Reglerteknik förekommer numera i de flesta tekniska system: motorstyrning, antisladdsystem och farthållare i bilar; effektstyrning för mobiltelefoner; banföljning i industrirobotar; styrautomater i flygplan; styrning av allehanda kvalitetsvariabler i processindustrin liksom många tillämpningar inom konsumentelektronik...[Bokinfo]

Mathematical models of real life systems and processes are essential in today’s industrial work. To be able to construct such models is therefore a fundamental skill in modern engineering...

The R2021b release of the System Identification ToolboxTM for MATLAB contains new features that enable the use of machine learning techniques for nonlinear system identification. With this release it is possible to build nonlinear ARX models with regression tree ensemble and Gaussian process regression mapping functions. The release contains several other enhancements including, but not limited to, (a) online state estimation using the extended Kalman filter and the unscented Kalman filter with code generation capability; (b) improved handling of initial conditions for transfer functions and polynomial models; (c) a new architecture of nonlinear black-box models that streamlines regressor handling, reduces memory footprint and improves numerical accuracy; and (d) easy incorporation of identification apps in teaching tools and interactive examples by leveraging the Live Editor tasks of MATLAB. Copyright (C) 2021 The Authors.

Nonlinear system identification is an extremely broad topic, since every system that is not linear is nonlinear. That makes it impossible to give a full overview of all aspects of the fi eld. For this reason, the selection of topics and the organization of the discussion are strongly colored by the personal journey of the authors in this nonlinear universe.

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This paper proposes a new method to identify nonlinear state-space systems from heterogeneous datasets. The method is described in the context of identifying biochemical/gene networks (i.e., identifying both reaction dynamics and kinetic parameters) from experimental data. Simultaneous integration of various datasets has the potential to yield better performance for system identification. Data collected experimentally typically vary depending on the specific experimental setup and conditions. Typically, heterogeneous data are obtained experimentally through 1) replicate measurements from the same biological system or 2) application of different experimental conditions such as changes/perturbations in biological inductions, temperature, gene knock-out, gene over-expression, etc. We formulate here the identification problem using a Bayesian learning framework that makes use of “sparse group” priors to allow inference of the sparsest model that can explain the whole set of observed heterogeneous data. To enable scale up to large number of features, the resulting nonconvex optimization problem is relaxed to a reweighted Group Lasso problem using a convex-concave procedure. As an illustrative example of the effectiveness of our method, we use it to identify a genetic oscillator (generalized eight species repressilator). Through this example we show that our algorithm outperforms Group Lasso when the number of experiments is increased, even when each single time-series dataset is short. We additionally assess the robustness of our algorithm against noise by varying the intensity of process noise and measurement noise.

The kernel-based regularization method has two core issues: kernel design and hyperparameter estimation. In this paper, we focus on the second issue and study the properties of several hyperparameter estimators including the empirical Bayes (EB) estimator, two Steins unbiased risk estimators (SURE) (one related to impulse response reconstruction and the other related to output prediction) and their corresponding Oracle counterparts, with an emphasis on the asymptotic properties of these hyperparameter estimators. To this goal, we first derive and then rewrite the first order optimality conditions of these hyperparameter estimators, leading to several insights on these hyperparameter estimators. Then we show that as the number of data goes to infinity, the two SUREs converge to the best hyperparameter minimizing the corresponding mean square error, respectively, while the more widely used EB estimator converges to another best hyperparameter minimizing the expectation of the EB estimation criterion. This indicates that the two SUREs are asymptotically optimal in the corresponding MSE senses but the EB estimator is not. Surprisingly, the convergence rate of two SUREs is slower than that of the EB estimator, and moreover, unlike the two SUREs, the EB estimator is independent of the convergence rate of Phi(T)Phi/N to its limit, where Phi is the regression matrix and N is the number of data. A Monte Carlo simulation is provided to demonstrate the theoretical results. (C) 2018 Elsevier Ltd. All rights reserved.

The first order stable spline (SS-1) kernel (also known as the tunedcorrelated kernel) is used extensively in regularized system identification, where the impulse response is modeled as a zero-mean Gaussian process whose covariance function is given by well designed and tuned kernels. In this paper, we discuss the maximum entropy properties of this kernel. In particular, we formulate the exact maximum entropy problem solved by the SS-1 kernel without Gaussian and uniform sampling assumptions. Under general sampling assumption, we also derive the special structure of the SS-1 kernel (e.g. its tridiagonal inverse and factorization have closed form expression), also giving to it a maximum entropy covariance completion interpretation.

Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem, differing in the nature of the penalty term assigned to the impulse response. Popular choices include atomic and nuclear norms (applied to Hankel matrices) as well as norms induced by the so called stable spline kernels. In this paper, a comparative study of estimators based on these different types of regularizers is reported. Our findings reveal that stable spline kernels outperform approaches based on atomic and nuclear norms since they suitably embed information on impulse response stability and smoothness. This point is illustrated using the Bayesian interpretation of regularization. We also design a new class of regularizers defined by "integral" versions of stable spline/TC kernels. Under quite realistic experimental conditions, the new estimators outperform classical prediction error methods also when the latter are equipped with an oracle for model order selection. (C) 2016 Elsevier Ltd. All rights reserved.

An established method for grey-box identification is to use maximum-likelihood estimation for the nonlinear case implemented via extended Kalman filtering. In applications of (nonlinear) model predictive control a more and more common approach for the state estimation is to use moving horizon estimation, which employs (nonlinear) optimization directly on a model for a whole batch of data. This paper shows that, in the linear case, horizon estimation may also be used for joint parameter estimation and state estimation, as long as a bias correction based on the Kalman filter is included. For the nonlinear case two special cases are presented where the bias correction can be determined without approximation. A procedure how to approximate the bias correction for general nonlinear systems is also outlined. (C) 2015 Elsevier Ltd. All rights reserved.