research-article

Closed loop analysis of control command software

Authors:

Romain Jobredeaux, and

Pierre-Loïc GarocheAuthors Info & Claims

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

April 2015

Pages 108 - 117

https://doi.org/10.1145/2728606.2728623

Published: 14 April 2015 Publication History

Abstract

Recent work addressing the stability analysis of controllers at code level has been mainly focused on the controller alone. However, most of the properties of interest of control software lie in how they interact with their environment. We introduce an extension of the analysis framework to reason on the stability of closed loop systems, i.e., controllers along with a model of their physical environment, the plant. The proposed approach focuses on the closed loop stability of discrete linear control systems with saturations, interacting with a discrete linear plant. The analysis is performed in the state space domain using Lyapunov-based quadratic invariants. We specifically address the automatic synthesis of such invariants and the treatment of floating-point imprecision.

References

[1]

S. Boldo and G. Melquiond. Flocq: A Unified Library for Proving Floating-point Algorithms in Coq. In Proceedings of the 20th IEEE Symposium on Computer Arithmetic, pages 243--252, Tübingen, Germany, July 2011.

Digital Library

[2]

O. Bouissou, E. Goubault, S. Putot, K. Tekkal, and F. Védrine. Hybridfluctuat: A static analyzer of numerical programs within a continuous environment. In A. Bouajjani and O. Maler, editors, Computer Aided Verification, 21st International Conference, CAV 2009, Grenoble, France, June 26 -- July 2, 2009. Proceedings, volume 5643 of Lecture Notes in Computer Science, pages 620--626. Springer, 2009.

Digital Library

[3]

S. Boyd, L. El Ghaoui, E. Féron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, volume 15 of SIAM. Philadelphia, PA, June 1994.

[4]

T. Coq development team. The Coq proof assistant reference manual, 2012. Version 8.4.

[5]

J. Feret. Static Analysis of Digital Filters. In ESOP, number 2986, 2004.

[6]

E. Féron. From Control Systems to Control Software. Control Systems, IEEE, 30(6), dec. 2010.

[7]

G. F. Franklin, M. L. Workman, and D. Powell. Digital Control of Dynamic Systems. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, 2nd edition, 1990.

[8]

T. M. Gawlitza, H. Seidl, A. Adjé, S. Gaubert, and E. Goubault. Abstract interpretation meets convex optimization. J. Symb. Comput., 47(12), 2012.

Digital Library

[9]

H. Herencia-Zapana, R. Jobredeaux, S. Owre, P.-L. Garoche, E. Feron, G. Perez, and P. Ascariz. Pvs linear algebra libraries for verification of control software algorithms in c/acsl. In NASA Formal Methods, pages 147--161, 2012.

Digital Library

[10]

N. J. Higham. Accuracy and Stability of Numerical Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1996.

Digital Library

[11]

IEEE Computer Society. IEEE Standard for Floating-Point Arithmetic. IEEE Standard 754--2008, 2008.

[12]

W. S. Levine. The control handbook. The electrical engineering handbook series. CRC Press New York, Boca Raton (Fl.), 1996.

[13]

A. M. Lyapunov. Problème général de la stabilité du mouvement. Annals of Mathematics Studies, 17, 1947.

[14]

E. Möhlmann and O. E. Theel. Stabhyli: a tool for automatic stability verification of non-linear hybrid systems. In C. Belta and F. Ivancic, editors, Proceedings of the 16th international conference on Hybrid systems: computation and control, HSCC 2013, April 8--11, 2013, Philadelphia, PA, USA, pages 107--112. ACM, 2013.

Digital Library

[15]

D. Monniaux. The pitfalls of verifying floating-point computations. ACM Trans. Program. Lang. Syst., 30(3), 2008.

Digital Library

[16]

A. Podelski and S. Wagner. Region stability proofs for hybrid systems. In J. Raskin and P. S. Thiagarajan, editors, Formal Modeling and Analysis of Timed Systems, 5th International Conference, FORMATS 2007, Salzburg, Austria, October 3--5, 2007, Proceedings, volume 4763 of Lecture Notes in Computer Science, pages 320--335. Springer, 2007.

Digital Library

[17]

P. Prabhakar and M. G. Soto. Abstraction based model-checking of stability of hybrid systems. In N. Sharygina and H. Veith, editors, Computer Aided Verification - 25th International Conference, CAV 2013, Saint Petersburg, Russia, July 13--19, 2013. Proceedings, volume 8044 of Lecture Notes in Computer Science, pages 280--295. Springer, 2013.

Digital Library

[18]

S. Ratschan and Z. She. Providing a basin of attraction to a target region of polynomial systems by computation of lyapunov-like functions. SIAM J. Control and Optimization, 48(7): 4377--4394, 2010.

Digital Library

[19]

P. Roux and P. Garoche. Computing quadratic invariants with min- and max-policy iterations: A practical comparison. In C. B. Jones, P. Pihlajasaari, and J. Sun, editors, FM 2014: Formal Methods - 19th International Symposium, Singapore, May 12--16, 2014. Proceedings, volume 8442 of Lecture Notes in Computer Science, pages 563--578. Springer, 2014.

[20]

P. Roux and P.-L. Garoche. Integrating policy iterations in abstract interpreters. In D. V. Hung and M. Ogawa, editors, ATVA, volume 8172 of Lecture Notes in Computer Science, pages 240--254. Springer, 2013.

[21]

P. Roux, R. Jobredeaux, P.-L. Garoche, and E. Féron. A generic ellipsoid abstract domain for linear time invariant systems. In HSCC. ACM, 2012.

Digital Library

[22]

S. M. Rump. Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19: 287--449, May 2010.

[23]

S. Sankaranarayanan and A. Tiwari. Relational abstractions for continuous and hybrid systems. In G. Gopalakrishnan and S. Qadeer, editors, Computer Aided Verification - 23rd International Conference, CAV 2011, Snowbird, UT, USA, July 14--20, 2011. Proceedings, volume 6806 of Lecture Notes in Computer Science, pages 686--702. Springer, 2011.

Digital Library

[24]

A. Suardi, S. Longo, E. C. Kerrigan, and G. A. Constantinides. Robust explicit mpc design under finite precision arithmetic. In World Congress of the International Federation of Automatic Control, volume 19, pages 2939--2944, 2014.

[25]

L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review, 38(1): 49--95, 1996.

Digital Library

[26]

T. Wang, R. Jobredeaux, H. Herencia-Zapana, P.-L. Garoche, A. Dieumegard, E. Feron, and M. Pantel. From design to implementation: an automated, credible autocoding chain for control systems. CoRR, abs/1307.2641, 2013.

[27]

Y. Xia, J. Yan, P. Shi, and M. Fu. Stability analysis of discrete-time systems with quantized feedback and measurements. Industrial Informatics, IEEE Transactions on, 9(1): 313--324, Feb 2013.

[28]

Q. Yang. Minimum Decay Rate of a Family of Dynamical Systems. PhD thesis, Stanford University, 1992.

Cited By

Guo XZhao JBu L(2024)Poles-based Invariant Generation for Verifying the BIBO Stability of Digital FiltersProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3650138(1-12)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3650138
Abate ABessa ICordeiro LDavid CKesseli PKroening DPolgreen E(2019)Automated formal synthesis of provably safe digital controllers for continuous plantsActa Informatica10.1007/s00236-019-00359-1Online publication date: 6-Dec-2019
https://doi.org/10.1007/s00236-019-00359-1
Davy GGarion CGaroche PRoux PThirioux X(2018)Preserving Functional Correctness of Cyber-Physical System Controllers: From Model to Code2018 Forum on Specification & Design Languages (FDL)10.1109/FDL.2018.8524044(5-16)Online publication date: Sep-2018
https://doi.org/10.1109/FDL.2018.8524044
Show More Cited By

Index Terms

Closed loop analysis of control command software

Recommendations

Closed loop stability of measure-driven impulsive control systems

Closed loop stabilization of impulsive control systems containing a measure in the dynamics is considered. It is proved that, as for regular affine systems, an almost everywhere continuous stabilizing impulsive feedback control law exists for such ...
Read More
Control Mechanism for Software Pipelining on Nested Loop
APDC '97: Proceedings of the 1997 Advances in Parallel and Distributed Computing Conference (APDC '97)

ILSP (Interlaced inner and outer Loop Software Pipelining) is an efficient algorithm of optimizing operations in the nested loops. To ensure the ILSP has a good time efficiency and a good space efficiency, there must be an efficient nested control ...
Read More
Modeling and analysis of software development management as closed loop control
ICSSP '12: Proceedings of the International Conference on Software and System Process

Managed software development organizations are de facto closed loop systems, in which management actions influence future behavior based on observations of previous behavior thus forming a closed feedback loop. It is well known from control theory that ...
Read More

Comments

Information & Contributors

Information

Published In

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 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]

Sponsors

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

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 14 April 2015

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Funding Sources

ANR
ARO
NSF

Conference

HSCC '15

Sponsor:

IEEE-CSS
SIGBED

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

April 14 - 16, 2015

Washington, Seattle

Acceptance Rates

Overall Acceptance Rate 153 of 373 submissions, 41%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8
Total Citations
View Citations
115
Total Downloads

Downloads (Last 12 months)13
Downloads (Last 6 weeks)1

Other Metrics

View Author Metrics

Citations

Cited By

Guo XZhao JBu L(2024)Poles-based Invariant Generation for Verifying the BIBO Stability of Digital FiltersProceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control10.1145/3641513.3650138(1-12)Online publication date: 14-May-2024
https://dl.acm.org/doi/10.1145/3641513.3650138
Abate ABessa ICordeiro LDavid CKesseli PKroening DPolgreen E(2019)Automated formal synthesis of provably safe digital controllers for continuous plantsActa Informatica10.1007/s00236-019-00359-1Online publication date: 6-Dec-2019
https://doi.org/10.1007/s00236-019-00359-1
Davy GGarion CGaroche PRoux PThirioux X(2018)Preserving Functional Correctness of Cyber-Physical System Controllers: From Model to Code2018 Forum on Specification & Design Languages (FDL)10.1109/FDL.2018.8524044(5-16)Online publication date: Sep-2018
https://doi.org/10.1109/FDL.2018.8524044
Ge NJenn EBreton NFonteneau Y(2018)Integrated formal verification of safety-critical softwareInternational Journal on Software Tools for Technology Transfer (STTT)10.1007/s10009-017-0475-020:4(423-440)Online publication date: 1-Aug-2018
https://dl.acm.org/doi/10.1007/s10009-017-0475-0
Abate ABessa ICattaruzza DCordeiro LDavid CKesseli PKroening DFrehse GMitra S(2017)Sound and Automated Synthesis of Digital Stabilizing Controllers for Continuous PlantsProceedings of the 20th International Conference on Hybrid Systems: Computation and Control10.1145/3049797.3049802(197-206)Online publication date: 13-Apr-2017
https://dl.acm.org/doi/10.1145/3049797.3049802
Abate ABessa ICattaruzza DCordeiro LDavid CKesseli PKroening DPolgreen E(2017)Automated Formal Synthesis of Digital Controllers for State-Space Physical PlantsComputer Aided Verification10.1007/978-3-319-63387-9_23(462-482)Online publication date: 13-Jul-2017
https://doi.org/10.1007/978-3-319-63387-9_23
Wang TGaroche PRoux PJobredeaux RFéron ÉAbate AFainekos G(2016)Formal Analysis of Robustness at Model and Code LevelProceedings of the 19th International Conference on Hybrid Systems: Computation and Control10.1145/2883817.2883824(125-134)Online publication date: 11-Apr-2016
https://dl.acm.org/doi/10.1145/2883817.2883824
Ge NJenn EBreton NFonteneau Y(2016)Formal Verification of a Rover Anti-collision SystemCritical Systems: Formal Methods and Automated Verification10.1007/978-3-319-45943-1_12(171-188)Online publication date: 13-Sep-2016
https://doi.org/10.1007/978-3-319-45943-1_12

View Options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents