| 1. |
- Bijl, Hildo, et al.
(author)
-
Mean and variance of the LQG cost function
- 2016
-
In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 67, s. 216-223
-
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.
|
|
| 2. |
|
|
| 3. |
|
|
| 4. |
- Chou, C. T., et al.
(author)
-
Continuous-Time Identification of SISO Systems using Laguerre Functions
- 1999
-
In: IEEE Transactions on Signal Processing. - 1053-587X. ; 47:2, s. 349-362
-
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.
|
|
| 5. |
- Doelman, Reinier, et al.
(author)
-
Identification of the dynamics of time-varying phase aberrations from time histories of the point-spread function
- 2019
-
In: Optical Society of America. Journal A. - : OPTICAL SOC AMER. - 1084-7529 .- 1520-8532. ; 36:5, s. 809-817
-
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.
|
|
| 6. |
- Dong, Jianfei, et al.
(author)
-
Robust Fault Detection With Statistical Uncertainty in Identified Parameters
- 2012
-
In: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 60:10, s. 5064-5076
-
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.
|
|
| 7. |
- Dong, Jianfei, et al.
(author)
-
Robust Fault Isolation With Statistical Uncertainty in Identified Parameters
- 2012
-
In: IEEE Transactions on Signal Processing. - : IEEE Signal Processing Society. - 1053-587X .- 1941-0476. ; 60:10, s. 5556-5561
-
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.
|
|
| 8. |
- Hansson, Anders, et al.
(author)
-
Distributed system identification with ADMM
- 2014
-
In: Proceedings of the 53rd IEEE Conference on Decision and Control. - Los Angeles. - 9781479977451 - 9781467360883 ; , s. 290-295
-
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.
|
|
| 9. |
|
|
| 10. |
- Haverkamp, B. R. J., et al.
(author)
-
Continuous-Time Subspace Model Identification Method Using Laguerre Filtering
- 1997
-
In: IFAC Proceedings Volumes. ; 30:11, s. 1093-1098
-
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.
|
|
