Abstract
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.
The paper was supported by the departmental program No RP.I.02, coordinated by the Institute of Automatic Control of the Warsaw Technical University.
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References
Brunovský P. A classification of linear controllable systems. Kybernetika. D.G. Cl. 3, 1970, pp.173–187.
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.
Gessing R. A Transformation for Solving a Singular Linear-Quadratic Problem. Sent to Journal of Optimization Theory and Applications.
Luenberger D.G. Canonical forms for linear multivariable systems. IEEE Trans. Automatic Control. Vol. AC-12, 1967, pp.290–293.
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© 1992 International Federation for Information Processing
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Gessing, R. (1992). A transformation for solving a discrete-time singular LQ problem. In: Davisson, L.D., et al. System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0113269
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DOI: https://doi.org/10.1007/BFb0113269
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