Synthesis of H2 optimal static structured controllers: Primal and dual formulations

Fu Lin, Makan Fardad, Mihailo R. Jovanovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We consider the design of H2 optimal static structured feedback gains for large-scale interconnected systems. The design of distributed controllers with access to measurements of a small number of the subsystems imposes particular sparsity constraints on the feedback gains. For this nonconvex constrained optimal control problem, we study both the primal and dual formulations to obtain optimality bounds. We exploit the sparsity structure present in large-scale systems by implementing an efficient quasi-Newton algorithm to solve the primal problem. We employ the subgradient method to solve the dual problem and obtain a lower bound for the optimal value of the performance index. Surprisingly, in many problems of practical interest, the upper bounds from solving primal problems and the lower bounds from solving dual problems are almost identical, suggesting the lack of duality gap in these applications and that the globally optimal structured gains have in fact been attained.

Original languageEnglish (US)
Title of host publication2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
Pages340-346
Number of pages7
DOIs
StatePublished - Dec 1 2009
Event2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 - Monticello, IL, United States
Duration: Sep 30 2009Oct 2 2009

Publication series

Name2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009

Other

Other2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
CountryUnited States
CityMonticello, IL
Period9/30/0910/2/09

Keywords

  • Decentralized control
  • Large-scale systems
  • Sparse matrices
  • Static feedback gains
  • Zero duality gap

ASJC Scopus subject areas

  • Computer Science(all)
  • Control and Systems Engineering
  • Communication

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    Lin, F., Fardad, M., & Jovanovic, M. R. (2009). Synthesis of H2 optimal static structured controllers: Primal and dual formulations. In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 (pp. 340-346). [5394784] (2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009). https://doi.org/10.1109/ALLERTON.2009.5394784