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Interconnection-based performance analysis for a class of decentralized controllers

Sojoudi, Somayeh and Aghdam, Amir G. (2010) Interconnection-based performance analysis for a class of decentralized controllers. Automatica, 46 (5). pp. 796-803. ISSN 0005-1098.

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This paper is concerned with decentralized controller design for large-scale interconnected systems of pseudo-hierarchical structure. Given such a system, one can use existing techniques to design a decentralized controller for the reference hierarchical model, obtained by eliminating certain weak interconnections of the original system. Although this indirect controller design is appealing as far as the computational complexity is concerned, it does not necessarily result in satisfactory performance for the original pseudo-hierarchical system. An LQ cost function is defined in order to evaluate the performance discrepancy between the pseudo-hierarchical system and its reference hierarchical model under the designed decentralized controller. A discrete Lyapunov equation is then solved to compute this performance index. However, due to the large-scale nature of the system, this equation cannot be handled efficiently in many real-world systems. Thus, attaining an upper bound on this cost function can be more desirable than finding its exact value, in practice. For this purpose, a novel technique is proposed which only requires solving a simple LMI optimization problem with three variables. The problem is then reduced to a scalar optimization problem, for which an explicit solution is provided. It is also shown that when the original model is exactly hierarchical, then the upper bounds obtained from the LMI and scalar optimization problems will both be equal to zero.

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Additional Information:© 2010 Elsevier Ltd. Received 13 March 2008; revised 7 March 2009; accepted 25 January 2010. Available online 26 March 2010. This work has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). The material in this paper was partially presented at 2008 American Control Conference. This paper was recommended for publication in revised form by Associate Editor Pirooz Vakili under the direction of Editor Berç Rüstem.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Subject Keywords:Decentralized control; Optimization; Matrix inequality
Issue or Number:5
Record Number:CaltechAUTHORS:20100624-083152404
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18787
Deposited By: Tony Diaz
Deposited On:10 Jul 2010 04:27
Last Modified:03 Oct 2019 01:47

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