Skip to main content
SpringerLink
Log in

Nonlinear positive normalized models of weakly formalized systems: Control of equilibrium states

  • Control Sciences
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

This paper considers the existence and control of equilibrium (asymptotically stable) states in nonlinear positive normalized models (PNMs) functioning in the positive unit cube K in the space R n. The representation of a PNM as a functional graph is discussed. The author introduces the notion of admissible control as a control action whose coordinates belong to the interval [0, 1], as well as establishes the convexity of the set of equilibrium states induced by admissible control actions. For PNMs with independent control and PNMs with linear state-feedback control, the model transition problem from an arbitrary initial state to a given equilibrium state is solved and the probability of such transition is defined. And finally, a numerical example illustrates all stages of the corresponding procedures.

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

Similar content being viewed by others

References

  1. McLukas, A.Ch., Improving Causal Mapping Practice Using the System Dynamics “Front-End” Tool, Proc. System Dynamics 2002, Int. System Dynamics Conf., Palermo, Italy, August 2002.

    Google Scholar 

  2. Vasil’ev, V.I. and Il’yasov, B.G., Intellektual’nye sistemy upravleniya. Teoriya i praktika (IntellectualSystems of Control: Theory and Practice), Moscow: Radiotekhnika, 2009.

    Google Scholar 

  3. Kornoushenko, E.K., Linear Approach to Steady-State Control Problem for Nonlinear Normalized Models, Probl. Upravlen., 2011, no. 2, pp. 16–22.

    Google Scholar 

  4. Kornoushenko, E.K., Control of Equilibrium States of Normalized Bilinear Models, Probl. Upravlen., 2012, no. 5, pp. 2–8.

    Google Scholar 

  5. Sinergetika i problemy upravleniya (Synergetics and Control Theory Problems), Kolesnikov, A.A., Ed., Moscow: Fizmatlit, 2004.

  6. Krasnosel’skii, M.A., Vainikko, G.M., and Zabreiko, P.P., Priblizhennoe reshenie operatornykh uravnenii(Approximate Solution of Operator Equations), Moscow: Nauka, 1969.

    Google Scholar 

  7. Danilov, V.I., Lektsii o nepodvizhnykh tochkakh (Lectures on Fixed Points), Moscow: RESh, 2006.

    Google Scholar 

  8. Kolesnikov, A.A., Theory and Methods of Synergetic Control, in Sinergetika i problemy upravleniya (Synergeticsand Control Theory Problems), Kolesnikov, A.A., Ed., Moscow: Fizmatlit, 2004, pp. 130–171.

Download references

Author information

Authors and Affiliations

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

    E. K. Kornoushenko

Authors
  1. E. K. Kornoushenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. K. Kornoushenko.

Additional information

Original Russian Text © E.K. Kornoushenko, 2014, published in Problemy Upravleniya, 2014, No. 2, pp. 18–25.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kornoushenko, E.K. Nonlinear positive normalized models of weakly formalized systems: Control of equilibrium states. Autom Remote Control 76, 1291–1301 (2015). https://doi.org/10.1134/S0005117915070140

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117915070140

Keywords

Search

Navigation