A New Kernel-Based Approach for NonlinearSystem Identification

We present a novel nonparametric approach for identification of nonlinear systems. Exploiting the framework of Gaussian regression, the unknown nonlinear system is seen as a realization from a Gaussian random field. Its covariance encodes the idea of "fading" memory in the predictor and co...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2011-12, Vol.56 (12), p.2825-2840
Main Authors: Pillonetto, G., Minh Ha Quang, Chiuso, A.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Bayesian estimation
Bayesian methods
Computer science
control theory
systems
Control theory. Systems
direct weight optimization
Dynamical systems
Exact sciences and technology
Gaussian
Gaussian processes
Kernel
kernel-based methods
Kernels
Mathematical models
Modelling and identification
Nonlinear dynamics
nonlinear system identification
Nonlinear systems
Optimization
Predictive models
Regression
regularization
Studies
System identification
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Description
Summary:We present a novel nonparametric approach for identification of nonlinear systems. Exploiting the framework of Gaussian regression, the unknown nonlinear system is seen as a realization from a Gaussian random field. Its covariance encodes the idea of "fading" memory in the predictor and consists of a mixture of Gaussian kernels parametrized by few hyperparameters describing the interactions among past inputs and outputs. The kernel structure and the unknown hyperparameters are estimated maximizing their marginal likelihood so that the user is not required to define any part of the algorithmic architecture, e.g., the regressors and the model order. Once the kernel is estimated, the nonlinear model is obtained solving a Tikhonov-type variational problem. The Hilbert space the estimator belongs to is characterized. Benchmarks problems taken from the literature show the effectiveness of the new approach, also comparing its performance with a recently proposed algorithm based on direct weight optimization and with parametric approaches with model order estimated by AIC or BIC.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2131830