Skip to main content
SpringerLink
Log in

Analysis of criteria for long-run average in the problem of stochastic linear regulator

  • Stochastic Systems, Queueing Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

The optimality criteria used in the problem of stochastic linear regulator over an infinite time horizon were analyzed. A certain criterion for long-run average and pathwise ergodic were shown to be inefficient with regard for the disturbance factor. Consideration was given to a new criterion of the extended long-run average and its use in the discounted control systems.

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.

Similar content being viewed by others

References

  1. Borkar, V.S., Arapostathis, A., and Ghosh, M.K., Ergodic Control of Diffusion Processes, Cambridge: Cambridge Univ. Press, 2012.

    MATH  Google Scholar 

  2. Belkina, T.A. and Palamarchuk, E.S., On Stochastic Optimality for a Linear Controller with Attenuating Disturbances, Autom. Remote Control, 2013, vol. 74, no. 4, pp. 628–641.

    Article  MathSciNet  MATH  Google Scholar 

  3. Palamarchuk, E.S., Asymptotic Behavior of the Solution to a Linear Stochastic Differential Equation and Almost Sure Optimality for a Controlled Stochastic Process, Comput. Math. Math. Phys., 2014, vol. 54, no. 1, pp. 83–96.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bosley, J.T. and Kelly, W.C., Discrete Controller Design for Gaussian and Waveform-type Disturbances, J. Guidance, Control, Dynamics, 1984, vol. 7, no. 4, pp. 483–489.

    Article  Google Scholar 

  5. Pittelkau, M.E., Optimal Periodic Control for Spacecraft Pointing and Attitude Determination, J. Guidance, Control, Dynamics, 1993, vol. 16, no. 6, pp. 1078–1084.

    Article  MATH  Google Scholar 

  6. Charalambous, C.D., Farhadi, A., and Denic, S.Z., Control of Continuous-time Linear Gaussian Systems over Additive Gaussian Wireless Fading Channels. A Separation Principle, IEEE Trans. Automat. Control, 2008, vol. 53, no. 4, pp. 1013–1019.

    Article  MathSciNet  Google Scholar 

  7. Liu, X., Dynamics of Discrete-time Linear Systems with Decaying Disturbances, in 26th Chinese Control and Decision Conf. (2014 CCDC), Changsha, 2014, pp. 55–60.

    Chapter  Google Scholar 

  8. Ma, C., Zhang, X., Xie, S., et al., Active Linear Quadratic Gaussian Control of the Vibration of a Flexible Beam with a Time-varying Mass, in Proc. Inst. Mechanical Engin., Part I, J.Syst. Control, 2015, vol. 229, no. 6, pp. 475–484.

    Google Scholar 

  9. Broderick, T., Wong-Lin, K.F., and Holmes, P., Closed-form Approximations of First-passage Distributions for a Stochastic Decision-making Model, Appl. Math. Res. EXpress, 2009, no. 2, pp. 123–141.

    MathSciNet  MATH  Google Scholar 

  10. Wang, S.G., Linear Quadratic Gaussian-alpha Control with Relative Stability and Gain Parameter for the Structural Benchmark Problems, J. Eng. Mech., 2004, vol. 130, no. 4, pp. 511–517.

    Article  Google Scholar 

  11. Palamarchuk, E.S., Stabilization of Linear Stochastic Systems with a Discount. Modeling and Estimation of the Long-run Effects from the Application of Optimal Control Strategies, Math. Models Comput. Simul., 2015, vol. 7, no. 4, pp. 381–388.

    Article  MathSciNet  Google Scholar 

  12. Turnovsky, S.J., Macroeconomic Analysis and Stabilization Policy, Cambridge: Cambridge Univ. Press, 1977.

    MATH  Google Scholar 

  13. Ichikawa, A. and Katayama, H., Linear Time Varying Systems and Sampled-data Systems, London: Springer, 2001.

    MATH  Google Scholar 

  14. Mueller, M. and Cantoni, M., Normalized Coprime Representations for Time-varying Linear System, in Proc. 49th IEEE Conf. on Decision and Control, New York, 2010, pp. 7718–7723.

    Google Scholar 

  15. Willems, J.L. and Callier, F.M., The Infinite Horizon and the Receding Horizon LQ-Problems with Partial Stabilization Constraints, in The Riccati Equation, Berlin: Springer, 1991, pp. 243–262.

    Chapter  Google Scholar 

  16. Kwakernaak, H. and Sivan, R., Linear Optimal Control Systems, New York: Wiley, 1972. Translated under the title Lineinye optimal’nye sistemy upravleniya, Moscow: Mir, 1977.

    MATH  Google Scholar 

  17. Palamarchuk, E.S., Probabilistic Optimality Criteria in Linear Controllable Systems, in Proc. XII VSPU 2014, Moscow, 2014, pp. 1193–1202.

    Google Scholar 

  18. Dragan, V., Morozan, T., and Stoica, A.-M., Mathematical Methods in Robust Control of Linear Stochastic Systems, New York: Springer, 2006.

    MATH  Google Scholar 

  19. Adrianova, L.V., Vvedenie v teoriyu lineinykh sistem differentsial’nykh uravnenii (Introduction to the Theory of Linear Systems of Differential Equations), St. Petersburg: S.-Peterburg. Gos. Univ., 1992.

    Google Scholar 

  20. Kohlmann, M. and Tang, S., Multidimensional Backward Stochastic Riccati Equations and Applications, SIAM J. Control Optim., 2003, vol. 41, no. 6, pp. 1696–1721.

    Article  MathSciNet  MATH  Google Scholar 

  21. Palamarchuk, E.S., Estimation of Risk in the Linear Economic Systems under Negative Time Preferences, Ekon. Mat. Metod., 2013, vol. 49, no. 3, pp. 99–116.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia

    E. S. Palamarchuk

  2. National Research University Higher School of Economics, Moscow, Russia

    E. S. Palamarchuk

Authors
  1. E. S. Palamarchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. S. Palamarchuk.

Additional information

Original Russian Text © E.S. Palamarchuk, 2016, published in Avtomatika i Telemekhanika, 2016, No. 10, pp. 78–92.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Palamarchuk, E.S. Analysis of criteria for long-run average in the problem of stochastic linear regulator. Autom Remote Control 77, 1756–1767 (2016). https://doi.org/10.1134/S0005117916100039

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117916100039

Search

Navigation