| 1. |
- Bijl, Hildo, et al.
(author)
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Mean and variance of the LQG cost function
- 2016
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In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 67, s. 216-223
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Journal article (peer-reviewed)abstract
- Linear Quadratic Gaussian (LQG) systems are well-understood and methods to minimize the expected cost are readily available. Less is known about the statistical properties of the resulting cost function. The contribution of this paper is a set of analytic expressions for the mean and variance of the LQG cost function. These expressions are derived using two different methods, one using solutions to Lyapunov equations and the other using only matrix exponentials. Both the discounted and the non-discounted cost function are considered, as well as the finite-time and the infinite-time cost function. The derived expressions are successfully applied to an example system to reduce the probability of the cost exceeding a given threshold.
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| 2. |
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| 3. |
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| 4. |
- Chou, C. T., et al.
(author)
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Continuous-Time Identification of SISO Systems using Laguerre Functions
- 1999
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In: IEEE Transactions on Signal Processing. - 1053-587X. ; 47:2, s. 349-362
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Journal article (peer-reviewed)abstract
- This paper looks at the problem of estimating the coefficients of a continuous-time transfer function given samples of its input and output data. We first prove that any nth-order continuous-time transfer function can be written as a fraction of the form /spl Sigma//sub k=0//sup n/b~/sub k/L/sub k/(s)//spl Sigma//sub k=0//sup n/a~/sub k/L/sub k/(s), where L/sub k/(s) denotes the continuous-time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme that consists of the following two steps: (1) filter both the input and output data by L/sub k/(s), and (2) estimate {a~/sub k/, b~/sub k/} and relate them to the coefficients of the transfer function. For practical implementation, we require the discrete-time approximation of L/sub k/(s) since only sampled data is available. We propose a scheme that is based on higher order Pade approximations, and we prove that this scheme produces discrete-time filters that are approximately orthogonal and, consequently, a well-conditioned numerical problem. Some other features of this new algorithm include the possibility to implement it as either an off-line or a quasi-on-line algorithm and the incorporation of constraints on the transfer function coefficients. A simple example is given to illustrate the properties of the proposed algorithm.
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| 5. |
- Doelman, Reinier, et al.
(author)
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Identification of the dynamics of time-varying phase aberrations from time histories of the point-spread function
- 2019
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In: Optical Society of America. Journal A. - : OPTICAL SOC AMER. - 1084-7529 .- 1520-8532. ; 36:5, s. 809-817
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Journal article (peer-reviewed)abstract
- To optimally compensate for time-varying phase aberrations with adaptive optics, a model of the dynamics of the aberrations is required to predict the phase aberration at the next time step. We model the time-varying behavior of a phase aberration, expressed in Zernike modes, by assuming that the temporal dynamics of the Zernike coefficients can be described by a vector-valued autoregressive (VAR) model. We propose an iterative method based on a convex heuristic for a rank-constrained optimization problem, to jointly estimate the parameters of the VAR model and the Zernike coefficients from a time series of measurements of the point-spread function (PSF) of the optical system. By assuming the phase aberration is small, the relation between aberration and PSF measurements can be approximated by a quadratic function. As such, our method is a blind identification method for linear dynamics in a stochastic Wiener system with a quadratic nonlinearity at the output and a phase retrieval method that uses a time-evolution-model constraint and a single image at every time step. (c) 2019 Optical Society of America.
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| 6. |
- Dong, Jianfei, et al.
(author)
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Robust Fault Detection With Statistical Uncertainty in Identified Parameters
- 2012
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In: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 60:10, s. 5064-5076
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Journal article (peer-reviewed)abstract
- Detection of faults that appear as additive unknown input signals to an unknown LTI discrete-time MIMO system is considered. State of the art methods consist of the following steps. First, either the state space model or certain projection matrices are identified from data. Then, a residual generator is formed based on these identified matrices, and this residual generator is used for online fault detection. Existing techniques do not allow for compensating for the identification uncertainty in the fault detection. This contribution explores a recent data-driven approach to fault detection. We show first that the identified parametric matrices in this method depend linearly on the noise contained in the identification data, and then that the on-line computed residual also depends linearly on the noise. This allows an analytic design of a robust fault detection scheme, that takes both the noise in the online measurements as well as the identification uncertainty into account. We illustrate the benefits of the new method on a model of aircraft dynamics extensively studied in literature.
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| 7. |
- Dong, Jianfei, et al.
(author)
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Robust Fault Isolation With Statistical Uncertainty in Identified Parameters
- 2012
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In: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 60:10, s. 5556-5561
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Journal article (peer-reviewed)abstract
- This correspondence is a companion paper to [J. Dong, M. Verhaegen, and F. Gustafsson, "Robust Fault Detection With Statistical Uncertainty in Identified Parameters," IEEE Trans. Signal Process., vol. 60, no. 10, Oct. 2012], extending it to fault isolation. Also, here, use is made of a linear in the parameters model representation of the input-output behavior of the nominal system (i.e. fault-free). The projection of the residual onto directions only sensitive to individual faults is robustified against the stochastic errors of the estimated model parameters. The correspondence considers additive error sequences to the input and output quantities that represent failures like drift, biased, stuck, or saturated sensors/actuators.
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| 8. |
- Hansson, Anders, et al.
(author)
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Distributed system identification with ADMM
- 2014
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In: Proceedings of the 53rd IEEE Conference on Decision and Control. - Los Angeles. - 9781479977451 - 9781467360883 ; , s. 290-295
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Conference paper (peer-reviewed)abstract
- This paper presents identification of both network connected systems as well as distributed systems governed by PDEs in the framework of distributed optimization via the Alternating Direction Method of Multipliers. This approach opens first the possibility to identify distributed models in a global manner using all available data sequences and second the possibility for a distributed implementation. The latter will make the application to large scale complex systems possible. In addition to outlining a new large scale identification method, illustrations are shown for identifying both network connected systems and discretized PDEs.
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| 9. |
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| 10. |
- Haverkamp, B. R. J., et al.
(author)
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Continuous-Time Subspace Model Identification Method Using Laguerre Filtering
- 1997
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In: IFAC Proceedings Volumes. ; 30:11, s. 1093-1098
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Journal article (peer-reviewed)abstract
- This paper introduces a time domain subspace model identification method, for the identification of continuous-time MIMO state-space models. The measured signals are assumed to be contaminated with both process and measurement noise. The method uses a bilinear transformation on the data, to identify the system in an alternative domain. Afterwards the system is transformed back. An example of the method is presented.
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| 11. |
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| 12. |
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| 13. |
- Johansson, Rolf, et al.
(author)
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Behavioral Model Identification
- 1998
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In: Proc. IEEE Conf. Decision and Control (CDC'98), Tampa, Florida, December 1998. ; , s. 126-131
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Conference paper (peer-reviewed)abstract
- This paper presents theory and algorithms for system identification suitable for the framework of behavioral system theory. An algorithm based on algebraic system theory and realization theory (Ho-Kalman realization) in a subspace model identification framework is presented. The novel approach considered consists of the formulation of input-output data as an impulse response model and the subsequent application of state-space realization. As a special case, behavioral model identification from finite data sequences is demonstrated.
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| 14. |
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| 15. |
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| 16. |
- Johansson, Rolf, et al.
(author)
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Residual Models and Stochastic Realization in State-Space Identification
- 2001
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In: International Journal of Control. - : Informa UK Limited. - 0020-7179 .- 1366-5820. ; 74:10, s. 988-995
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Journal article (peer-reviewed)abstract
- This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Our formulation includes the problem of rank-deficient residual covariance matrices, a case which is encountered in applications with mixed stochastic-deterministic input-output properties as well as for cases where outputs are linearly dependent. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.
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| 17. |
- Johansson, Rolf, et al.
(author)
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Residual Models and Stochastic Realization in State-Space System Identification
- 1998
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In: Proceedings of the 37th IEEE Conference on Decision and Control.
-
Conference paper (peer-reviewed)abstract
- This paper presents theory and algorithms for validation in system identification of state-space models from finite input-output sequences in a subspace model identification framework. Similar to the case of prediction-error identification, it is shown that the resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.
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| 18. |
- Johansson, Rolf, et al.
(author)
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State-Space System Identification of Robot Manipulator Dynamics
- 2000
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In: Mechatronics. - 0957-4158. ; 10:3, s. 403-418
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Journal article (peer-reviewed)abstract
- We have applied and evaluated system identification methods using both commercial software and dedicated subspace model identification software (MOESP). Results using the different software tools have been similar (but not identical) in accuracy and predictive power, the main differences being the time required for computation and occasional failures of one algorithm in delivery of a stable model. For linear model identification all methods tested failed to provide residuals, i.e. model misfit, uncorrelated with input and without significant autocorrelation. As a result, no linear stochastic innovations model could be formulated in any satisfactory manner. However, model-order tests based on singular values suggest that a low model order be sufficient for input-output modeling to within a modeling accuracy of 2-5%. Thus, the identification of a state-space model combined with a friction model provides effective means to modeling in robotics.
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| 19. |
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| 20. |
- Johansson, Rolf, et al.
(author)
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Stochastic Theory of Continuous-Time State-Space Identification
- 1999
-
In: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-587X. ; 47:1, s. 41-51
-
Journal article (peer-reviewed)abstract
- This paper presents theory, algorithms, and validation results for system identification of continuous-time state-space models from finite input-output sequences. The algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous-time context. The resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs, thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem.
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| 21. |
- Johansson, Rolf, et al.
(author)
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Stochastic Theory of Continuous-Time State-Space Identification
- 1997
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In: Proceedings of the 36th IEEE Conference on Decision and Control. ; , s. 1866-1871
-
Conference paper (peer-reviewed)abstract
- Presents theory, algorithms and validation results for system identification of continuous-time state-space models from finite input-output sample sequences. The algorithms developed are methods of subspace model identification and stochastic realization adapted to the continuous-time context. The resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem
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| 22. |
- Klingspor, Måns, et al.
(author)
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Input selection in N2SID using group lasso regularization
- 2017
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In: IFAC PAPERSONLINE. - : ELSEVIER SCIENCE BV. ; , s. 9474-9479
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Conference paper (peer-reviewed)abstract
- Input selection is an important and oftentimes difficult challenge in system identification. In order to achieve less complex models, irrelevant inputs should be methodically and correctly discarded before or under the estimation process. In this paper we introduce a novel method of input selection that is carried out as a natural extension in a subspace method. We show that the method robustly and accurately performs input selection at various noise levels and that it provides good model estimates. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
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| 23. |
- Scobee, Dexter, et al.
(author)
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Nuclear Norm Minimization for Blind Subspace Identification (N2BSID)
- 2015
-
In: 2015 IEEE 54th Annual Conference on Decision and Control (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781479978861 - 9781479978847 - 9781479978854 - 9781479978878 ; , s. 2127-2132
-
Conference paper (peer-reviewed)abstract
- In many practical applications of system identification, it is not feasible to measure both the inputs applied to the system as well as the output. In such situations, it is desirable to estimate both the inputs and the dynamics of the system simultaneously; this is known as the blind identification problem. In this paper, we provide a novel extension of subspace methods to the blind identification of multiple-input multiple-output linear systems. We assume that our inputs lie in a known subspace, and we are able to formulate the identification problem as rank constrained optimization, which admits a convex relaxation. We show the efficacy of this formulation with a numerical example.
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| 24. |
- Verdult, Vincent, et al.
(author)
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Identification of Composite Local Linear State-Space Models using a Projected Gradient Search
- 2002
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In: International Journal of Control. - : Informa UK Limited. - 0020-7179 .- 1366-5820. ; 75:16, s. 1385-1398
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Journal article (peer-reviewed)abstract
- An identification method is described to determine a weighted combination of local linear state-space models from input and output data. Normalized radial basis functions are used for the weights, and the system matrices of the local linear models are fully parameterized. By iteratively solving a non-linear optimization problem, the centres and widths of the radial basis functions and the system matrices of the local models are determined. To deal with the non-uniqueness of the fully parameterized state-space system, a projected gradient search algorithm is described. It is pointed out that when the weights depend only on the input, the dynamical gradient calculations in the identification method are stable. When the weights also depend on the output, certain difficulties might arise. The methods are illustrated using serveral examples that have been studied in the literature before.
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| 25. |
- Verhaegen, Michel, et al.
(author)
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N2SID: Nuclear norm subspace identification of innovation models
- 2016
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In: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 72, s. 57-63
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Journal article (peer-reviewed)abstract
- The identification of multivariable state space models in innovation form is solved in a subspace identification framework using convex nuclear norm optimization. The convex optimization approach allows to include constraints on the unknown matrices in the data-equation characterizing subspace identification methods, such as the lower triangular block-Toeplitz of weighting matrices constructed from the Markov parameters of the unknown observer. The classical use of instrumental variables to remove the influence of the innovation term on the data equation in subspace identification is avoided. The avoidance of the instrumental variable projection step has the potential to improve the accuracy of the estimated model predictions, especially for short data length sequences. (C) 2016 Elsevier Ltd. All rights reserved.
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