| 1. |
- Eckhard, Diego, et al.
(författare)
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Cost function shaping of the output error criterion
- 2017
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 76, s. 53-60
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Tidskriftsartikel (refereegranskat)abstract
- Identification of an output error model using the prediction error method leads to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because in most cases both the corresponding objective function and the search space are nonconvex. The difficulty in solving the optimization problem depends mainly on the experimental conditions, more specifically on the spectra of the input/output data collected from the system. It is therefore possible to improve the convergence of the algorithms by properly choosing the data prefilters; in this paper we show how to perform this choice. We present the application of the proposed approach to case studies where the standard algorithms tend to fail to converge to the global minimum.
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| 2. |
- Eckhard, Diego, et al.
(författare)
-
Input design as a tool to improve the convergence of PEM
- 2013
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 49:11, s. 3282-3291
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Tidskriftsartikel (refereegranskat)abstract
- The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The shape of the cost function, and hence the difficulty in solving the optimization problem, depends directly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. Therefore, it seems plausible to improve the convergence to the global minimum by properly choosing the spectrum of the input; in this paper, we address this problem. We present a condition for convergence to the global minimum of the cost function and propose its inclusion in the input design. We present the application of the proposed approach to case studies where the algorithms tend to get trapped in nonglobal minima.
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| 3. |
- Eckhard, Diego, et al.
(författare)
-
Mean-squared error experiment design for linear regression models
- 2012
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Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 1629-1634
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Konferensbidrag (refereegranskat)abstract
- This work solves an experiment design problem for a linear regression problem using a reduced order model. The quality of the model is assessed using a mean square error measure that depends linearly on the parameters. The designed input signal ensures a predefined quality of the model while minimizing the input energy.
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| 4. |
- Eckhard, Diego, et al.
(författare)
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On the convergence of the Prediction Error Method to its global minimum
- 2012
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Ingår i: 16th IFAC Symposium on System Identification. - : IFAC. - 9783902823069 ; , s. 698-703
-
Konferensbidrag (refereegranskat)abstract
- The Prediction Error Method (PEM) is related to an optimization problem built on input/output data collected from the system to be identified. It is often hard to find the global solution of this optimization problem because the corresponding objective function presents local minima and/or the search space is constrained to a nonconvex set. The existence of local minima, and hence the difficulty in solving the optimization, depends mainly on the experimental conditions, more specifically on the spectrum of the input/output data collected from the system. It is therefore possible to avoid the existence of local minima by properly choosing the spectrum of the input; in this paper we show how to perform this choice. We present sufficient conditions for the convergence of PEM to the global minimum and from these conditions we derive two approaches to avoid the existence of nonglobal minima. We present the application of one of these two approaches to a case study where standard identification toolboxes tend to get trapped in nonglobal minima.
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