Optimal controller synthesis for linear stochastic systems with incomplete information regarding the state. Necessary conditions and numerical methods (original) (raw)

Abstract

Necessary optimality conditions for a linear incomplete feedback controller for stochastic systems operating on an unbounded time interval are proved. Numerical methods for optimal controller synthesis that ensure the system’s stability and cost optimality of stabilization with respect to a given criterion are proposed. The stabilization problem for an orbit of an Earth satellite under disturbances and different compositions of measurements is considered.

Access this article

Log in via an institution

Subscribe and save

Buy Now

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. Letov, A.M., Matematicheskaya teoriya protsessov upravleniya (Mathematical Theory of Control Processes), Moscow: Nauka, 1981.
    Google Scholar
  2. Khrustalev, M.M., Optimal and Stable Controllable Stochastic Systems Synthesis with Incomplete State Information on an Unbounded Time Interval, Autom. Remote Control, 2011, vol. 72, no. 11, pp. 2379–2394.
    Article MATH MathSciNet Google Scholar
  3. Khrustalev, M.M., Nash Equilibrium Conditions in Stochastic Differential Games under Incomplete Information about the State. Lagrange’s Method, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1996, no. 1, pp. 72–79.
    Google Scholar
  4. Pervozvanskii, A.A., Kurs teorii avtomaticheskogo upravleniya (A Course in Automated Control Theory), Moscow: Nauka, 1986.
    Google Scholar
  5. Andreev, Yu.N., Upravlenie konechnomernymi lineinymi ob”ektami (Control over Finite-Dimensional Linear Objects), Moscow: Nauka, 1976.
    Google Scholar
  6. Bortakovskii, A.S and Panteleev, A.V., Lineinaya algebra v primerakh i zadachakh (Linear Algebra in Examples and Problems), Moscow: Vysshaya Shkola, 2005.
    Google Scholar
  7. Abgaryan, K.A., Khrustalev, M.M., and Zhirnova, E.V., Upravlyaemost’ i nablyudaemost’ lineinykh sistem (Controllability and Observability of Linear Systems), Moscow: Mosk. Aviats. Inst., 1977.
    Google Scholar
  8. Kalman, R., Falb, P., and Arbib, M., Topics in Mathematical System Theory, New York: McGraw-Hill, 1969. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: URSS, 2004.
    MATH Google Scholar
  9. Davis, M.H.A., Linear Estimation and Stochastic Control, London: Chapman & Hall, 1977. Translated under the title Lineinoe otsenivanie i stokhasticheskoe upravlenie, Moscow: Nauka, 1984.
    MATH Google Scholar
  10. Rumyantsev, D.S. and Khrustalev, M.M., Optimal Control for Quasilinear Systems of Diffuse Type under Incomplete Information Regarding the State, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2006, no. 5, pp. 43–51.
    Google Scholar

Download references

Author information

Authors and Affiliations

  1. Moscow Aviation Institute (National Research University), Moscow, Russia
    M. M. Khrustalev & A. S. Khalina
  2. Blagonravov Institute of Mechanical Engineering, Russian Academy of Sciences, Moscow, Russia
    M. M. Khrustalev & A. S. Khalina

Authors

  1. M. M. Khrustalev
  2. A. S. Khalina

Corresponding author

Correspondence toM. M. Khrustalev.

Additional information

Original Russian Text © M.M. Khrustalev, A.S. Khalina, 2014, published in Avtomatika i Telemekhanika, 2014, No. 11, pp. 70–87.

Rights and permissions

About this article

Cite this article

Khrustalev, M.M., Khalina, A.S. Optimal controller synthesis for linear stochastic systems with incomplete information regarding the state. Necessary conditions and numerical methods.Autom Remote Control 75, 1948–1963 (2014). https://doi.org/10.1134/S0005117914110058

Download citation

Keywords