Structure identification of nonlinear dynamic systems—a survey on input/output approaches

https://www.dtc.umn.edu/s/resources/gg-se.pdf

A bibliography on nonlinear system identification

Structural classification and parameter estimation (SCPE) methods are used for studying single-input single-output (SISO) parallel linear-nonlinear-linear (LNL), linear-nonlinear (LN), and nonlinear-linear (NL) system models from input-output (I-O) measurements. The uniqueness of the I-O mappings of some model structures is discussed. The uniqueness of I-O mappings of different models tells us in what conditions given model structures can be differentiated from one another. Parameter uniqueness of the I-O mapping of a given structural model is also discussed, which tells us in what conditions a given model's parameters can be uniquely estimated from I-O measurements. These methods are then generalized so that they can be used to study single-input multi-output (SIMO), multi-input single-output (MISO), as well as multi-input multi-output (MIMO) nonlinear system models. Parameter estimation of the two-input single-output nonlinear system model, which was left unsolved previously, can now be obtained using the newly derived algorithms. Applications of SCPE methods for modeling visual cortical neurons, system fault detection, modeling and identification of communication networks, biological systems, and natural and artificial neural networks are also discussed. The feasibility of these methods is demonstrated using simulated examples. SCPE methods presented in this paper can be further developed to study more complicated block-structured models, and will therefore have future potential for modeling and identifying highly complex multi-input multi-output nonlinear systems. >

Modeling and identification of parallel nonlinear systems: structural classification and parameter estimation methods

Hammerstein system -- Wiener system -- Wiener-Hammerstein (sandwich) system -- Large-scale interconnected systems -- Structure detection and model order selection -- Time-varying systems -- Simulation studies -- Summary.

Combined Parametric-Nonparametric Identification of Block-Oriented Systems

The paper studies approximations for a class of nonlinear filters known as Volterra filters. Although the Volterra filter provides a relatively simple and general representation for nonlinear filtering, it is often highly overparameterized. Due to the large number of parameters, the utility of the Volterra filter is limited. The overparameterization problem is addressed in the paper using a tensor product basis approximation (TPBA). In many cases, a Volterra filter may be well approximated using the TPBA with far fewer parameters. Hence, the TPBA offers considerable advantages over the original Volterra filter in terms of both implementation and estimation complexity. Furthermore, the TPBA provides useful insight into the filter response. The paper studies the crucial issue of choosing the approximation basis. Several methods for designing an appropriate approximation basis and error bounds on the resulting mean-square output approximation error are derived. Certain methods are known to be nearly optimal.

Tensor product basis approximations for Volterra filters

Block-oriented models having only one multiplier and the Volterra kernels that describe them are summarized. The kernel estimation of the discrete Volterra series is dealt with. It is pointed out that while the Volterra kernels can easily be derived from the block-oriented models, the structure and the parameters of the block-oriented models cannot be computed in a trivial way from the estimated Volterra kernels. Both graphical and analytical procedures are recommended for the structural identification. The method is supported by several simulation examples.

R. Haber

Papers

Structural identification of quadratic block-oriented models based on estimated Volterra kernels