Design of optimal controllers for spatially invariant systems with finite communication speed

Makan Fardad, Mihailo R. Jovanović

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We consider the problem of designing optimal distributed controllers whose impulse response has limited propagation speed. We introduce a state-space framework in which all spatially invariant systems with this property can be characterized. After establishing the closure of such systems under linear fractional transformations, we formulate the H2 optimal control problem using the model-matching framework. We demonstrate that, even though the optimal control problem is non-convex with respect to some state-space design parameters, a variety of numerical optimization algorithms can be employed to relax the original problem, thereby rendering suboptimal controllers. In particular, for the case in which every subsystem has scalar input disturbance, scalar measurement, and scalar actuation signal, we investigate the application of the SteiglitzMcBride, GaussNewton, and Newton iterative schemes to the optimal distributed controller design problem. We apply this framework to examples previously considered in the literature to demonstrate that, by designing structured controllers with infinite impulse response, superior performance can be achieved compared to finite impulse response structured controllers of the same temporal degree.

Original languageEnglish (US)
Pages (from-to)880-889
Number of pages10
JournalAutomatica
Volume47
Issue number5
DOIs
StatePublished - May 2011

Bibliographical note

Funding Information:
Dr. Jovanović’s research focuses on modeling, dynamics, and control of large-scale and distributed systems. He is a member of IEEE, SIAM, and APS and an Associate Editor of the IEEE Control Systems Society Conference Editorial Board. He received a CAREER Award from the National Science Foundation in 2007, and an Early Career Award from the University of Minnesota Initiative for Renewable Energy and the Environment in 2010.

Keywords

  • Cone causality
  • Finite propagation speed
  • Funnel causality
  • Optimal distributed control
  • Quadratic invariance
  • Spatially invariant systems

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