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Minimum energy controllers with inequality constraints on output variances
Author(s) -
Hsieh C.,
Skelton R. E.,
Damra F. M.
Publication year - 1989
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660100405
Subject(s) - weighting , constraint (computer aided design) , mathematics , diagonal , norm (philosophy) , mathematical optimization , variance (accounting) , control theory (sociology) , inequality , dual (grammatical number) , linear matrix inequality , energy (signal processing) , control (management) , computer science , statistics , medicine , art , mathematical analysis , geometry , accounting , literature , artificial intelligence , political science , law , business , radiology
Abstract We consider the design of control systems to minimize the input energy subject to output variance inequality constraints. Necessary and sufficient conditions are developed for state feedback, measurement feedback and dynamic controllers. We find that all these problems are equivalent to LQ problems with a diagonal output weighting matrix Q , where Q has some interesting properties which reflect the importance of each constraint. An algorithm which iteratively selects the weight Q is given. Similar results are also derived for the dual problem where input variance inequality constraints are desired. All these results can be applied to the deterministic case with inequality constraints on the L ∞ ,‐norm of the outputs.