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Distributed Design Methods for Linear Quadratic Control and Their Limitations

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2 Author(s)
Langbort, C. ; Dept. of Aerosp. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA ; Delvenne, J.

We introduce the notion of distributed design methods, which construct controllers by accessing a plant's description in a constrained manner. We propose performance and information metrics for these design methods, and investigate the connection between closed-loop performance of the best controller they can produce and the amount of exchanged information about the plant. For a class of linear discrete-time, time invariant plants, we show that any communication-less distributed control method results in controllers whose performance is, at least, twice the optimal in the worst-case. We then give a bound on the minimal amount of exchanged information necessary to beat the best communication-less design strategy. We also show that, in the case of continuous-time plants, the worst-case performance of controllers constructed by communication-less design strategies is unbounded.

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Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 9 )