On the optimal design of structured feedback gains for interconnected systems

Makan Fardad, Fu Lin, Mihailo R. Jovanović

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

36 Scopus citations

Abstract

We consider the design of optimal static feedback gains for interconnected systems subject to architectural constraints on the distributed controller. These constraints are in the form of sparsity requirements for the feedback matrix, which means that each controller has access to information from only a limited number of subsystems. We derive necessary conditions for the optimality of structured static feedback gains in the form of coupled matrix equations. In general these equations have multiple solutions, each of which is a stationary point of the objective function. For stable open-loop systems, we show that in the limit of expensive control, the optimal controller can be found analytically using perturbation techniques. We use this feedback gain to initialize homotopy-based gradient and Newton iterations that find an optimal solution to the original (non-expensive) control problem. For unstable open-loop systems, the centralized truncated gain is used as an initial estimate for the iterative schemes aimed at finding the optimal structured feedback gain. We consider both spatially invariant and spatially varying problems and illustrate our developments with several examples.

Original languageEnglish (US)
Title of host publicationProceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Pages978-983
Number of pages6
DOIs
StatePublished - Dec 1 2009
Event48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China
Duration: Dec 15 2009Dec 18 2009

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
CountryChina
CityShanghai
Period12/15/0912/18/09

Keywords

  • Architectural constraints
  • Interconnected systems
  • Optimal decentralized control
  • Structured feedback gains

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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