Optimization of Volterra models with asymmetrical kernels based on generalized orthonormal functions

Braga, Márcia F., Machado, Jeremias B., Campello, Ricardo J.G.B., and Amaral, Wagner C. (2011) Optimization of Volterra models with asymmetrical kernels based on generalized orthonormal functions. In: Proceedings of the 19th Mediterranean Conference on Control & Automation, pp. 1052-1058. From: 2011 MED: 19th Mediterranean Conference on Control & Automation, 20-23 June 2011, Corfu, Greece.

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Abstract

An improved approach to determine exact search directions for the optimization of Volterra models based on Generalized Orthonormal Bases of Functions (GOBF) is proposed. The proposed approach extends the work in, where a novel, exact technique for optimizing the GOBF parameters (poles) for Volterra models of any order was presented. The proposed extensions take place in two different ways: (i) the formulation here is derived in such a way that each multidimensional kernel of the model is decomposed into a set of independent orthonormal bases (rather than a single, common basis), each of which is parameterized by an individual set of poles intended for representing the dominant dynamic of the kernel along a particular dimension; and (ii) a novel, more computationally efficient method to analytically and recursively calculate the search directions (gradients) for the bases poles is derived. A simulated example is presented to illustrate the performance of the proposed approach. A comparison between the proposed method, which uses asymmetric kernels with multiple orthonormal bases, and the original method, which uses symmetric kernels with a single basis, is presented.

Item ID: 46791
Item Type: Conference Item (Research - E1)
ISBN: 978-1-4577-0123-8
Date Deposited: 11 Jul 2017 03:31
FoR Codes: 01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010299 Applied Mathematics not elsewhere classified @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100%
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