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Optimal Continuous Stochastic Control Systems with Incomplete Feedback: Approximate Synthesis

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Abstract

The sufficient ε-optimality conditions for the control of the nonlinear continuous stochastic systems with incomplete feedback were formulated and proved. They enabled one to estimate the precision of approximate control as compared with the value-optimal performance functional. Relations were established to determine the ε-optimal control, and a strategy was worked out to determine its use in minimizing the total mismatch of the resulting relations.

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References

  1. Fleming, W.H., Optimal Control of Partially Observable Diffusions, SIAM J. Control, 1968, vol. 6, no. 2, pp. 194–214.

    Article  MathSciNet  MATH  Google Scholar 

  2. Panteleev, A.V. and Semenov, V.V., Optimal Control of Nonlinear Probabilistic Systems on the Basis of an Incomplete State Vector, Autom. Remote Control, 1984, vol. 45, no. 1, pp. 79–87.

    MathSciNet  MATH  Google Scholar 

  3. Panteleev, A.V., Sufficient Conditions for Optimality of Continuous Stochastic Control Systems on the Basis of an Incomplete State Vector, Soviet Math., 1990, vol. 34, no. 11, pp. 62–75.

    MathSciNet  MATH  Google Scholar 

  4. Savastyuk, S.V. and Khrustalev, M.M., Optimization of Stochastic Diffusion Systems with Constraints on the Control-Observation Process, Autom. Remote Control, 1991, vol. 52, no. 7, pp. 958–963; no. 8, pp. 1109–1114.

    MATH  Google Scholar 

  5. Fleming, W.H. and Soner, H.M., Controlled Markov Processes and Viscosity Solutions, New York: Springer, 2006.

    MATH  Google Scholar 

  6. Wonham, W.M. and Cashman, W.F., A Computational Approach to Optimal Control of Stochastic Saturating Systems, Int. J. Control, 1968, vol. 10, no. 1, pp. 77–98.

    Article  MathSciNet  MATH  Google Scholar 

  7. Bodner, V.A., Rodnishchev, N.E., and Yurikov, E.P., Optimizatsiya terminal’nykh stokhasticheskikh sistem (Optimization of Terminal Stochastic Systems), Moscow: Mashinostroenie, 1987.

    Google Scholar 

  8. Kushner, H.J. and Dupuis, P.G., Numerical Methods for Stochastic Control Problems in Continuous Time, New York: Springer, 2001.

    Book  MATH  Google Scholar 

  9. Bertsekas, D.P., Dynamic Programming and Optimal Control, Cambridge: Athena Scientific, 2013.

    Google Scholar 

  10. Panteleev, A.V., Rybakov, K.A., and Sotskova, I.L., Spektral’nyi metod analiza nelineinykh stokhasticheskikh sistem upravleniya (Spectral Analysis of Nonlinear Stochastic Control Systems), Moscow: Vuzovskaya Kniga, 2015.

    Google Scholar 

  11. Panteleev, A.V. and Rybakov, K.A., Analyzing Nonlinear Stochastic Control Systems in the Class of Generalized Characteristic Functions, Autom. Remote Control, 2011, vol. 72, no. 2, pp. 393–404.

    Article  MathSciNet  MATH  Google Scholar 

  12. Panteleev, A.V. and Rybakov, K.A., Design of Optimal Nonlinear Stochastic Systems by Spectral Method, Informat. Primen., 2011, vol. 5, no. 2, pp. 69–81.

    Google Scholar 

  13. Khrustalev, M.M., The Necessary and Sufficient Conditions in the Form of Bellman Equation, Dokl. Akad. Nauk SSSR, 1978, vol. 242, no. 5, pp. 1023–1026.

    MathSciNet  Google Scholar 

  14. Panteleev, A.V. and Orlovskaya, N.M., Solution of the Problem of Satellite Stabilization by Bioinspired Methods of Optimization, Nauchn. Vestn. MGTU GA, 2015, no. 220 (10), pp. 5–12.

    Google Scholar 

  15. Averbukh, V.I. and Smolyanov, O.G., Theory of Differentiation in Linear Topological Spaces, Russian Math. Surveys, 1967, vol. 22, no. 6 (138), pp. 201–258.

    Article  MATH  Google Scholar 

  16. Rybakov, K.A., Multiparametric Basic Systems for Representation of Functions in Unlimited Domains, Nauchn. Vestn. MGTU GA, 2013, no. 195 (9), pp. 45–50.

    Google Scholar 

  17. Panteleev, A.V., Skavinskaya, D.V., and Aleshina, E.A., Metaevristicheskie algoritmy poiska optimal’nogo programmnogo upravleniya (Metaheuristic Algorithms to Seek the Optimal Program Control), Moscow: INFRA-M, 2016.

    Book  Google Scholar 

  18. Rybakov, K.A., Optimal Control of Stochastic Systems with Random Sampling Period, Tr. MFTI, 2015, vol. 7, no. 1 (25), pp. 145–165.

    MathSciNet  Google Scholar 

  19. Rybakov, K.A. and Sotskova, I.L., An Optimal Control for Random-Structure Nonlinear Systems under Incomplete State Vector Information, Autom. Remote Control, 2006, no. 7, pp. 1070–1081.

    Article  MATH  Google Scholar 

  20. Gurman, V.I., Printsip rasshireniya v zadachakh upravleniya (Principle of Extension in Problems of Control), Moscow: Nauka, 1997.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow Aviation Institute (National State University), Moscow, Russia

    A. V. Panteleev & K. A. Rybakov

Authors
  1. A. V. Panteleev
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  2. K. A. Rybakov
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Correspondence to A. V. Panteleev.

Additional information

Original Russian Text © A.V. Panteleev, K.A. Rybakov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 1, pp. 130–146.

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

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Panteleev, A.V., Rybakov, K.A. Optimal Continuous Stochastic Control Systems with Incomplete Feedback: Approximate Synthesis. Autom Remote Control 79, 103–116 (2018). https://doi.org/10.1134/S0005117918010095

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  • DOI: https://doi.org/10.1134/S0005117918010095

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