Novel approaches for parameter estimation of local linear models for dynamical system identification

• Published in: Applied intelligence (Dordrecht, Netherlands) Vol. 44; no. 1; pp. 149 - 165
• Main Authors: Barreto, Guilherme A., M. Souza, Luís Gustavo
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2016; Springer Nature B.V
• Subjects: Algorithms; Approximation; Artificial Intelligence; Computer Science; Construction; Dynamical systems; Identification; Machines; Manufacturing; Mathematical analysis; Mechanical Engineering; Neural networks; Neurons; Parameter estimation; Partitions; Performance evaluation; Processes; Vectors (mathematics); Global models; Feedforward neural networks; Vector quantization; Self-organizing maps; Local linear models; Nonlinear system identification
• ISSN: 0924-669X; 1573-7497
• DOI: 10.1007/s10489-015-0699-1

In this paper we introduce two novel techniques for local linear modeling of dynamical systems. As in the standard approach, we use vector quantization (VQ) algorithms, such as the Self-Organizing Map, to partition the joint input-output space into smaller regions. Then, to each neuron we associate a vector of parameters which must be suitably estimated. The first estimation technique uses the prototypes of the i -th neuron and its K nearest neighbors to build the corresponding local linear model. The second technique builds the i -th local linear model using the data vectors that are mapped into the regions comprised of the Voronoi cells of the i -th neuron and its K nearest neighbors. A comprehensive evaluation of the proposed techniques is carried out for the task of inverse identification of three benchmarking Single Input/Single Output (SISO) dynamical systems. Their performances are compared to those achieved by the Multilayer Perceptron and the Extreme Learning Machine networks. We also evaluate how robust are the proposed techniques with respect to the VQ algorithm used to partition the input-output space. The results show that proposed techniques consistently outperform standard approaches for all evaluated datasets.