Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

State covariance assignment problem

State covariance assignment 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

Covariance control theory provides a parameterisation of all controllers which assign a specified state covariance matrix to the closed-loop system according to different requirements on system performance. In this study, an innovative scheme for covariance system description based on the original linear stochastic system is proposed. The main idea of the proposed scheme is based on a special rearrangement of the corresponding covariance matrix Riccati equation to a new linear deterministic state space system. The variances of the states and cross-covariance between each two states of the original system would be the states of the new covariance system. By some mathematical manipulations, the covariance assignment problem is reformulated as a standard disturbance rejection problem. Since the new covariance system is linear and deterministic, all conventional and well-defined control strategies can be applied on it. Results are presented by a covariance feedback control law based on an integral control action applied to the new covariance system. The control law causes a stable closed-loop system and assigns a pre-specified state covariance matrix to the states of the closed-loop system.

Inspec keywords: linear systems; state-space methods; stochastic systems; covariance matrices; closed loop systems; stability

Other keywords: Riccati equation; state covariance matrix; integral control; stable system; closed loop system; mathematical manipulations; covariance assignment problem; covariance feedback control law; covariance control theory; disturbance rejection problem; linear stochastic system; state space system

Subjects: Stability in control theory; Control system analysis and synthesis methods; Algebra; Time-varying control systems

References

    1. 1)
      • Delorenzo, M.L., Skelton, R.E.: `Weight selection for variance-constrained LQG regulators with application to the Hoop–Column antenna', Fourth Symp. Dynamics and Control of large Structures, 1983, Blacksburg, VA.
    2. 2)
      • F. Schweppe . (1973) Uncertain dynamic systems.
    3. 3)
      • Kalandros, M., Pao, L.Y.: `Controlling target estimate covariance in centralized multisensor systems', American Control Conf., 1998, Philadelphia, PA.
    4. 4)
      • R. Dorf . (1998) Modern control systems.
    5. 5)
      • A. Hotz , R.E. Skelton . Covariance control theory. Int. J. Control , 1 , 13 - 32
    6. 6)
      • H.Y. Chung , W.J. Chang , M.K. Tsay . On the controller design for perturbed bilinear stochastic systems. JSME Int. J. Ser. , 4 , 559 - 566
    7. 7)
      • C. Hsieh , R.E. Skelton . All covariance controllers for linear discrete-time systems. IEEE Trans. Autom. Control , 8 , 908 - 915
    8. 8)
      • Baromand, S., Khaloozadeh, H.: `Covariance control of linear discrete-time stochastic systems', Control and Automation, ICCA 2007. IEEE Int. Conf., May 2007, p. 2664–2668.
    9. 9)
      • Skelton, R.E., Delorenzo, M.L.: `On selection of weighting matrices in the LQG problem', 20thAnnual Allerton Conf. Circuit and Systems Theory, 1982, Allerton.
    10. 10)
      • Skelton, R.E., Kherat, S.M., Yaz, E.: `Covariance control of discrete stochastic bilinear systems', Proc. ACC, 1991, Boston, MA, p. 2660–2664.
    11. 11)
      • H. Chung , W. Chang . Covariance control with variance constraints for continuous perturbed stochastic systems. Syst. Control Lett. , 5 , 413 - 417
    12. 12)
      • Zbu, G., Corless, M., Skelton, R.E.: `Robustness properties of covariance controllers', Proc. Allerton Conf., 1969, Monticello, p. 877–883.
    13. 13)
      • A. Hotz , R.E. Skelton . Controller design for robust stability and performance. ACC, Seattle , 1813 - 1817
    14. 14)
      • D. Williamson . Round off noise minimization and pole-zero sensitivity in fixed point digital filters using residue feedback. IEEE Trans. F. ASSP , 1013 - 1016
    15. 15)
      • Baromand, S., Khaloozadeh, H.: `Optimal covariance tracking for linear discrete-time stochastic systems', 13thIEEE IFAC Conf. Methods and Models in Automation and Robotics (MMAR07), August 2007, Szczecin, Poland.
    16. 16)
      • R.E. Skelton . (1988) Dynamic system control.
    17. 17)
      • Yaz, E.: `State covariance assignment for discrete time systems with jump Markov parameters', Proc. European Contribution Conf., 1991, Grenoble, France, p. 1147–1151.
    18. 18)
      • J.H. Xu , R.E. Skelton , G. Zhu . Upper and lower covariance bounds for perturbed linear systems. IEEE Trans. Automat Control , 8 , 944 - 948
    19. 19)
      • H. Xu , R.E. Skelton . An improved covariance assignment theory for discrete systems. IEEE Trans. Autom. Control , 10 , 1588 - 1590
    20. 20)
      • E.G. Collins , R.E. Skelton . A theory of state covariance assignment for discrete systems. IEEE Trans. Autom. Control , 1 , 35 - 41
    21. 21)
      • K.M. Grigoriadis , R.E. Skelton . Alternating convex projection methods for covariance control design. Int. J. Control , 6 , 1083 - 1106
    22. 22)
      • C. Harris , X. Hong , Q. Gan . (2002) Adaptive modelling, estimation and fusion from data.
    23. 23)
      • Baromand, S., Khaloozadeh, H., Rajat, M.R.: `Output covariance tracking as a disturbance rejection problem', Proc. 46th IEEE Conf. Decision and Control (CDC 2007), December 2007, New Orleans, USA, p. 3679–3684.
    24. 24)
      • Ohkubo, K., Yagishita, Y., Katayama, T.: `An analysis of quantization errors in digital control systems', Proc. IEEE Int. Conf. (ICTT'96), 1996, China, p. 61–65.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2008.0359
Loading

Related content

content/journals/10.1049/iet-cta.2008.0359
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
Print this page
This is a required field
Please enter a valid email address