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A cost‐effective sparse communication strategy for networked linear control systems: an SVD‐based approach
Author(s) -
Kong He,
Goodwin Graham C.,
Seron Maria M.
Publication year - 2014
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3188
Subject(s) - telecommunications link , orthonormal basis , computer science , control theory (sociology) , base station , mathematical optimization , singular value decomposition , controller (irrigation) , actuator , basis function , basis (linear algebra) , control (management) , mathematics , algorithm , computer network , artificial intelligence , mathematical analysis , physics , geometry , quantum mechanics , agronomy , biology
Summary In networked control, there is often an incentive to communicate only what is absolutely necessary to achieve the desired performance goals. This is true to both the downlink (between a control base station and actuators) and the uplink (between the sensors and base station). Here, we present a strategy aimed at this problem based on a singular value decomposition of the Hessian of the quadratic performance index generally considered in Model Predictive Control. The singular vectors are employed to generate an orthonormal basis function expansion of the unconstrained solution to the finite horizon optimal control problem. These are preloaded into each actuator and each sensor. On the downlink, the actuators are informed, in real‐time, about which basis functions they should use. On the uplink, after a ‘burn in period’, the sensors need only communicate when their response departs from that pre‐calculated for the given basis functions. We show that this strategy facilitates communication in both the downlink and uplink in a cost‐effective fashion. We also show that the strategy can be modified so that input constraints are satisfied. We illustrate the proposed results by applying them to a simulation of the cross direction control of a paper machine. Potential extensions and other applications of the proposed strategy are also discussed. Copyright © 2014 John Wiley & Sons, Ltd.