cited By

Liniger ALygeros J(2019)Real-Time Control for Autonomous Racing Based on Viability TheoryIEEE Transactions on Control Systems Technology10.1109/TCST.2017.277290327:2(464-478)Online publication date: Mar-2019
https://doi.org/10.1109/TCST.2017.2772903
Raković SFontes FKolmanovsky I(2017)Reachability and Invariance for Linear Sampled–data SystemsIFAC-PapersOnLine10.1016/j.ifacol.2017.08.67550:1(3057-3062)Online publication date: Jul-2017
https://doi.org/10.1016/j.ifacol.2017.08.675
Mitchell IYeh JLaine FTomlin C(2016)Ensuring safety for sampled data systems: An efficient algorithm for filtering potentially unsafe input signals2016 IEEE 55th Conference on Decision and Control (CDC)10.1109/CDC.2016.7799417(7431-7438)Online publication date: Dec-2016
https://doi.org/10.1109/CDC.2016.7799417

Index Terms

An improved algorithm for robust safety analysis of sampled data systems

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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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New York, NY, United States

Publication History

Published: 14 April 2015

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Natural Sciences and Engineering Research Council of Canada

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HSCC '15

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IEEE-CSS
SIGBED

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

April 14 - 16, 2015

Washington, Seattle

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Cited By

Liniger ALygeros J(2019)Real-Time Control for Autonomous Racing Based on Viability TheoryIEEE Transactions on Control Systems Technology10.1109/TCST.2017.277290327:2(464-478)Online publication date: Mar-2019
https://doi.org/10.1109/TCST.2017.2772903
Raković SFontes FKolmanovsky I(2017)Reachability and Invariance for Linear Sampled–data SystemsIFAC-PapersOnLine10.1016/j.ifacol.2017.08.67550:1(3057-3062)Online publication date: Jul-2017
https://doi.org/10.1016/j.ifacol.2017.08.675
Mitchell IYeh JLaine FTomlin C(2016)Ensuring safety for sampled data systems: An efficient algorithm for filtering potentially unsafe input signals2016 IEEE 55th Conference on Decision and Control (CDC)10.1109/CDC.2016.7799417(7431-7438)Online publication date: Dec-2016
https://doi.org/10.1109/CDC.2016.7799417

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