Kernel-based system identification from noisy and incomplete input-output data

In this contribution, we propose a kernel-based method for the identification of linear systems from noisy and incomplete input-output datasets. We model the impulse response of the system as a Gaussian process whose covariance matrix is given by the recently introduced stable spline kernel. We adopt an empirical Bayes approach to estimate the posterior distribution of the impulse response given the data. The noiseless and missing data samples, together with the kernel hyperparameters, are estimated maximizing the joint marginal likelihood of the input and output measurements. To compute the marginal-likelihood maximizer, we build a solution scheme based on the Expectation-Maximization method. Simulations on a benchmark dataset show the effectiveness of the method.Comment: 16 pages, submitted to IEEE Conference on Decision and Control 201

System Identification Based on Errors-In-Variables System Models

We study the identification problem for errors-in-variables (EIV) systems. Such an EIV model assumes that the measurement data at both input and output of the system involve corrupting noises. The least square (LS) algorithm has been widely used in this area. However, it results in biased estimates for the EIV-based system identification. In contrast, the total least squares (TLS) algorithm is unbiased, which is now well-known, and has been effective for estimating the system parameters in the EIV system identification. In this dissertation, we first show that the TLS algorithm computes the approximate maximum likelihood estimate (MLE) of the system parameters and that the approximation error converges to zero asymptotically as the number of measurement data approaches infinity. Then we propose a graph subspace approach (GSA) to tackle the same EIV-based system identification problem and derive a new estimation algorithm that is more general than the TLS algorithm. Several numerical examples are worked out to illustrate our proposed estimation algorithm for the EIV-based system identification. We also study the problem of the EIV system identification without assuming equal noise variances at the system input and output. Firstly, we review the Frisch scheme, which is a well-known method for estimating the noise variances. Then we propose a new method which is GSA in combination with the Frisch scheme (GSA-Frisch) algorithm via estimating the ratio of the noise variances and the system parameters iteratively. Finally, a new identification algorithm is proposed to estimate the system parameters based on the subspace interpretation without estimating noise variances or the ratio. This new algorithm is unbiased, and achieves the consistency of the parameter estimates. Moreover, it is low in complexity. The performance of the identification algorithm is examined by several numerical examples, and compared to the N4SID algorithm that has the Matlab codes available in Matlab toolboxes, and also to the GSA-Frisch algorithm

Econometrics: A bird's eye view

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledge and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks and forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of the "real time econometrics". This paper attempts to provide an overview of some of these developments

Data-Driven and Model-Based Control Techniques for a Wind Turbine Benchmark Model

Wind turbine plants are complex dynamic and uncertain processes driven by stochastic inputs and disturbances, as well as different loads represented by gyroscopic, centrifugal, and gravitational forces. Moreover, as their aerodynamic models are nonlinear, both modelling and control become challenging problems. On one hand, high–fidelity simulators should contain different parameters and variables in order to accurately describe the main dynamic system behaviour. Therefore, the development of modelling and control for wind turbine systems should consider these complexity aspects. On the other hand, these control solutions have to include the main wind turbine dynamic characteristics without becoming too complicated. The main point of this paper is thus to provide two practical examples of development of robust control strategies when applied to a simulated wind turbine plant. Extended simulations with the wind turbine benchhmark model and the Monte–Carlo tool represent the instruments for assessing the robustness and reliability aspects of the developed control methodologies when the model–reality mismatch and measurement errors are also considered. Advantages and drawbacks of these regulation methods are also highlighted with respect to different control strategies via proper performance metrics

An identification approach to dynamic errors-in-variables systems with a preliminary clustering of observations

Errors-in-variables models are statistical models in which not only dependent but also independent variables are observed with error, i.e. they exhibit a symmetrical model structure in terms of noise. The application field for these models is diverse including computer vision, image reconstruction, speech and audio processing, signal processing, modal and spectral analysis, system identification, econometrics and time series analysis. This paper explores applying the errors-in-variables approach to parameter estimation of discrete-time dynamic linear systems. In particular, a framework is introduced in which a preliminary separation step is applied to group observations prior to parameter estimation. As a result, instead of one, two sets of estimates are derived simultaneously, comparing which can yield estimates for noise parameters. The proposed approach is compared to other schemes with simulation examples

Econometrics: A Bird’s Eye View

As a unified discipline, econometrics is still relatively young and has been transforming and expanding very rapidly over the past few decades. Major advances have taken place in the analysis of cross sectional data by means of semi-parametric and non-parametric techniques. Heterogeneity of economic relations across individuals, firms and industries is increasingly acknowledged and attempts have been made to take them into account either by integrating out their effects or by modeling the sources of heterogeneity when suitable panel data exists. The counterfactual considerations that underlie policy analysis and treatment evaluation have been given a more satisfactory foundation. New time series econometric techniques have been developed and employed extensively in the areas of macroeconometrics and finance. Non-linear econometric techniques are used increasingly in the analysis of cross section and time series observations. Applications of Bayesian techniques to econometric problems have been given new impetus largely thanks to advances in computer power and computational techniques. The use of Bayesian techniques have in turn provided the investigators with a unifying framework where the tasks of forecasting, decision making, model evaluation and learning can be considered as parts of the same interactive and iterative process; thus paving the way for establishing the foundation of “real time econometrics”. This paper attempts to provide an overview of some of these developments.history of econometrics, microeconometrics, macroeconometrics, Bayesian econometrics, nonparametric and semi-parametric analysis