Near Optimal LQR Performance in the Decentralized Setting

In this paper, we consider the use of a linear periodic controller (LPC) for the control of linear time-invariant (LTI) plants in the decentralized setting. If a plant has an unstable decentralized fixed mode (DFM), it is well known that no decentralized LTI controller can stabilize it, let alone pr...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2014-02, Vol.59 (2), p.327-340
Main Authors: Miller, Daniel E., Davison, Edward J.
Format: Article
Language:English
Subjects:
Channel estimation
Context
Decentralized control
decentralized fixed modes (DFMs)
linear periodic control
lQR optimal control
Optimal control
Output feedback
State feedback
Vectors
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Summary:In this paper, we consider the use of a linear periodic controller (LPC) for the control of linear time-invariant (LTI) plants in the decentralized setting. If a plant has an unstable decentralized fixed mode (DFM), it is well known that no decentralized LTI controller can stabilize it, let alone provide good performance. Here we show that, if the plant is centrally controllable and observable and the graph associated with the plant is strongly connected, then even if the plant has an unstable DFM, we can still design a decentralized LPC to provide LQR performance as close to the centralized optimal performance as desired; the proposed controller in each channel consists of a sampler, a zero-order-hold, and a discrete-time linear periodic compensator, which makes it easy to implement.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2013.2281880