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Mixed H 2 / H ∞ control with pole placement in a class of regions
Author(s) -
Bambang Riyanto T.,
Shimemura Etsujiro,
Uchida Kenko
Publication year - 1994
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.4660150302
Subject(s) - lagrange multiplier , mathematics , norm (philosophy) , optimization problem , control theory (sociology) , complex plane , lti system theory , constraint (computer aided design) , mathematical optimization , transfer function , constrained optimization , linear system , invariant (physics) , computer science , mathematical analysis , control (management) , geometry , electrical engineering , artificial intelligence , political science , law , mathematical physics , engineering
The problem of mixed H 2 / H ∞ control with pole placement is considered for linear time‐invariant systems. This is the problem of determining a controller for linear time‐invariant systems which minimizes the H 2 ‐norm of a certain closed‐loop transfor function subject to an H ∞ ‐norm constraint on another closed‐loop transfer function and an additional constraint on the location of the closed‐loop poles in the complex plane. An optimization problem is posed for the pole‐constrained H 2 / H ∞ , problem in such a way that the objective function is expressed as a weighted sum of the actual H 2 cost and its upper bound. A necessary condition for the optimization problem is derived via the Lagrange multiplier technique. The condition involves a set of highly coupled equations. By sacrificing the H 2 performance, an alternative optimization problem is posed in order to simplify the necessary condition. An iterative algorithm for solving the coupled equations arising in the necessary conditions is proposed and numerical examples are presented.