Linear quadratic optimization in feedback control class

  • A. Cheremensky
  • V. Fomin
Part of the Mathematics and Its Applications book series (MAIA, volume 345)


In this chapter, two different methods of investigation of optimal control are developed.The first one is an abstract variant of the Wiener method: it is based on the reduction of the control problem to the problem of the minimization of a quadratic functional on a given subspace of some Hilbert space. The second method is based on the special representation of the performance index. This method rises from the known “frequency” theorems (Kalman- Yakubovich and Kalman-Czege lemmas) and is connected with the special factorization of the weight operator (of the performance index). Due to these methods, an abstract variant of SLQP is investigated.


Optimal Control Problem Performance Index External Disturbance Transfer Operator Admissible Control 
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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • A. Cheremensky
    • 1
  • V. Fomin
    • 2
  1. 1.Institute of MechanicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Department of Mathematics and MechanicsSt Petersburg UniversitySt Petersburg-PetrodvoretzRussia

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