Algorithm of Real-Time Minimization of Control Norm for Incompletely Determined Linear Control Systems

  • Olga Ivanovna Kostyukova
Conference paper
Part of the International Series of Numerical Mathematics book series (ISNM, volume 124)


As a rule, a real control system acts in presence of some indeterminacy (it may be an unknown disturbance or another kind of indeterminacy). The classical control method for such system is using the control of feedback type. In the first papers on optimal control synthesis, it was supposed that the current system state is known exactly at every current moment. In this case, the optimal feedback with respect to the system state was constructed. Later on, the more complicated practical situations were investigated. Now it is assumed, that the available information about control system behaviour consists of incomplete and inexact measurements of system states. In this connection, the problem of constructing the optimal feedback with respect to such incomplete and inexact measurements arises. This problem is complex. It includes the observation problem and control problem connected with each other.

In this paper such a complex problem of linear dynamic system optimization is investigated. The Mathematical model of this problem is considered to be known exactly but the initial state and errors of measuring device (sensor) are supposed to be unknown.

The finite algorithm of constructing the program control for some incompletely determined linear system was suggested in [1]. The aim of this paper is to develop the results [1,2] to feedback control.


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  1. [1]
    Gabasov, R.; Kirillova, F. M.: Finite Algorithm of Constructing Program Control for Incompletely Determined Linear Optimal Control Problem. Automation and Remote Control, #7, 1991.Google Scholar
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    Gabasov, R.; Kirillova, F. M.; Kostyukova, O. I.: Construction of Optimal Controls of Feedback Type in a Linear Problem. Soviet Math. Dokl. vol. 44, #2, 1992.Google Scholar
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    Gabasov, R.; Kirillova, F. M.; Kostyukova, O. I.: Optimization Controls of a Linear Control System under Real-Time Conditions. J. Comput. Syst. Sci. 31, #4, 1993.Google Scholar
  4. [4]
    Gabasov, R.; Kirillova, F. M.; Kostyukova, O. I.: Optimal Positional Observation of Linear System. Doklady RAN, vol. 339, #4, 1994.Google Scholar
  5. [5]
    Kostyukova, O. I.: Researching of the Set of Optimal Control Problems Depended on Parameters. Submitted to J. Differential Equations.Google Scholar

Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Olga Ivanovna Kostyukova
    • 1
  1. 1.Institute of MathematicsAcademy of SciencesMinskBelarus

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