| 1. |
- Avventi, Enrico, et al.
(författare)
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Graphical Models of Autoregressive Moving-Average Processes
- 2010
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Ingår i: The 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010).
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Konferensbidrag (refereegranskat)abstract
- Consider a Gaussian stationary stochastic vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrix-valued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive moving-average (ARMA) model to the same data. We develop a theoretical framework which also spreads further light on previous approaches and results.
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| 2. |
- Ebadat, Afrooz, et al.
(författare)
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Applications Oriented Input Design for Closed-Loop System Identification : a Graph-Theory Approach
- 2014
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Ingår i: 2014 IEEE 53RD ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781467360906 ; , s. 4125-4130
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Konferensbidrag (refereegranskat)abstract
- A new approach to experimental design for identification of closed-loop models is presented. The method considers the design of an experiment by minimizing experimental cost, subject to probabilistic bounds on the input and output signals, and quality constraints on the identified model. The input and output bounds are common in many industrial processes due to physical limitations of actuators. The aforementioned constraints make the problem non-convex. By assuming that the experiment is a realization of a stationary process with finite memory and finite alphabet, we use results from graph-theory to relax the problem. The key feature of this approach is that the problem becomes convex even for non-linear feedback systems. A numerical example shows that the proposed technique is an attractive alternative for closed-loop system identification.
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| 3. |
- Hägg, Per, et al.
(författare)
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On Identification of Parallel Cascade Serial Systems
- 2011
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Ingår i: IFAC Proceedings Volumes (IFAC-PapersOnline). - : IFAC.
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Konferensbidrag (refereegranskat)abstract
- We consider identification of systems with a parallel serial (cascade) structure with multiple-input and multiple-output signals. The statistical properties of estimated models are studied with respect to input signals and possible sensor locations. The quality of the estimates are analyzed by means of the asymptotic covariance matrix of the estimated parameters. This is an extension of previous work on identification of cascaded linear systems. The key result concerns systems where the sub-systems have common dynamics. An interesting observation is that for this case the variance for the parameters belonging to the unmeasured subsystem always is larger than for the other sub-systems. This is not true for general parameters. The variance results can be used for optimal input and sensor location design. The results are illustrated by some simple FIR examples and numerical evaluations.
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| 4. |
- Hägg, Per, et al.
(författare)
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On subspace identification of cascade structured systems
- 2010
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. - : IEEE. - 9781424477456 ; , s. 2843-2848
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Konferensbidrag (refereegranskat)abstract
- In identification it is important to take a priori structural information into account in many applications, something that is difficult when using subspace methods. Here will study how to incorporate a special structure, a cascade structure with two subsystems. Two new methods are derived for estimating system with this structure. The problem when using subspace identification on cascade structured system is that the states from the first subsystem are mixed with states from the second subsystem via a unknown similarity transform. The first indirect method finds a similarity transform that takes the system back to a form such that the subsystems can be recovered. The second method uses the fact that the structure of the extended observability matrix is known for cascade systems. However, it only works when both subsystems have order one. In practice this is still a common case. The results of the two methods seem promising, as illustrated by applying the methods to a real process, the double tank process. The performance is comparable with state of the art methods. Finally the problem of optimal input design for cascade systems are introduced, and illustrated by a simple example.
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| 5. |
- Krishnamurthy, Vikram, et al.
(författare)
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Computing monotone policies for Markov decision processes by exploiting sparsity
- 2013
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Ingår i: 2013 3rd Australian Control Conference, AUCC 2013. - : IEEE. - 9781479924974 ; , s. 6697239-
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Konferensbidrag (refereegranskat)abstract
- This paper considers Markov decision processes whose optimal policy is a randomized mixture of monotone increasing policies. Such monotone policies have an inherent sparsity structure. We present a two-stage convex optimization algorithm for computing the optimal policy that exploits the sparsity. It combines an alternating direction method of multipliers (ADMM) to solve a linear programming problem with respect to the joint action state probabilities, together with a sub-gradient step that promotes the monotone sparsity pattern in the conditional probabilities of the action given the state. In the second step, sum-of-norms regularization is used to stress the monotone structure of the optimal policy.
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| 6. |
- Oomen, Tom, et al.
(författare)
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Analyzing Iterations in Identification with Application to Nonparametric H∞-Norm Estimation
- 2011
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Ingår i: Proceedings of the 18th World Congress, The International Federation of Automatic Control, Milano (Italy) August 28 - September 2, 2011. - : IFAC Papers Online. ; , s. 9972-9977
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Konferensbidrag (refereegranskat)abstract
- In the last decades, many iterative approaches in the field of system identification for control have been proposed. Many successful implementations have been reported, despite the lack of a solid analysis with respect to the convergence and value of these iterations. The aim of this paper is to present a thorough analysis of a specific iterative algorithm that involves nonparametric H-infinity-norm estimation. The pursued approach involves a novel frequency domain approach that appropriately deals with additive stochastic disturbances and input normalization. The results of the novel convergence analysis are twofold: i) the presence of additive disturbances introduces a bias in the estimation procedure, and ii) the iterative procedure can be interpreted as experiment design for H-infinity-norm estimation, revealing the value of iterations and limits of accuracy in terms of the Fisher information matrix. The results are confirmed by means of a simulation example.
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| 7. |
- Pattarello, Giorgio, et al.
(författare)
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Demo abstract : The KTH open testbed for smart HVAC control
- 2013
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Ingår i: Proceedings of the 5th ACM Workshop on Embedded Systems For Energy-Efficient Buildings - BuildSys 2013. - New York, NY, USA : Association for Computing Machinery (ACM).
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Konferensbidrag (refereegranskat)abstract
- To facilitate the assessment of the feasibility, opportunities and weaknesses of advanced Heating, Ventilation and Air Conditioning (HVAC) control schemes we propose the remotely accessible KTH open testbed for smart HVAC control. This testbed allows researchers from all over the world to test estimators and controllers on a real facility, and aims to become a benchmark for the evaluation of the effectiveness of the control schemes proposed in the literature. This demo describes the testbed through a series of videos and Graphical User Interfaces (GUIs), and illustrates the potentialities and limitations of the remotely accessible hardware.
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| 8. |
- Rojas, Cristian R., 1980-, et al.
(författare)
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A sparse estimation technique for general model structures
- 2013
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Ingår i: 2013 European Control Conference, ECC 2013. - : IEEE. - 9783033039629 ; , s. 2410-2414
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Konferensbidrag (refereegranskat)abstract
- In this paper, a general sparse estimator is proposed, based on the maximum likelihood / prediction error method (or any √N-consistent estimator). This procedure does not rely on the convexity of the cost function of the underlying estimator (in case such estimator is an M-estimator), and it provides an automatic tuning of the (implicit) regularization parameter. The idea behind the proposed method is a three step procedure, where the first step consists in a standard √N-consistent estimation, the second step seeks for the sparsest estimate in a neighborhood of the initial estimate, and the last step is a refinement based on the sparseness pattern estimated in the second step. A rigorous statistical analysis is provided, which establishes conditions for consistency, asymptotic variable selection and the so-called Oracle property. A simulation example is given to demonstrate the performance of the method.
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| 9. |
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Three Decades of Progress in Control Sciences : Dedicated to Chris Byrnes and Anders Lindquist
- 2010. - 1
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Samlingsverk (redaktörskap) (övrigt vetenskapligt/konstnärligt)abstract
- Features contributions from experts in control researchCelebrates the 60th birthday of Chris Byrnes and Anders LindquistHas a celebrative flavor and at the same time contains reference material for researchers interested in control theoryIn this edited collection we commemorate the 60th birthday of Prof. Christopher Byrnes and the retirement of Prof. Anders Lindquist from the Chair of Optimization and Systems Theory at KTH. These papers were presented in part at a 2009 workshop in KTH, Stockholm, honoring the lifetime contributions of Professors Byrnes and Lindquist in various fields of applied mathematics.
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| 10. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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An ADMM Algorithm for a Class of Total Variation Regularized Estimation Problems
- 2012
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Ingår i: Preprints of the 16th IFAC Symposium on System Identification. ; , s. 83-88
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 11. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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New Square-Root Factorization of Inverse Toeplitz Matrices
- 2010
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Ingår i: IEEE Signal Processing Letters. - : IEEE. - 1070-9908 .- 1558-2361. ; 17:2, s. 137-140
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Tidskriftsartikel (refereegranskat)abstract
- Square-root (in particular, Cholesky) factorization of Toeplitz matrices and of their inverses is a classical area of research. The Schur algorithm yields directly the Cholesky factorization of a symmetric Toeplitz matrix, whereas the Levinson algorithm does the same for the inverse matrix. The objective of this letter is to use results from the theory of rational orthonormal functions to derive square-root factorizations of the inverse of an positive definite Toeplitz matrix. The main result is a new factorization based on the Takenaka-Malmquist functions, that is parameterized by the roots of the corresponding auto-regressive polynomial of order. We will also discuss briefly the connection between our analysis and some classical results such as Schur polynomials and the Gohberg-Semencul inversion formula.
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| 12. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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Non-parametric methods for L-2-gain estimation using iterative experiments
- 2010
-
Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 46:8, s. 1376-1381
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we develop non-parametric methods to estimate the L-2-gain (H-infinity-norm) of a linear dynamical system from iterative experiments. This work is mainly motivated by model error modeling, where the error dynamics are more complex than can be captured by a low order parametric model. The standard system identification approach to the gain estimation problem is to estimate a parametric model of the system, which is then used to calculate the gain. If it is possible to update the input signal during the experiment, an alternative way is to iteratively optimize the input signal in order to maximize the estimated input to output gain. A key observation is that the gradient of the gain with respect to the input signal can, without knowing a model, be found from two experiments. Iterative numerical methods for calculation of eigenvalues of matrices, e.g., the Power Method or the Lanczos Method, can then be applied to update the input signal sequence between experiments in order to find the maximum gain. The main difficulty compared to the corresponding eigenvalue problem in numerical analysis is the effects of additive measurement noise, which require modified schemes that avoid bias errors. Three such related methods are derived and evaluated by a numerical example. Partial results on convergence and statistical properties of the gain estimator are given. A constrained stochastic gradient method with local optimization of step-length gives the best numerical results in the case of noisy data.
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| 13. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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On estimation of the gain of a dynamical system
- 2011
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Ingår i: 2011 Digital Signal Processing and Signal Processing Education Meeting, DSP/SPE 2011. - : IEEE. - 9781612842271 ; , s. 364-369
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Konferensbidrag (refereegranskat)abstract
- We analyze and compare methods to estimate the 2-gain ( ∞-norm) of a stable linear dynamical system, that is the maximum of the absolute value of the corresponding frequency response. The standard approach is to estimate a parametric model of the system, which then is used for gain calculation. An asymptotic error variance expression for ∞-norm estimates based on finite impulse response (FIR) models is presented. We then study the problem of finding the minimum variance excitation signal that satisfies a given error variance bound for the FIR model gain estimate. It is shown that a sinusoidal signal with frequency equal to the peak frequency of the system is minimum variance optimal. The second approach to gain estimation is based on iterative experiments, and is inspired by numerical methods eigenvalue calculation. The asymptotic statistical properties of such gain estimation methods are compared to the FIR model approach. A transparent expression for the additional variance cost of using iterative experiments is derived. Finally, we present some ideas for input sequence estimation based on iterative experiments.
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| 14. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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On l1 Mean and Variance Filtering
- 2011
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Ingår i: Proceedings of the 45th Annual Asilomar Conference on Signals, Systems, and Computers 2011. - : IEEE. - 9781467303231 ; , s. 1913-1916
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Konferensbidrag (refereegranskat)abstract
- This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumption is that the mean value is piecewise constant in time, and the task is to estimate the change times and the mean values within the segments. The second case is when the mean value is constant, but the variance can change. The assumption is that the variance is piecewise constant in time, and we want to estimate change times and the variance values within the segments. To find solutions to these problems, we will study an l_1 regularized maximum likelihood method, related to the fused lasso method and l_1 trend filtering, where the parameters to be estimated are free to vary at each sample. To penalize variations in the estimated parameters, the $l_1$-norm of the time difference of the parameters is used as a regularization term. This idea is closely related to total variation denoising. The main contribution is that a convex formulation of this variance estimation problem, where the parametrization is based on the inverse of the variance, can be formulated as a certain $l_1$ mean estimation problem. This implies that results and methods for mean estimation can be applied to the challenging problem of variance segmentation/estimation
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| 15. |
- Wahlberg, Bo, 1959-, et al.
(författare)
-
On optimal input design in system identification for control
- 2010
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Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781424477463 ; , s. 5548-5553
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Konferensbidrag (refereegranskat)abstract
- This paper considers a recently proposed framework for experiment design in system identification for control. We study model based control design methods, such as Model Predictive Control, where the model is obtained by means of a prediction error system identification method. The degradation in control performance due to uncertainty in the model estimate is specified by an application cost function. The objective is to find a minimum variance input signal, to be used in system identification experiment, such that the control application specification is guaranteed with a given probability when using the estimated model in the control design. We provide insight in the potentials of this approach by finite impulse response model examples, for which it is possible to analytically solve the optimal input problem. The examples show how the control specifications directly affect the excitation conditions in the system identification experiment.
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| 16. |
- Wahlberg, Bo, 1959-, et al.
(författare)
-
On optimal input signal design for frequency response estimation
- 2010
-
Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781424477463 ; , s. 302-307
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Konferensbidrag (refereegranskat)abstract
- This paper studies optimal input excitation design for parametric frequency response estimation. The objective is to minimize the uncertainty of functions of the frequency response estimate at a specified frequency ω while limiting the power of the input signal. We focus on least-squares estimation of Finite Impulse Response (FIR) models and minimum variance input design. The optimal input problem is formulated as a convex optimization problem (semi-definite program) in the second order statistics of the input signal. We analytically characterize the optimal solution for first order FIR systems with two parameters, and perform a numerical study to obtain insights in the optimal solution for higher order models. The optimal solution is compared to the case when a sinusoidal input signal, with frequency ω and amplitude that gives the same accuracy as the optimal input, is used as excitation signal. For first order FIR models with two parameters the input signal power can be reduced at best by a factor of two by using the optimal input signal compared with such a sinusoidal input signal. Numerical studies show that less is in general gained for higher order systems, for which a sinusoidal input signal with frequency ω often is optimal. We consider estimation of the ℋ ∞-norm of a stable linear system, that is the maximum of the absolute value of the corresponding frequency response. An asymptotic error variance expression for ℋ∞-norm estimates is derived.
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| 17. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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On Optimal Input Signal Design for Identification of Output Error Models
- 2011
-
Ingår i: Proceedings of the IEEE Conference on Decision and Control. - : IEEE. - 9781612848006
-
Konferensbidrag (refereegranskat)abstract
- This paper extends recent results on minimum variance input signal design for identification of Finite Impulse Response (FIR) models to the Output Error (OE) system identification case. The idea is to use "the useful input parametrization" for OE models proposed by Stoica and Söderström (1982). The advantage of this parametrization is that the Toeplitz covariance matrix structure instrumental in the FIR analysis also holds for this OE model input representation after a transformation. However, an issue is that the corresponding minimum variance cost function for the OE case will be more complicated than for FIR models, and that the dimension of the optimization problem will be of one degree higher than for the corresponding FIR case. The proposed OE framework is applied to minimum variance input signal design in system identification frequency response estimation and model predictive control. The results are illustrated by numerical examples.
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| 18. |
- Wahlberg, Bo, 1959-, et al.
(författare)
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On the Performance of Optimal Input Signals for Frequency Response Estimation
- 2012
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE. - 0018-9286 .- 1558-2523. ; 57:5, s. 766-771
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem of minimum-variance excitation design for frequency response estimation based on finite impulse response (FIR) and output error (OE) models. The objective is to minimize the power of the input signal to be used in the system identification experiment subject to a model accuracy constraint. For FIR and OE models this leads to a finite dimensional semi-definite programming optimization problem. We study, in detail, how to apply this approach to the estimation of the frequency response at a given frequency, . The first case concerns minimizing the asymptotic variance of the estimated frequency response based on an FIR model estimate. We compare the optimal input signal with a sinusoidal signal with frequency that gives the same model accuracy, and show that the input power can, at best, be reduced by a factor of two when using the optimal input signal. Conditions are given under which the sinusoidal signal is optimal, and it is shown that this is a common case for higher order FIR models. Next, we study FIR model based estimation of the absolute value and phase of the frequency response at a given frequency, . We derive the corresponding optimal input signals and compare their performances with that of a sinusoidal input signal with frequency . The relative reduction of input power when using the optimal solution is at best a factor of two. Finally, we discuss how to extend the FIR results to OE system identification by using an input parametrization proposed by Stoica and Söderström (1982).
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