Skip to main content
SpringerLink
Log in

Observer-Aided Output Feedback Synthesis as an Optimization Problem

  • LINEAR SYSTEMS
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

An Erratum to this article was published on 01 November 2022

This article has been updated

Abstract

A new approach is proposed for solving the problem of suppressing nonrandom bounded exogenous disturbances in linear control systems using dynamic output feedback. The approach is based on reducing the problem to a matrix optimization problem with the feedback matrix and the observer matrix as the variables. A gradient method for finding dynamic output feedback is written out and justified. A number of examples are considered.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

Change history

Notes

  1. The corresponding result is established by analogy with the proof of Lemma 5 in [15].

REFERENCES

  1. Izmailov, R.N., The “peak” effect in stationary linear systems with scalar inputs and outputs, Autom. Remote Control, 1987, vol. 48, no. 8, pp. 1018–1024.

    Google Scholar 

  2. Polotskii, V.N., On the maximum errors of the asymptotic state identifier, Avtom. Telemekh., 1978, no. 8, pp. 26–32.

  3. Korovin, S.K. and Fomichev, V.V., Nablyudateli sostoyaniya dlya lineinykh sistem s neopredelennost’yu (State Observers for Linear Systems with Uncertainty), Moscow: Fizmatlit, 2007.

    Google Scholar 

  4. Polyak, B.T. and Topunov, M.V., Suppression of bounded exogenous disturbances: output feedback, Autom. Remote Control, 2008, vol. 69, no. 5, pp. 801–818.

    Article  MathSciNet  MATH  Google Scholar 

  5. Boyd, S., El Ghaoui, L., Feron, E., et al., Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994.

    Book  MATH  Google Scholar 

  6. Polyak, B.T., Khlebnikov, M.V., and Shcherbakov, P.S., Upravlenie lineinymi sistemami pri vneshnikh vozmushcheniyakh: Tekhnika lineinykh matrichnykh neravenstv (Control of Linear Systems under Exogenous Disturbances: Technique of Linear Matrix Inequalities), Moscow: LENAND, 2014.

    Google Scholar 

  7. Luenberger, D.G., An introduction to observers, IEEE Trans. Autom. Control, 1971, vol. AC-16, no. 6, pp. 596–620.

    Article  MathSciNet  Google Scholar 

  8. Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of Control Laws Based on Linear Matrix Inequalities), Moscow: Fizmatlit, 2007.

    Google Scholar 

  9. Levine, W. and Athans, M., On the determination of the optimal constant output feedback gains for linear multivariable systems, IEEE Trans. Autom. Control, 1970, vol. 15, no. 1, pp. 44–48.

    Article  MathSciNet  Google Scholar 

  10. Fazel, M., Ge, R., Kakade, S., and Mesbahi, M., Global convergence of policy gradient methods for the linear quadratic regulator, Proc. 35th Int. Conf. Mach. Learn. (Stockholm, Sweden, July 10–15), 2018, vol. 80, pp. 1467–1476.

  11. Mohammadi, H., Zare, A., Soltanolkotabi, M., and Jovanović, M.R., Global exponential convergence of gradient methods over the nonconvex landscape of the linear quadratic regulator, Proc. 2019 IEEE 58th Conf. Decision Control (Nice, France, December 11–13, 2019), pp. 7474–7479.

  12. Zhang, K., Hu, B., and Baar, T., Policy optimization for \( \mathcal H_2 \) linear control with \( \mathcal H_{\infty } \) robustness guarantee: implicit regularization and global convergence, 2020. .

  13. Bu, J., Mesbahi, A., Fazel, M., and Mesbahi, M., LQR through the lens of first order methods: discrete-time case, 2019. .

  14. Fatkhullin, I. and Polyak, B., Optimizing static linear feedback: gradient method, SIAM J. Control Optim., 2021, vol. 59, no. 5, pp. 3887–3911.

    Article  MathSciNet  MATH  Google Scholar 

  15. Polyak, B.T. and Khlebnikov, M.V., Static controller synthesis for peak-to-peak gain minimization as an optimization problem, Autom. Remote Control, 2021, vol. 82, no. 9, pp. 1530–1553.

    Article  MathSciNet  MATH  Google Scholar 

  16. Polyak, B.T., Khlebnikov, M.V., and Shcherbakov, P.S., Linear matrix inequalities in control systems with uncertainty, Autom. Remote Control, 2021, vol. 82, no. 1, pp. 1–40.

    Article  MathSciNet  MATH  Google Scholar 

  17. Khlebnikov, M.V., Suppression of bounded exogenous disturbances: a linear dynamic output controller, Autom. Remote Control, 2011, vol. 72, no. 4, pp. 699–712.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

This work was supported by the Russian Science Foundation, project no. 21-71-30005.

Author information

Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    B. T. Polyak & M. V. Khlebnikov

  2. Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141701, Russia

    B. T. Polyak & M. V. Khlebnikov

Authors
  1. B. T. Polyak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. V. Khlebnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to B. T. Polyak or M. V. Khlebnikov.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Polyak, B.T., Khlebnikov, M.V. Observer-Aided Output Feedback Synthesis as an Optimization Problem. Autom Remote Control 83, 303–324 (2022). https://doi.org/10.1134/S0005117922030018

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117922030018

Keywords

Search

Navigation