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Linear Parameter-Varying Subspace Identification A Unified Framework

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Document pages: 16 pages

Abstract: In this paper, we establish a unified framework for subspace identification(SID) of linear parameter-varying (LPV) systems to estimate LPV state-space(SS) models in innovation form. This framework enables us to derive novel LPVSID schemes that are extensions of existing linear time-invariant (LTI)methods. More specifically, we derive the open-loop, closed-loop, andpredictor-based data-equations, an input-output surrogate form of the SSrepresentation, by systematically establishing an LPV subspace identificationtheory. We show the additional challenges of the LPV setting compared to theLTI case. Based on the data-equations, several methods are proposed to estimateLPV-SS models based on a maximum-likelihood or a realization based argument.Furthermore, the established theoretical framework for the LPV subspaceidentification problem allows us to lower the number of to-be-estimatedparameters and to overcome dimensionality problems of the involved matrices,leading to a decrease in the computational complexity of LPV SIDs in general.To the authors knowledge, this paper is the first in-depth examination of theLPV subspace identification problem. The effectiveness of the proposed subspaceidentification methods are demonstrated and compared with existing methods in aMonte Carlo study of identifying a benchmark MIMO LPV system.

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