Asymmetric Volterra Models Based on Ladder-Structured Generalized Orthonormal Basis Functions

In this paper, an improved method to construct and estimate Volterra models using Generalized Orthonormal Basis Functions (GOBF) is presented. The proposed method extends results obtained in previous works, where an exact technique for optimizing the GOBF parameters (poles) for symmetric Volterra mo...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2015-11, Vol.60 (11), p.2879-2891
Main Authors: Machado, Jeremias B., Campello, Ricardo J. G. B., Amaral, Wagner C.
Format: Article
Language:English
Subjects:
Accuracy
Basis functions
Computation
Computational modeling
Data models
Dynamical systems
Generalized Orthonormal Basis Functions
Kernel
Kernels
Mathematical model
Mathematical models
Nonlinear dynamical systems
Nonlinear dynamics
Nonlinear Systems
Optimization
Poles
System Identification
Volterra Models
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Summary:In this paper, an improved method to construct and estimate Volterra models using Generalized Orthonormal Basis Functions (GOBF) is presented. The proposed method extends results obtained in previous works, where an exact technique for optimizing the GOBF parameters (poles) for symmetric Volterra models of any order was presented. The proposed extensions take place in two different ways: (i) the new formulation 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 responsible for representing the dominant dynamic of the kernel along a particular dimension; and (ii) the new formulation is based on a ladder-structured GOBF architecture that is characterized by having only real-valued parameters to be estimated, regardless of whether the GOBF poles encoded by these parameters are real- or complex-valued. The exact gradients of an error functional with respect to the parameters to be optimized are computed analytically and provide exact search directions for an optimization process that uses only input-output data measured from the dynamic system to be modeled. Computational experiments are presented to illustrate the benefits of the proposed approach when modeling nonlinear systems.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2015.2423912