Parameter identification of PWARX models using fuzzy distance weighted least squares method |
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Affiliation: | 1. Department of Instrumentation & Control, SVIT, Vasad, Gujarat, India;2. Department of Instrumentation & Control, Nirma University, Ahmedabad, Gujarat, India;1. School of Mathematical Sciences, Anhui University, Hefei, Anhui 230601, China;2. Signal and Image Processing Institute, Department of Electrical Engineering, University of Southern California, Los Angeles, CA 90007, USA;1. Department of Applied Physics, University of Calcutta, Kolkata, India;2. Department of Electrical Engineering, Jadavpur University, Kolkata 700032, India |
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Abstract: | PieceWise AutoRegressive eXogenous (PWARX) models represent one of the broad classes of the hybrid dynamical systems (HDS). Among many classes of HDS, PWARX model used as an attractive modeling structure due to its equivalence to other classes. This paper presents a novel fuzzy distance weight matrix based parameter identification method for PWARX model. In the first phase of the proposed method estimation for the number of affine submodels present in the HDS is proposed using fuzzy clustering validation based algorithm. For the given set of input–output data points generated by predefined PWARX model fuzzy c-means (FCM) clustering procedure is used to classify the data set according to its affine submodels. The fuzzy distance weight matrix based weighted least squares (WLS) algorithm is proposed to identify the parameters for each PWARX submodel, which minimizes the effect of noise and classification error. In the final phase, fuzzy validity function based model selection method is applied to validate the identified PWARX model. The effectiveness of the proposed method is demonstrated using three benchmark examples. Simulation experiments show validation of the proposed method. |
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Keywords: | PieceWise AutoRegressive eXogenous Hybrid dynamical system Fuzzy-c-means clustering Fuzzy distance weight matrix Weighted least squares |
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