Augmented lagrangian approach to design of structured optimal state feedback gains

Fu Lin, Makan Fardad, Mihailo R. Jovanovic

Research output: Contribution to journalArticlepeer-review

146 Scopus citations


We consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers. These constraints are in the form of sparsity requirements for the feedback matrix, implying that each controller has access to information from only a limited number of subsystems. The minimizer of this constrained optimal control problem is sought using the augmented Lagrangian method. Notably, this approach does not require a stabilizing structured gain to initialize the optimization algorithm. Motivated by the structure of the necessary conditions for optimality of the augmented Lagrangian, we develop an alternating descent method to determine the structured optimal gain. We also utilize the sensitivity interpretation of the Lagrange multiplier to identify favorable communication architectures for structured optimal design. Examples are provided to illustrate the effectiveness of the developed method.

Original languageEnglish (US)
Article number5893917
Pages (from-to)2923-2929
Number of pages7
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 2011


  • Augmented Lagrangian
  • Optimal distributed design
  • Sparse matrices
  • Structured feedback gains

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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