http://www.ifac-papersonline.net/ en Copyright 09:49 AM Tuesday 21, 2013 IFAC-PapersOnline http://www.ifacpapersonline.com 09:49 AM Tuesday 21, 2013 09:49 AM Tuesday 21, 2013 ET webmaster@ifac-papersonline.net webmaster@ifac-papersonline.net http://www.ifac-papersonline.net/Detailed/54429.html 04:00 PM Wednesday 31, 1969 http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54431.html 04:00 PM Wednesday 31, 1969 Advanced motion systems like pick-and-place machine used in the semiconductor industry challenge the frontiers of systems and control theory and practice. Since experimentation is fast, a machine in the loop procedure can be explored to close the design loop from experiment, experimental model building, model-based control design, implementation and performance evaluation. Nevertheless, reliable numerical tools are required to meet the challenges posed with respect to dimensionality and model complexity, including the open problem of determining disturbance models and suitable specification models. Extension of linear modelling techniques towards some classes of nonlinear systems is relevant for improved control of specific motion systems, such as with friction. Other challenging applications in need for advanced modelling and control are fuel efficient vehicles, including ultra-clean engines, and vehicle electric and hybrid power trains. Another area where a lot of development for identification and control is necessary, is the control of unstable phenomena in plasma’s for nuclear fusion reactors. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54433.html 04:00 PM Wednesday 31, 1969 Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N-L and L-N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a unied framework for the identication of these systems that is valid for SISO and MIMO systems, discrete and continuous-time setting, and with the only a priori knowledge that the system is either Wiener or Hammerstein. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54435.html 04:00 PM Wednesday 31, 1969 This paper considers the identification of linear systems based on binary measurements of the output. In contrast to existing techniques with strict requirements on the excitation signals, the identification is performed based on a sequence of short and independent measurements. The linear systems are represented using Finite Impulse Response (FIR) models, whose parameters are estimated by exploiting the known characteristics of the binary measurement. Two different methods are derived, both yielding convex parameter estimation problems that can be solved with standard software. The first achieves a high prediction accuracy but yields constrained optimization problems. A second alternative is therefore derived with a slightly worse performance but without constraints, such that solutions can be found more quickly. The identification procedure for both is illustrated on a simulation model. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54437.html 04:00 PM Wednesday 31, 1969 In this paper, a novel method is proposed for the identification of a fairly general nonlinear structure called Linear Fractional Representation (LFR), also related to Lur'e type systems. It consists of one static nonlinearity (SNL) connected to the input and the output via a multiple-input-multiple-output (MIMO) linear time-invariant (LTI) block. The nonlinear LFR structure encompasses, e.g., Wiener-Hammerstein and nonlinear feedback models. The procedure starts from 2 state-space models corresponding to the best linear approximation at 2 input variance levels. The MIMO LTI block is estimated by exploiting the approximate structural relationships, taking the state transformations carefully into account. Using the measured input and output, the input and the output of the SNL block are then reconstructed, yielding a nonparametric estimate of the SNL, which is finally converted into a parametric estimate. In the whole procedure, the internal signals, the linear and the nonlinear part need not be known. No stability requirement was imposed on the linear models used. The functional form of the SNL is not needed to find the MIMO LTI block and the nonparametric SNL estimate. The simulation results, supporting the theory, show the superior quality of the obtained initial estimate of the LFR nonlinear model compared to both linear models. This shows that the method is a very promising approach in the field of block-oriented nonlinear modelling. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54439.html 04:00 PM Wednesday 31, 1969 Model identification is addressed for nonparametric Hammerstein-Wiener systems with static input nonlinearity and backlash output nonlinearity. Interestingly, both input and output nonlinearities are allowed to be nonparametric and nonsmooth. A frequency identification method is developed that involves the application of conveniently designed pulse width modulated (PWM) input signals. PWM inputs feature frequency-decoupling of the underlying Wiener subsystem, making possible its accurate frequency identification whatever the input nonlinearity. Then, a set of points on the input nonlinearity are in turn estimated applying PWM input signals repeatedly with fixed frequency but different amplitudes. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54441.html 04:00 PM Wednesday 31, 1969 The continuous-time model identification problem of closed-loop Hammerstein-Wiener system with unknown controller and different noise situations is studied. A two-stage approach is proposed, based on the refined instrumental variable method. With the assumption of monotonic nonlinear function, the closed-loop non linear model is iteratively estimated as an over-parameterized MISO LTI model. To obtain an accurate model in the closed-loop case, the identification is implemented in two stages: 1) identification between the input and the reference signal, which produces estimate of the noise-free input, 2) identification between the output and estimated noise-free input signal. Monte Carlo simulation analysis is carried out to illustrate the effectiveness of the proposed method, in both output and process noise circumstances. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54443.html 04:00 PM Wednesday 31, 1969 In this paper, we investigate the identification of the class of block-oriented nonlinear systems presented by Li et al. [2011] by using an iterative method. Firstly, a common model is proposed to represent such block-oriented systems. Then identifying the common model is formulated as a biconvex optimization problem. Based on this, a normalized alterative convex search (NACS) algorithm is proposed under a given arbitrary nonzero initial condition. It is shown that we only need to find the unique partial optimum point of a biconvex cost function in the formulated optimization problem in order to obtain its global minimum point. Thus, the convergence property of the proposed algorithm is established under arbitrary nonzero initial conditions. The approach presented in this paper provides a unified framework for the identification of block-oriented systems. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54445.html 04:00 PM Wednesday 31, 1969 Most research on system identification is focused on the identification of parametric models, for example a transfer function or a state space model where the information is condensed in a few parameters. In the daily practice, nonparametric methods, like frequency response function measurements, are intensively used. Recently, it was indicated that nonparametric identification methods could be used to robustify the parametric identification framework. A nonparametric preprocessing step can also be used to reduce or even eliminate the required user interaction, making system identification accessible for a much wider user group. For that reason, there is an increasing interest in nonparametric identification. In order to choose, compare, and to benchmark these nonparametric methods, it is very important to select the proper criteria. In this paper we identify and discuss the important choices that should be considered. It will be shown that these strongly depend on the intended use of the nonparametric model. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54447.html 04:00 PM Wednesday 31, 1969 Recently, Hägg, Hjalmarsson and Wahlberg proposed a novel non-parametric method that directly estimates the frequency response at N equidistant frequencies when N measurements are available. The specific feature of the method is that together with these estimates, the transient, or, equivalently, the leakage, is explicitly estimated. The estimates are obtained by solving a least-squares problem. The method involves three design variables, the number of estimated transient terms, a number of auxiliary impulse response coefficients (that also are estimated), and the size of a frequency window. At present there is no analysis of how these design variables affect the properties of the method, which we will call TRIMM (TRansient Impulse response Modeling Method). In this contribution we provide bias and variance analysis for two extreme cases of the window size. We show that at one extreme value, the method coincides with the Empirical Transfer Function Estimate, and at the other extreme it is close to directly estimating a FIR model. This indicates that TRIMM provides an intermediate between non-parametric and parametric estimation. The results allows us to quantify bias and variance errors at the two extreme cases under study, and gives insight into how to choose the design variables in a systematic way. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54449.html 04:00 PM Wednesday 31, 1969 A review of the relationship between the frequency response function of linear system and the DFT of the input and output signals show that the output DFT is a sum of two terms. The first term contain the FRF multiplied with the input DFT and the second term capture the effect when the system is not operating in a periodic fashion. The utilization of these two terms when performing non-parametric frequency response function estimation has led to the previously developed Local Polynomial Method. This paper acknowledge that the two terms can better be approximated by local rational functions with a common denominator polynomial and a new method called Local Rational Method has been developed. Numerical simulations illustrate the performance of the new rational method in comparison with the polynomial one. The results suggest that the new rational method gives better performance when the system has a resonant behavior. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54451.html 04:00 PM Wednesday 31, 1969 This paper analyzes two recent methods for the nonparametric estimation of the Frequency Response Function (FRF) from input-output data using Prediction Error identification. Such FRF estimate can be the main goal of the identification exercise, or it can be a tool for the computation of a nonparametric estimate of the noise spectrum. We show that the choice of the method depends on the signal to noise ratio and on the objective. The method that delivers the best FRF estimate may not deliver the best estimate of the noise spectrum. Our theoretical analysis is illustrated by simulations. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54453.html 04:00 PM Wednesday 31, 1969 This paper extends the Local Polynomial Method (LPM) for linear and time invariant systems excited by periodic signals. LPM is a robust and fast method for finding a non- parametric Frequency Response Function (FRF) estimate. A good FRF estimate is important in designing a good controller. Since both the system FRF and the transient behave smooth as a function of the frequency, LPM assumes that these functions can be approximated locally by a low degree polynomial. However, if the FRF varies strongly as a function of the frequency this assumption results in bias errors due to under-modeling. That is why this paper presents a transient LPM. This transient LPM suppresses the transients as well as the original LPM but does not introduce bias errors due to under-modeling. The variance of the FRF estimate via the transient LPM will be slightly larger than the variance of the FRF estimate via LPM. However, when these non-parametric FRF estimates are used to find a parametric estimate, this variance difference will not affect the result. Thus, the reduced bias of the FRF estimate via the transient LPM will lead to a better parametric FRF estimate. A disadvantage is that the transient LPM cannot estimate the level of the nonlinear distortions. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54455.html 04:00 PM Wednesday 31, 1969 A method of finite-frequency identification for stable plants with time-delay in the presence of unknown-but-bounded disturbance and measurement noise is proposed. This method uses test signal which is a sum of harmonics. Quantity of harmonics does not exceed count of plant coefficients. Conditions of convergence of identification process are also given. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54457.html 04:00 PM Wednesday 31, 1969 In recent years there has been growing interest in convex optimization techniques for system identification and time series modeling. This interest is motivated by the success of convex methods for sparse optimization and rank minimization in signal processing, statistics, and machine learning, and by the development of new classes of algorithms for large-scale nondifferentiable convex optimization. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54459.html 04:00 PM Wednesday 31, 1969 Change detection has traditionally been seen as a centralized problem. Many change detection problems are however distributed in nature and the need for distributed change detection algorithms is therefore significant. In this paper a distributed change detection algorithm is proposed. The change detection problem is first formulated as a convex optimization problem and then solved distributively with the alternating direction method of multipliers (ADMM). To further reduce the computational burden on each sensor, a homotopy solution is also derived. The proposed method have interesting connections with Lasso and compressed sensing and the theory developed for these methods are therefore directly applicable. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54461.html 04:00 PM Wednesday 31, 1969 We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that is separable in the difference between consecutive variable blocks. Examples of such problems include Fused Lasso estimation, total variation denoising, and multi-period portfolio optimization with transaction costs. In each iteration of our method, the first step involves separately optimizing over each variable block, which can be carried out in parallel. The second step is not separable in the variables, but can be carried out very efficiently. We apply the algorithm to segmentation of data based on changes in mean (l_1 mean filtering) or changes in variance (l_1 variance filtering). In a numerical example, we show that our implementation is around 10000 times faster compared with the generic optimization solver SDPT3. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54463.html 04:00 PM Wednesday 31, 1969 Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear program, namely, l1-minimization, guarantees recovery of sparse parameter signals even when the system is underdetermined. In this paper, we consider a more challenging problem: when the phase of the output measurements from a linear system is omitted. Using a lifting technique, we show that even though the phase information is missing, the sparse signal can be recovered exactly by solving a semidefinite program when the sampling rate is sufficiently high. This is an interesting finding since the exact solutions to both sparse signal recovery and phase retrieval are combinatorial. The results extend the type of applications that compressive sensing can be applied to those where only output magnitudes can be observed. We demonstrate the accuracy of the algorithms through extensive simulation and a practical experiment. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54465.html 04:00 PM Wednesday 31, 1969 Cointegrated Vector AutoRegressive (VAR) processes arise in the study of long run equilibrium relations of stochastic dynamical systems. In this paper we introduce a novel convex approach for the analysis of these type of processes. The idea relies on an error correction representation and amounts at solving a penalized empirical risk minimization problem. The latter finds a model from data by minimizing a trade-off between a quadratic error function and a nuclear norm penalty used as a proxy for the cointegrating rank. We elaborate on properties of the proposed convex program; we then propose an easily implementable and provably convergent algorithm based on FISTA. This algorithm can be conveniently used for computing the regularization path, i.e., the entire set of solutions associated to the trade-off parameter. We show how such path can be used to build an estimator for the cointegrating rank and illustrate the proposed ideas with experiments.  http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54467.html 04:00 PM Wednesday 31, 1969 A variant of Gaussian Process is proposed in this study for nonlinear non-parametric system identification. Only local data is used to construct the estimate. Moreover, the hyper- parameters are adjusted to minimize the local weighted prediction errors. The proposed scheme seems to have semi-global modeling properties of Gaussian Process for limited data sets and also possess local convergence properties if the data set is sufficient rich. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54469.html 04:00 PM Wednesday 31, 1969 Multi-step ahead prediction is a common approach for the simulation of dynamic system behavior. Recently, Gaussian Processes combined with an autoregressive model structure gathered much attention for this task. In order to overcome the computational burden of standard Gaussian Processes at large data sets and to provide a reliable variance prediction for time-dependent use cases, we introduce in the present paper the combination of several sparse Gaussian Process approximations with the framework of uncertainty propagation. We show the results of the proposed approaches at an artificial, chaotic time series and a real world example stemming from an engine air system. The real world example also contains a comparison of the modeling performance to other data-based methods, in particular ordinary least squares and multi-layer perceptrons. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54471.html 04:00 PM Wednesday 31, 1969 FIR (finite impulse response) model is widely used in tackling the problem of the impulse response estimation with quantized measurements. Its use is, however, limited, in the case when a high order FIR model is required to capture a slowly decaying impulse response. This is because the high variance for high order FIR models would override the low bias and thus lead to large MSE (mean square error). In this contribution, we apply the recently introduced regularized FIR model approach to the problem of the impulse response estimation with binary measurements. We show by Monte Carlo simulations that the proposed approach can yield both better accuracy and better robustness than a recently introduced FIR model based approach. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54473.html 04:00 PM Wednesday 31, 1969 A new nonparametric approach for system identification has been recently proposed where, in place of postulating parametric classes of impulse responses, the estimation process starts from an infinite-dimensional space. In particular, the impulse response is seen as the realization of a zero-mean Gaussian process. Its covariance, the so called stable spline kernel, encodes information on system stability and depends on few hyperparameters estimated from data via marginal likelihood optimization. This approach has been proved to compare much favorably with classical parametric methods but, in data rich situations, a possible drawback may be represented by its computational complexity which scales with the cube of the number of available samples. In this work we design a new computational strategy which may reduce significantly the computational load required by the stable spline estimator, thus extending its practical applicability also to large-scale scenarios. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54475.html 04:00 PM Wednesday 31, 1969 It has been argued in the recent literature that linear system identification can be tackled in a Bayesian framework provided a suitable class of priors is considered. These priors essentially encode stability of the system but have to be flexible enough to adapt to a wide range of situations. Part of this flexibility is achieved introducing hyperparameters in the prior distribution which have to be estimated from data. In this paper we study the properties of a class of empirical Bayes estimators in terms of their Mean Squared Error. We do so in a simplified scenario which however captures some of the essential features arising in system identification. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/54477.html 04:00 PM Wednesday 31, 1969 Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif