A geometrical formulation of the μ-lower bound problem

Access Full Text

A geometrical formulation of the μ-lower bound problem

For access to this article, please select a purchase option:

Buy article PDF
£12.50
(plus tax if applicable)
Add to cart
Buy Knowledge Pack
10 articles for £75.00
(plus taxes if applicable)
Add to cart

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Learn more about IET membership 

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Your details
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:
 
 
 
 
 
IET Control Theory & Applications — Recommend this title to your library

Thank you

Your recommendation has been sent to your librarian.

© The Institution of Engineering and Technology
Published

A new problem formulation for the structured singular value μ in the case of purely real (possibly repeated) uncertainties is presented. The approach is based on a geometrical interpretation of the singularity constraint arising in the μ lower bound problem. An interesting feature of this problem formulation is that the resulting parametric search space is independent of the number of times any parameter is repeated in the structured uncertainty matrix. A corresponding lower bound algorithm combining randomisation and optimisation methods is developed, and some probabilistic performance guarantees are derived. The potential usefulness of the proposed approach is demonstrated on two high-order real μ analysis problems from the aerospace and systems biology literature.

Inspec keywords: control system analysis; optimisation; random processes

Other keywords: μ-lower bound problem; probabilistic performance; randomisation method; parametric search space; optimisation method; geometrical formulation; singularity constraint

Subjects: Control system analysis and synthesis methods; Optimisation techniques; Other topics in statistics

References

    1. 1)
      • G. Ferreres , J.M. Biannic . (2003) Skew mu toolbox: a presentation.
    2. 2)
      • R. Tempo , G. Calfiore , F. Dabbene . (2005) Randomized algorithms for analysis and control of uncertain systems.
    3. 3)
      • M. Fu , S. Dasgupta . Computational complexity of real structured singular value in lp setting. IEEE Trans. Autom. Control , 11 , 2173 - 2176
    4. 4)
      • L. Ma , P.A. Iglesias . Quantifying robustness of biochemical network models. BMC Bioinform. , 38
    5. 5)
      • G. Ferreres , J.M. Biannic . Reliable computation of the robustness margin for a flexible aircraft. Control Eng. Pract. , 1267 - 1278
    6. 6)
      • R.L. Dailey . (1990) A new algorithm for the real structured singular value, Proc. Am. Control Conf..
    7. 7)
      • M. Fu . The real structured singular value is hardly approximable. IEEE Trans. Autom. Control , 9 , 1286 - 1288
    8. 8)
      • H. Chernoff . A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Stat. , 4 , 493 - 507
    9. 9)
      • G.J. Balas , J.C. Doyle , K. Glover , A. Packard , R. Smith . (2001) µ-Analysis and synthesis toolbox: for use with MATLAB, User's Guide, Version 3.
    10. 10)
      • Kim, J., Bates, D.G., Postlethwaite, I., Lan, M., Iglesias, P.A.: `Robustness analysis of biochemical networks using µ-analysis and hybrid optimisation', Proc. Joint 44th Conf. Decision and Control and European Control Conf., Dec 2005, Seville, Spain.
    11. 11)
      • M.T. Laub , W.F. Loomis . A molecular network that produces spontaneous oscillations in excitable cells of dictyostelium. Mol. Biol. Cell. , 3521 - 3532
    12. 12)
      • G. Ferreres . (1999) A practical approach to robustness analysis with aeronautical applications.
    13. 13)
      • S. Skogestad , I. Postlethwaite . (1996) Multivariable feedback control: analysis and design.
    14. 14)
      • (2004) MATLAB function reference.
    15. 15)
      • (2003) Optimization toolbox (Version 2) for use with MATLAB.
    16. 16)
      • Young, P., Newlin, M., Doyle, J.C.: `Practical computation of the mixed µ problem', Proc. Am. Control Conf., Jun 1992.
    17. 17)
      • C. Fielding , A. Varga , S. Bennani , M. Selier . (2002) Advanced techniques for clearance of flight control laws.
    18. 18)
      • S.L. Gatley , D.G. Bates , M.J. Hayes , I. Postlethwaite . Robustness analysis of an integrated flight and propulsion control system using µ and the ν-gap metric. Control Eng. Pract. , 3 , 261 - 275
    19. 19)
      • M.J. Hayes , D.G. Bates , I. Postlethwaite . New tools for computing tight bounds on the real structured singular value. J. Guidance Control Dyn. , 6 , 1204 - 1213
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2007.0391
Loading

Related content

content/journals/10.1049/iet-cta.2007.0391
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading