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A numerical solution to the matrix ℋ︁ 2 /ℋ︁ ∞ optimal control problem
Author(s) -
Halikias G. D.,
Jaimoukha I. M.,
Wilson D. A.
Publication year - 1997
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199711)7:7<711::aid-rnc251>3.0.co;2-8
Subject(s) - norm (philosophy) , mathematics , mathematical optimization , linear matrix inequality , convex optimization , constraint (computer aided design) , infinite impulse response , reduction (mathematics) , multivariable calculus , projection (relational algebra) , regular polygon , filter (signal processing) , control theory (sociology) , computer science , algorithm , control (management) , digital filter , engineering , geometry , control engineering , artificial intelligence , political science , law , computer vision
In this paper a numerical solution is obtained to the problem of minimizing an ℋ 2 ‐type cost subject to an ℋ ∞ ‐norm constraint. The method employed is based on the convex alternating projection algorithm and generalizes a recent technique to the multivariable case. The solution is derived in terms of the Markov parameters of an FIR filter of arbitrary length; this is finally approximated by a low‐order IIR filter using Hankel‐norm model‐reduction techniques. The results are illustrated with a numerical example. © 1997 John Wiley & Sons, Ltd.