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Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems
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DOI：10.1109/TAC.2014.2370271.png)
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Abstract
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We propose a dissipativity-preserving structured model reduction method for distributed control systems. As a fundamental tool to develop structured model reduction, we first establish dissipativity-preserving model reduction for general linear systems on the basis of a singular perturbation approximation. To this end, by deriving a tractable expression of singular perturbation models, we characterize dissipativity preservation in terms of a projection-like transformation of storage functions, and we show that the resultant approximation error is relevant to the sum of neglected eigenvalues of an index matrix. Next, utilizing this dissipativity-preserving model reduction, we develop a structured controller reduction method for distributed control systems. The major significance of this method is to preserve the spatial distribution of dissipative controllers and to provide an a priori bound for the performance degradation of closed-loop systems in terms of the H-2-norm. The efficiency of the proposed method is verified through a numerical example of vibration suppression control for interconnected second-order systems.
Keywords:
Dissipativity preservation
distributed control systems
singular perturbation approximation
structured model reduction
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