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| 2. |
- Barenthin, Märta, et al.
(författare)
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Identification for control of multivariable systems: Controller validation and experiment design via LMIs
- 2008
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 44:12, s. 3070-3078
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a new controller validation method for linear multivariable time-invariant models. Classical prediction error system identification methods deliver uncertainty regions which are nonstandard in the robust control literature. Our controller validation criterion computes an upper bound for the worst case performance, measured in terms of the H-infinity-norm of a weighted closed loop transfer matrix, achieved by a given controller over all plants in such uncertainty sets. This upper bound on the worst case performance is computed via an LMI-based optimization problem and is deduced via the separation of graph framework. Our main technical contribution is to derive, within that framework, a very general parametrization for the set of multipliers corresponding to the nonstandard uncertainty regions resulting from PE identification of MIMO systems. The proposed approach also allows for iterative experiment design. The results of this paper are asymptotic in the data length and it is assumed that the model structure is flexible enough to capture the true system.
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| 3. |
- Barenthin, Märta, et al.
(författare)
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Mixed H-2 and H-Infinity$ Input Design for Multivariable Systems
- 2006
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Ingår i: 14th IFAC Symposium on System Identification. ; , s. 1335-1340
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Konferensbidrag (refereegranskat)abstract
- In this contribution a new procedure for input design for identification of linear multivariable systems is proposed. The goal is to minimize the input power used in the system identification experiment. The quality constraint on the estimated model is formulated in H∞. The input design problem is converted to linear matrix inequalities by a separation of graphs theorem. For illustration, the proposed method is applied on a chemical distillation column and the result shows that it is optimal to amplify the low gain direction of the plant.
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| 4. |
- Bombois, Xavier, et al.
(författare)
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Identification for robust H-2 deconvolution filtering
- 2010
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 46:3, s. 577-584
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Tidskriftsartikel (refereegranskat)abstract
- This paper addresses robust deconvolution filtering when the system and noise dynamics are obtained by parametric system identification. Consistent with standard identification methods, the uncertainty in the estimated parameters is represented by an ellipsoidal uncertainty region. Three problems are considered: (1) computation of the worst case H-2 performance of a given deconvolution filter in this uncertainty set; (2) design of a filter which minimizes the worst case H-2 performance in this uncertainty set; (3) input design for the identification experiment, subject to a limited input power budget, such that the filter in (2) gives the smallest possible worst case H-2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to (1) and (2) while the third problem can be treated via iterating between two convex optimization problems.
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| 5. |
- Bombois, Xavier, et al.
(författare)
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On the informativity of direct identification experiments in dynamical networks
- 2023
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 148, s. 110742-
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Tidskriftsartikel (refereegranskat)abstract
- Data informativity is a crucial property to ensure the consistency of the prediction error estimate. This property has thus been extensively studied in the open-loop and in the closed-loop cases, but has only been briefly touched upon in the dynamic network case. In this paper, we consider the prediction error identification of the modules in a row of a dynamic network using the full input approach. Our main contribution is to propose a number of easily verifiable data informativity conditions for this identification problem. Among these conditions, we distinguish a sufficient data informativity condition that can be verified based on the topology of the network and a necessary and sufficient data informativity condition that can be verified via a rank condition on a matrix of coefficients that are related to a full-order model structure of the network. These data informativity conditions allow to determine different situations (i.e., different excitation patterns) leading to data informativity. In order to be able to distinguish between these different situations, we also propose an optimal experiment design problem that allows to determine the excitation pattern yielding a certain pre-specified accuracy with the least excitation power.
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| 6. |
- Bombois, Xavier, et al.
(författare)
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Optimal experiment design for hypothesis testing applied to functional magnetic resonance imaging
- 2011
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Ingår i: Proceedings of the 18th IFAC World Congress. ; , s. 9953-9958
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Konferensbidrag (refereegranskat)abstract
- Hypothesis testing is a classical methodology of making decisions using experimental data. In hypothesis testing one seeks to discover evidence that either accepts or rejects a given null hypothesis H0. The alternative hypothesis H1 is the hypothesis that is accepted when H0 is rejected. In hypothesis testing, the probability of deciding H1 when in fact H0 is true is known as the false alarm rate, whereas the probability of deciding H1when in fact H1is true is known as the detection rate (or power) of the test. It is not possible to optimize both rates simultaneously. In this paper, we consider the problem of determining the data to be used for hypothesis testing that maximize the detection rate for a given false alarm rate. We consider in particular a hypothesis test which is relevant in functional magnetic resonance imaging (fMRI).
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| 7. |
- Bombois, Xavier, et al.
(författare)
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Optimal identification experiment design for the interconnection of locally controlled systems
- 2018
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 89, s. 169-179
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers the identification of the modules of a network of locally controlled systems (multi-agent systems). Its main contribution is to determine the least perturbing identification experiment that will nevertheless lead to sufficiently accurate models of each module for the global performance of the network to be improved by a redesign of the decentralized controllers. Another contribution is to determine the experimental conditions under which sufficiently informative data (i.e. data leading to a consistent estimate) can be collected for the identification of any module in such a network.
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| 8. |
- Bombois, Xavier, et al.
(författare)
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Optimal input design for robust H2 deconvolution filtering
- 2009
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Ingår i: 15th IFAC Symposium on System Identification, SYSID 2009. - : Elsevier BV. ; , s. 934-939
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Konferensbidrag (refereegranskat)abstract
- Deconvolution filtering where the system and noise dynamics are obtained by parametric system identification is considered. Consistent with standard identification methods, ellipsoidal uncertainty in the estimated parameters is considered. Three problems are considered: 1) Computation of the worst case H2 performance of a given deconvolution filter in this uncertainty set. 2) Design of a filter which minimizes the worst case H2 performance in this uncertainty set. 3) Input design for the identification experiment, subject to a limited input power budget, such that the filter in 2) gives the smallest possible worst-case H2 performance. It is shown that there are convex relaxations of the optimization problems corresponding to 1) and 2) while the third problem can be treated via iterating between two convex optimization problems.
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| 9. |
- Bombois, Xavier, et al.
(författare)
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Robust optimal identification experiment design for multisine excitation
- 2021
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Ingår i: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 125
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Tidskriftsartikel (refereegranskat)abstract
- In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal.
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| 10. |
- Colin, Kevin, et al.
(författare)
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Data Informativity for the Closed-Loop Identification of MISO ARX Systems
- 2021
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Ingår i: IFAC PAPERSONLINE. - : Elsevier BV. - 2405-8963. ; , s. 779-784
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Konferensbidrag (refereegranskat)abstract
- In the Prediction Error identification framework, it is crucial that the collected data are informative with respect to the chosen model structure to get a consistent estimate. In this work, we focus on the data informativity property for the identification of multi-inputs single-output ARX systems in closed-loop and we derive a necessary and sufficient condition to verify if a given multisine external excitation combined with the feedback introduced by the controller yields informative data with respect to the chosen model structure.
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