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Automation and Remote Control

, Volume 78, Issue 6, pp 1006–1027 | Cite as

Design of optimal strategies in the problems of discrete system control by the probabilistic criterion

  • V. M. Azanov
  • Yu. S. Kan
Stochastic Systems

Abstract

A modification was proposed for the relations of the method of dynamic programming in the problems of optimal stochastic control of the discrete systems by the probabilistic performance criterion. It enabled one to simplify the process of finding the optimal Markov strategy and obtain a suboptimal solution. Its efficiency was verified by the examples of maneuver optimization of the stationary satellite in the neighborhood of a geostationary orbit. An explicit form of the optimal control for the bilinear system with probabilistic terminal criterion was determined using the results obtained.

Keywords

stochastic optimal control probabilistic criterion discrete systems method of dynamic programming 

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References

  1. 1.
    Malyshev, V.V. and Kibzun, A.I., Analiz i sintez vysokotochnogo upravleniya letatel’nymi apparatami (Analysis and Design of High-precision Control of Flight Vehicles), Moscow: Mashinostroenie, 1987.Google Scholar
  2. 2.
    Jasour, A.M., Aybat, N.S., and Lagoa, C.M, Semidefinite Programming for Chance Constrained Optimization Over Semialgebraic Sets, SIAM J. Optim., 2015, vol. 25, no. 3, pp. 1411–1440.MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Jasour, A.M. and Lagoa, C.M., Convex Chance Constrained Model Predictive Control, arXiv preprint arXiv:1603.07413, 2016.CrossRefGoogle Scholar
  4. 4.
    Jasour, A.M. and Lagoa, C.M, Convex Relaxations of a Probabilistically Robust Control Design Problem, in 52nd IEEE Conf. on Decision and Control, 2013, pp. 1892–1897.CrossRefGoogle Scholar
  5. 5.
    Zubov, V.I., Lektsii po teorii upravleniya (Lectures on Control Theory), Moscow: Nauka, 1975.MATHGoogle Scholar
  6. 6.
    Afanas’ev, V.N., Kolmanovskii, V.B., and Nosov V.R., Matematicheskaya teoriya konstruirovaniya sistem upravleniya (Mathematical Theory of Control System Design), Moscow: Vysshaya Shkola, 2003.Google Scholar
  7. 7.
    Krasovskii, N.N, On Optimal Control under Random Perturbations, Prikl. Mat. Mekh., 1960, vol. 24, no. 1, pp. 64–79.Google Scholar
  8. 8.
    Kan, Yu.S. and Kibzun, A.I., Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami (Problems of Stochastic Programming with Probabilistic Criteria), Moscow: Fizmatlit, 2009.MATHGoogle Scholar
  9. 9.
    Krasil’shchikov, M.N., Malyshev, V.V., and Fedorov, A.V, Autonomous Realization of Dynamic Operations on the Geostationary Orbit. I, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2015, no. 6, pp. 82–95.Google Scholar
  10. 10.
    Malyshev, V.V., Starkov, A.V., and Fedorov, A.V, Design of Optimal Control at Solving the Problem of Keeping Spacecraft in the Orbital Grouping, Kosmonavt. Raketostr., 2012, no. 4, pp. 150–158.Google Scholar
  11. 11.
    Malyshev, V.V., Starkov, A.V., and Fedorov A.V, Superposition of the Problems of Keeping and Deviation in the Neighborhood of the Reference Geostationary Orbit, Vestn. Mosk. Gor. Ped. Univ., Ser. Ekon., 2013, no. 1, pp. 68–74.Google Scholar
  12. 12.
    Azanov, V.M. and Kan, Yu.S., Optimization of Correction of the Near-circle Orbit of Artificial Earth Satellite by the Probabilistic Criterion, Tr. Inst. Sist. Anal. Ross. Akad. Nauk, 2015, no. 2, pp. 18–26.Google Scholar
  13. 13.
    Azanov, V.M. and Kan, Yu.S., One-parameter Problem of Optimal Correction of the Flight Vehicle Trajectory by the Probability Criterion, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2016, no. 2, pp. 1–13.Google Scholar
  14. 14.
    Azanov, V.M, Optimal Control for Linear Discrete Systems with Respect to Probabilistic Criteria, Autom. Remote Control, 2014, vol. 75, no. 10, pp. 1743–1753.MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Malyshev, V.V, Optimal Discrete Control of the Final State of a Linear Stochastic System, Autom. Remote Control, 1967, vol. 28, no. 5, pp. 746–752.Google Scholar
  16. 16.
    Malyshev, V.V., Krasil’shchikov, M.N., Bobronnikov, V.T., et al., Sputnikovye sistemy monitoringa (Satellite Monitoring Systems), Moscow: Mosk. Aviats. Inst., 2000.Google Scholar
  17. 17.
    Yaroshevskii, V.A. and Petukhov, S.V, Optimal One-parameter Correction of Spececraft Trajectories, Kosm. Issled., 1970, vol. 8, no. 4, pp. 515–525.Google Scholar
  18. 18.
    Yaroshevskii, V.A. and Parysheva, G.V, Optimal Distribution of Correcting Pulses under Oneparametric Correction, Kosm. Issled., 1966, vol. 4, no. 1, pp. 3–16.Google Scholar
  19. 19.
    Kan, Yu.S., On Substantiation of the Principle of Uniformity in the Problem of Optimization of the Probabilistic Performance, Autom. Remote Control, 2000, vol. 61, no. 1, pp. 50–64.MathSciNetMATHGoogle Scholar
  20. 20.
    Barmish, B.R. and Lagoa, C.M, The Uniform Distribution: A Rigorous Justification for Its Use in Robustness Analysis, Math. Control, Signals, Syst., 1997, vol. 10, pp. 203–222.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Moscow State Aviation InstituteMoscowRussia

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