Optimal H2/ℓ1 control: the SISO case

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Abstract

In this paper we consider the problem of minimizing the H2-norm of the closed loop map while maintaining its ℓ1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed loop maps. Utilizing duality theory, it is shown that the optimal solution is unique and has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the ℓ1-constraint are established.

Original languageEnglish (US)
Pages (from-to)3181-3186
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume4
StatePublished - 1994

ASJC Scopus subject areas

  • Chemical Health and Safety
  • Control and Systems Engineering
  • Safety, Risk, Reliability and Quality

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