Convergence analysis of the alternating RGLS algorithm for the identification of the reduced complexity Volterra model |
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Affiliation: | 1. Electrical Engineering Department, National School of Engineering of Monastir (ENIM), Av Ibn Al Jazzar, Monastir 5019, Tunisia;2. Electrical Engineering Department, High Institute of Applied Science and Technology (ISSAT), Cité Ibn Khaldoun, Sousse 4003, Tunisia;1. College of Mechanical Engineering, Taiyuan University of Technology, Taiyuan, Shanxi 030024, PR China;2. School of Computing and Engineering, University of Huddersfield, Huddersfield HD1 3DH, UK;3. Signal Processing and Algorithms Group, School of Engineering, Manchester Metropolitan University, All Saints Building, All Saints, Manchester M15 6BH, UK;4. College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, Shanxi 030024, PR China |
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Abstract: | In this paper we provide a convergence analysis of the alternating RGLS (Recursive Generalized Least Square) algorithm used for the identification of the reduced complexity Volterra model describing stochastic non-linear systems. The reduced Volterra model used is the 3rd order SVD-PARAFC-Volterra model provided using the Singular Value Decomposition (SVD) and the Parallel Factor (PARAFAC) tensor decomposition of the quadratic and the cubic kernels respectively of the classical Volterra model. The Alternating RGLS (ARGLS) algorithm consists on the execution of the classical RGLS algorithm in alternating way. The ARGLS convergence was proved using the Ordinary Differential Equation (ODE) method. It is noted that the algorithm convergence canno׳t be ensured when the disturbance acting on the system to be identified has specific features. The ARGLS algorithm is tested in simulations on a numerical example by satisfying the determined convergence conditions. To raise the elegies of the proposed algorithm, we proceed to its comparison with the classical Alternating Recursive Least Squares (ARLS) presented in the literature. The comparison has been built on a non-linear satellite channel and a benchmark system CSTR (Continuous Stirred Tank Reactor). Moreover the efficiency of the proposed identification approach is proved on an experimental Communicating Two Tank system (CTTS). |
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Keywords: | Convergence ODE PARAFAC RGLS Stochastic system Volterra model |
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