Dual Problem in Multi-Objective Hp Control

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Abstract

In this paper, we approach a multi­objective Hp prob­
lem with several Hp constraints from the Banach
duality point of view. The problem is reduced to an
abstract norm minimization problem, and the dual
problem is derived using the classical Banach re­
sult. It completes the primal­dual pair which can
be used to solve the problem numerically by nite­
dimensional approximations. While the approxima­
tion of the primal problem gives an upper bound
of the optimal value, the approximation of the dual
problem provides a lower bound, and the gap be­
tween them can be done arbitrary small. In view of
growing computational power of modern computers,
it gives a good alternative to the standard mixed­
objective approach.
Original languageEnglish
Publication statusPublished - 2001

Subject classification (UKÄ)

  • Control Engineering

Free keywords

  • multiple objectives
  • convex duality
  • linear system

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