| 1. |
- Bottegal, Giulio, et al.
(författare)
-
A new kernel-based approach to system identification with quantized output data
- 2017
-
Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 85, s. 145-152
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data. (C) 2017 Elsevier Ltd. All rights reserved.
|
|
| 2. |
- Bottegal, Giulio, et al.
(författare)
-
Analysis and identification of complex stochastic systems admitting a flocking structure
- 2014
-
Ingår i: IFAC Proceedings Volumes (IFAC-PapersOnline). - : Elsevier BV. - 1474-6670. - 9783902823625 ; , s. 2323-2328
-
Konferensbidrag (refereegranskat)abstract
- We discuss a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The flocking component describes a sort of collective orderly motion which admits a much simpler mathematical description than the whole ensemble while the idiosyncratic component describes weakly correlated noise. The extraction of the dynamic flocking component is discussed for time-stationary systems.
|
|
| 3. |
- Bottegal, Giulio, et al.
(författare)
-
Bayesian kernel-based system identification with quantized output data
- 2015
-
Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963. ; 48:28, s. 455-460
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.
|
|
| 4. |
- Bottegal, Giulio, et al.
(författare)
-
Blind system identification using kernel-based methods
- 2015
-
Ingår i: IFAC-PapersOnLine. - : Elsevier. - 2405-8963.
-
Konferensbidrag (refereegranskat)abstract
- We propose a new method for blind system identification (BSI). Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussian process. The structure of the covariance matrix (or kernel) of such a process is given by the stable spline kernel, which has been recently introduced for system identification purposes and depends on an unknown hyperparameter. We assume that the input can be linearly described by few parameters. We estimate these parameters, together with the kernel hyperparameter and the noise variance, using an empirical Bayes approach. The related optimization problem is efficiently solved with a novel iterative scheme based on the Expectation-Maximization (EM) method. In particular, we show that each iteration consists of a set of simple update rules. Through some numerical experiments we show that the proposed method give very promising performance.
|
|
| 5. |
- Bottegal, Giulio, et al.
(författare)
-
Modeling Complex Systems by Generalized Factor Analysis
- 2015
-
Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 60:3, s. 759-774
-
Tidskriftsartikel (refereegranskat)abstract
- We propose a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The flocking component describes a sort of collective orderly motion which admits a much simpler mathematical description than the whole ensemble while the idiosyncratic component describes weakly correlated noise. We first discuss static GFA representations and characterize in a rigorous way the properties of the two components. The extraction of the dynamic flocking component is discussed for time-stationary linear systems and for a simple classes of separable random fields.
|
|
| 6. |
- Bottegal, Giulio, 1984-, et al.
(författare)
-
Modeling random flocks through Generalized Factor Analysis
- 2013
-
Ingår i: 2013 European Control Conference, ECC 2013. - : EUCA. - 9783952417348 ; , s. 2421-2426
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we study modeling and identification of stochastic systems by Generalized Factor Analysis models. Although this class of models was originally introduced for econometric purposes, we present some possible applications of engineering interest. In particular, we show that there is a natural connection between Generalized Factor Analysis models and multi-agents systems. The common factor component of the model has an interpretation as a flocking component of the system behavior.
|
|
| 7. |
- Bottegal, Giulio, 1984-, et al.
(författare)
-
On the variance of identified SIMO systems with spatially correlated output noise
- 2014
-
Ingår i: Proceedings of the IEEE Conference on Decision and Control. - : IEEE conference proceedings. ; , s. 2636-2641
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we study the problem of evaluating the accuracy of identified linear single-input multi-output (SIMO) dynamical models, where the disturbances affecting the output measurements are spatially correlated. Assuming that the input is an observed white noise sequence, we provide an expression for the covariance matrix of the parameter estimates when weighted least-squares (WLS) are adopted to identify the parameters. Then, we show that, by describing one of the subsystems composing the SIMO structure using less parameters than the other subsystems, substantial improvement on the accuracy of the estimates of some parameters can be obtained. The amount of such an improvement depends critically on the covariance matrix of the output noise and we provide a condition on the noise correlation structure under which the mentioned model parametrization gives the lowest variance in the identified model. We illustrate the derived results through some numerical experiments.
|
|
| 8. |
- Bottegal, Giulio, et al.
(författare)
-
Outlier robust kernel-based system identification using l1-Laplace techniques
- 2015
-
Ingår i: 2015 54th IEEE Conference on Decision and Control. - : Institute of Electrical and Electronics Engineers (IEEE). ; , s. 2109-2114
-
Konferensbidrag (refereegranskat)abstract
- Regularized kernel-based methods for system identification have gained popularity in recent years. However, current formulations are not robust with respect to outliers. In this paper, we study possible solutions to robustify kernel-based methods that rely on modeling noise using the Laplacian probability density function (pdf). The contribution of this paper is two-fold. First, we introduce a new outlier robust kernel-based system identification method. It exploits the representation of Laplacian pdfs as scale mixture of Gaussians. The hyperparameters characterizing the problem are chosen using a new maximum a posteriori estimator whose solution is computed using a novel iterative scheme based on the expectation-maximization method. The second contribution of the paper is the review of two other robust kernel-based methods. The three methods are compared by means of numerical experiments, which show that all of them give substantial performance improvements compared to standard kernel-based methods for linear system identification.
|
|
| 9. |
- Bottegal, Giulio, et al.
(författare)
-
Outlier robust system identification : A Bayesian kernel-based approach
- 2014
-
Ingår i: IFAC Proceedings Volumes (IFAC-PapersOnline). - : IFAC Papers Online. - 9783902823625 ; , s. 1073-1078
-
Konferensbidrag (refereegranskat)abstract
- In this paper, we propose an outlier-robust regularized kernel-based method for linear system identification. The unknown impulse response is modeled as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. To build robustness to outliers, we model the measurement noise as realizations of independent Laplacian random variables. The identification problem is cast in a Bayesian framework, and solved by a new Markov Chain Monte Carlo (MCMC) scheme. In particular, exploiting the representation of the Laplacian random variables as scale mixtures of Gaussians, we design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods.
|
|
| 10. |
- Bottegal, Giulio, et al.
(författare)
-
Robust EM kernel-based methods for linear system identification
- 2016
-
Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 67, s. 114-126
-
Tidskriftsartikel (refereegranskat)abstract
- Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not robust with respect to outliers. In this paper, we introduce a novel method to robustify kernel-based system identification methods. To this end, we model the output measurement noise using random variables with heavy-tailed probability density functions (pdfs), focusing on the Laplacian and the Student's t distributions. Exploiting the representation of these pdfs as scale mixtures of Gaussians, we cast our system identification problem into a Gaussian process regression framework, which requires estimating a number of hyperparameters of the data size order. To overcome this difficulty, we design a new maximum a posteriori (MAP) estimator of the hyperparameters, and solve the related optimization problem with a novel iterative scheme based on the Expectation-Maximization (EM) method. In the presence of outliers, tests on simulated data and on a real system show a substantial performance improvement compared to currently used kernel-based methods for linear system identification. (C) 2016 Elsevier Ltd. All rights reserved.
|
|
