Linear-quadratic discrete-time control and constant directions

David J. Clements; Brian D.O. Anderson

doi:10.1016/0005-1098(77)90052-8

Linear-quadratic discrete-time control and constant directions

David J. Clements^*, Brian D.O. Anderson

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

The general linear-quadratic discrete-time minimization problem is studied, in which no restrictions are placed on the singularity or otherwise of certain matrices, or the appearance of cross-product terms in the performance indices. Constant directions are characterized in a number of ways, and an algorithm is presented for replacing a prescribed problem with constant directions by one of lower state and/or control dimension, lacking constant directions. The replacement is achieved using a series of state and input co-ordinate basis changes, and allows simplification of the calculations obtaining the optimal control law and performance index of the original problem.

Original language	English
Pages (from-to)	255-264
Number of pages	10
Journal	Automatica
Volume	13
Issue number	3
DOIs	https://doi.org/10.1016/0005-1098(77)90052-8
Publication status	Published - May 1977
Externally published	Yes

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keywords = "(Riccati equations), discrete time systems, Linear systems, optimal control",

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year = "1977",

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AU - Clements, David J.

AU - Anderson, Brian D.O.

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AB - The general linear-quadratic discrete-time minimization problem is studied, in which no restrictions are placed on the singularity or otherwise of certain matrices, or the appearance of cross-product terms in the performance indices. Constant directions are characterized in a number of ways, and an algorithm is presented for replacing a prescribed problem with constant directions by one of lower state and/or control dimension, lacking constant directions. The replacement is achieved using a series of state and input co-ordinate basis changes, and allows simplification of the calculations obtaining the optimal control law and performance index of the original problem.

KW - (Riccati equations)

KW - discrete time systems

KW - Linear systems

KW - optimal control

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DO - 10.1016/0005-1098(77)90052-8

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SN - 0005-1098

VL - 13

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EP - 264

JO - Automatica

JF - Automatica

IS - 3

ER -

Linear-quadratic discrete-time control and constant directions

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