Skip to main content
Log in

Numerical Procedures for Anisotropic Analysis of Time-Invariant Systems and Synthesis of Suboptimal Anisotropic Controllers and Filters

  • Topical Issue
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This paper briefly considers solutions of primary statements of problem of anisotropic analysis of time-invariant systems and problems of synthesis of suboptimal and γ-optimal anisotropic controllers and filters for the time-invariant systems. Numerical procedures for finding the respective solutions are described. To demonstrate the efficiency of the proposed algorithms, illustrative numerical examples are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Semyonov, A.V., Vladimirov, I.G., and Kurdjukov, A.P., Stochastic Approach to H -Optimization, Proc. 33rd IEEE Conf. Decision Control, Florida, USA, 1994, pp. 2249–2250.

    Google Scholar 

  2. Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., Anisotropy of Signals and Entropy of Linear Stationary Systems, Dokl. Math., 1995, vol. 74, no. 3, pp. 388–390.

    Google Scholar 

  3. Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., On Computing the Anisotropic Norm of Linear Discrete-Time-Invariant Systems, Proc. 13th IFAC World Congr., San-Francisco, California, USA, 1996, pp. 179–184.

    Google Scholar 

  4. Vladimirov, I.G., Kurdyukov, A.P., and Semyonov, A.V., The Stochastic Problem of H Optimization, Dokl. Math., 1995, vol. 52, pp. 155–157.

    MATH  Google Scholar 

  5. Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., State-Space Solution to Anisotropy-Based Stochastic H -Optimization Problem, Proc. 13th IFAC World Congr., San-Francisco, USA, 1996, pp. 427–432.

    Google Scholar 

  6. Diamond, P., Kurdjukov, A.P., Semyonov, A.V., and Vladimirov, I.G., Homotopy Methods and Anisotropy-based Stochastic H -Optimization of Control Systems, CADSMAP Research Report 97-14, The University of Queensland, Australia, 1997, pp. 1–22.

    Google Scholar 

  7. Vladimirov, I.G., Kurdyukov, A.P., Maximov, E.A., and Timin, V.N., Anizotropiinaya teoriya upravleniya— novyi podkhod k stokhasticheskomu robastnomu upravleniyu (Anisotropic Control Theory as a New Approach to Robust Stochastic Control), Trudy IV konferentsii “Identifikatsiya sistem i zadachi upravleniya” (Proc. IV Conf. “Identification of Systems and Control Problems”), Moscow, Russia, 2005, pp. 9–32.

    Google Scholar 

  8. Vladimirov, I.G., Diamond, F., and Kloeden, P., Anisotropy-Based Robust Performance Analysis of Finite Horizon Linear Discrete Time Varying Systems, Autom. Remote Control, 2006, vol. 67, no. 8, pp. 1265–1282.

    Article  MathSciNet  MATH  Google Scholar 

  9. Diamond, P., Vladimirov, I.G., Kurdyukov, A.P., and Semyonov, A.V., Anisotropy-Based Performance Analysis of Linear Discrete Time Invariant Control Systems, Int. J. Control, 2001, no. 74, pp. 28–42.

    Article  MathSciNet  MATH  Google Scholar 

  10. Tchaikovsky, M.M., Kurdyukov, A.P., and Timin, V.N., Strict Anisotropic Norm Bounded Real Lemma in Terms of Inequalities, Prep. 18th IFAC World Congr., Milano, Italy, 2011, pp. 2332–2337.

    Google Scholar 

  11. Tchaikovsky, M.M. and Kurdyukov, A.P., Strict Anisotropic Norm Bounded Real Lemma in Terms of Matrix Inequalities, Dokl. Math., 2011, vol. 84, no. 3, pp. 895–898.

    Article  MathSciNet  MATH  Google Scholar 

  12. Tchaikovsky, M.M., Static Output Feedback Anisotropic Controller Design by LMI-based Approach: General and Special Cases, Proc. 2012 Am. Control Conf., Montreal, Canada, 2012, pp. 5208–5213.

    Google Scholar 

  13. Tchaikovsky, M.M., Multichannel Synthesis Problems for Anisotropic Control, Autom. Remote Control, 2016, vol. 77, no. 8, pp. 1351–1369.

    Article  MathSciNet  MATH  Google Scholar 

  14. Vladimirov, I.G., Anisotropy-based Optimal Filtering in Linear Discrete Time Invariant Systems, CADSMAP Research Report 01-03, The University of Queensland, Australia, 2001.

    Google Scholar 

  15. Timin, V.N., Tchaikovsky, M.M., and Kurdyukov, A.P., A Solution to Anisotropic Suboptimal Filtering Problem by Convex Optimization, Dokl. Math., 2012, vol. 85, no. 3, pp. 443–445.

    Article  MathSciNet  MATH  Google Scholar 

  16. Timin, V.N., Anisotropy-Based Suboptimal Filtering for the Linear Discrete Time Invariant Systems, Autom. Remote Control, 2013, vol. 74, no. 11, pp. 1773–1785.

    Article  MathSciNet  MATH  Google Scholar 

  17. Polyak, B.T., Introduction to Optimization, New York: Optimization Software, 1987.

    MATH  Google Scholar 

  18. Gahinet, P., Explicit Controller Formulas for LMI-based H Synthesis, Automatica, 1996, vol. 32, pp. 1007–1014.

    Article  MathSciNet  MATH  Google Scholar 

  19. Tchaikovsky, M.M., Nikiforov, V.M., Gusev, A.A., and Andreev, K.A., Digital Control of a Gyrostabilized Platform under the Influence of Uncertain Disturbances in the Presence of Measurement Noise, Proc. 23 Saint-Petersburg Int. Conf. Integrated Navigat. Syst., Saint-Petersburg, Russia, 2016, pp. 236–241.

    Google Scholar 

  20. Tchaikovsky, M.M., Kurdyukov, A.P., and Nikiforov, V.M., LMI-based Design of Multichannel Anisotropic Suboptimal Controllers with Application to Control of Gyrostabilized Platform, Proc. 2012 IEEE Multiconf. Syst. Control, Dubrovnik, Croatia, 2012, pp. 1455–1460.

    Google Scholar 

  21. Mariton, M. and Bertrand, R., A Homotopy Algorithm for Solving Coupled Riccati Equations, Optim. Control Appl. Meth., 1985, vol. 6, pp. 351–357.

    Article  MathSciNet  Google Scholar 

  22. Khargonekar, P.P., Rotea, M.A., and Baeyens, E., Mixed H 2/H Filtering, Int. J. Robust Nonlin. Control, 1996, vol. 6, pp. 313–330.

    Article  MATH  Google Scholar 

  23. Timin, V.N. and Kurdyukov, A.P., Mnogokriterial’naya suboptimal’naya anizotropiinaya fil’tratsiya lineinykh diskretnykh statsionarnykh sistem (Multiobjective Suboptimal Anisotropic Filtering of Linear Discrete Time-Invariant Systems), XII Vseross. soveshchanie po problemam upravleniya (XII All-Russian Meeting on Control Problems), Moscow, Russia, 2014, pp. 901–910.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. M. Tchaikovsky.

Additional information

Original Russian Text © M.M. Tchaikovsky, V.N. Timin, A.Yu. Kustov, A.P. Kurdyukov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 1, pp. 162–182.

This paper was recommended for publication by A.I. Kibzun, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tchaikovsky, M.M., Timin, V.N., Kustov, A.Y. et al. Numerical Procedures for Anisotropic Analysis of Time-Invariant Systems and Synthesis of Suboptimal Anisotropic Controllers and Filters. Autom Remote Control 79, 128–144 (2018). https://doi.org/10.1134/S0005117918010113

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117918010113

Keywords

Navigation