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Automation and Remote Control

, Volume 72, Issue 1, pp 74–87 | Cite as

Optimal control based on a preposteriori estimates of set-membership uncertainty

  • R. Gabasov
  • F. M. Kirillova
  • E. I. Poyasok
Stochastic Systems
  • 30 Downloads

Abstract

We consider the optimal control problem for a linear nonstationary dynamical system under set-membership uncertainty with a combined discrete closable loop. Our solution is based on an a preposteriori analysis of the surveillance and control subsystems. Based on the surveillance subsystem analysis, we introduce closures and construct an optimal closable program (a preposteriori analysis of the control subsystem) that yields a positional solution for the optimal control problem. We present an optimal control quasi-realization method with optimal estimators and a real-time controller. We illustrate our results with an example.

Keywords

Remote Control Optimal Control Problem Control Object Optimal Controller Optimal Loop 
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References

  1. 1.
    Fel’dbaum, A.A., Osnovy teorii optimal’nykh avtomaticheskikh sistem (Fundamentals of Optimal Automated Systems Theory), Moscow: Fizmatgiz, 1963.Google Scholar
  2. 2.
    Bellman, R., Adaptive Control Processes: A Guided Tour, Princeton: Princeton Univ. Press, 1961, Translated under the title Protsessy regulirovaniya s adaptatsiei, Moscow: Nauka, 1964.zbMATHGoogle Scholar
  3. 3.
    Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., and Mishchenko, E.F., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Nauka, 1976.Google Scholar
  4. 4.
    Gabasov, R. and Kirillova, F.M., Principles of Optimal Control, Dokl. Belarus. Nat. Akad. Nauk, 2004, vol. 48, no. 1, pp. 15–18.zbMATHMathSciNetGoogle Scholar
  5. 5.
    Gabasov, R., Kirillova, F.M., and Poyasok, E.I., Optimal Preposterior Observation of Dynamic Systems, Autom. Remote Control, 2009, vol. 70, no. 8, pp. 1327–1339.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Gabasov, R., Dmitruk, N.M., and Kirillova, F.M., Optimal Control for Multidimensional Systems Based on Imprecise Measurements of Their Output Signals, Tr. Inst. Mat. Mekh., UrO RAN, 2004, vol. 10, no. 2, pp. 35–57.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • R. Gabasov
    • 1
  • F. M. Kirillova
    • 2
  • E. I. Poyasok
    • 1
  1. 1.Belarussian State UniversityMinskBelarus
  2. 2.Institute of MathematicsBelarussian National Academy of SciencesMinskBelarus

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