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A constrained H ∞ smooth optimization technique
Author(s) -
Fisher M. E.,
Moore J. B.,
Teo K. L.
Publication year - 1990
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.4660110404
Subject(s) - constrained optimization problem , optimization problem , vector optimization , robustness (evolution) , mathematical optimization , constrained optimization , singular value , sequence (biology) , mathematics , transfer function , computer science , range (aeronautics) , optimal control , multi swarm optimization , engineering , eigenvalues and eigenvectors , biochemistry , chemistry , physics , genetics , quantum mechanics , aerospace engineering , biology , electrical engineering , gene
In H ∞ optimal control the cost function is the maximum singular value of a transfer function matrix over a frequency range. The optimization is over all stabilizing controllers. In constrained H ∞ control the controllers typically have a fixed structure, perhaps conveniently parametrized in terms of a parameter vector. Also, there may be functional constraints involving singular values representing, for example, robustness requirements. Such problems are usually cast as non‐smooth optimization problems. In this paper we consider a general class of constrained H ∞ optimization problems and show that these problems can be approximated by a sequence of smooth optimization problems. Thus each of the approximate problems is readily solvable by standard optimization software packages such as those available in the NAG or IMSL library. The proposed approach via smooth optimization is simple in terms of mathematical content, easy to implement and computationally efficient.