A transformation for solving a discrete-time singular LQ problem

  • R. Gessing
I Optimality And Duality
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


A Linear-Quadratic (LQ) discrete-time problem with singular weighting matrix of the controls in the performance index is considered. The transformation of the state is proposed for solving the considered problem. The transformation gives the converted state equations having, partially the Luenberger-Brunovský controllable canonical form. Using this form the transformed nonsingular LQ problem with inconstant dimensions of state and control is constructed.


Optimal control discrete-time systems canonical forms singular problems 


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    Brunovský P. A classification of linear controllable systems. Kybernetika. D.G. Cl. 3, 1970, pp.173–187.Google Scholar
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    Clements A.E., Anderson B.D.O. Singular Optimal Control; The Linear-Quadratic Problem. Lectures Notes in Control and Information Sciences 5, Springer Verlag 1978.Google Scholar
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    Gessing R. A Transformation for Solving a Singular Linear-Quadratic Problem. Sent to Journal of Optimization Theory and Applications.Google Scholar
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    Luenberger D.G. Canonical forms for linear multivariable systems. IEEE Trans. Automatic Control. Vol. AC-12, 1967, pp.290–293.CrossRefMathSciNetGoogle Scholar

Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • R. Gessing
    • 1
  1. 1.Institute of Automatic ControlSilesian Technical UniversityGliwicePoland

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