| 1. |
- Wills, Adrian, et al.
(författare)
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Affinely Parametrized State-space Models: Ways to Maximize the Likelihood Function
- 2018
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Ingår i: 18th IFAC Symposium on System Identification (SYSID), Proceedings. - : ELSEVIER SCIENCE BV. ; , s. 718-723
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Konferensbidrag (refereegranskat)abstract
- Using Maximum Likelihood (or Prediction Error) methods to identify linear state space model is a prime technique. The likelihood function is a nonconvex function and care must be exercised in the numerical maximization. Here the focus will be on affine parameterizations which allow some special techniques and algorithms. Three approaches to formulate and perform the maximization are described in this contribution: (1) The standard and well known Gauss Newton iterative search, (2) a scheme based on the EM (expectation-maximization) technique, which becomes especially simple in the affine parameterization case, and (3) a new approach based on lifting the problem to a higher dimension in the parameter space and introducing rank constraints. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
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| 2. |
- Yu, Chengpu, et al.
(författare)
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Constrained Subspace Method for the Identification of Structured State-Space Models (COSMOS)
- 2020
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 65:10, s. 4201-4214
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Tidskriftsartikel (refereegranskat)abstract
- In this article, a unified identification framework called constrained subspace method for structured state-space models (COSMOS) is presented, where the structure is defined by a user-specified linear or polynomial parametrization. The new approach operates directly from the input and output data, which differs from the traditional two-step method that first obtains a state-space realization followed by the system-parameter estimation. The new identification framework relies on a subspace inspired linear regression problem which may not yield a consistent estimate in the presence of process noise. To alleviate this problem, the linear regression formulation is imposed by structured and low-rank constraints in terms of a finite set of system Markov parameters and the user specified model parameters. The nonconvex nature of the constrained optimization problem is dealt with by transforming the problem into a difference-of-convex optimization problem, which is then handled by the sequential convex programming strategy. Numerical simulation examples show that the proposed identification method is more robust than the classical prediction-error method initialized by random initial values in converging to local minima, but at the cost of heavier computational burden.
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| 3. |
- Yu, Chengpu, et al.
(författare)
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Gray Box Identification Using Difference of Convex Programming
- 2017
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Ingår i: IFAC PAPERSONLINE. - : ELSEVIER SCIENCE BV. ; , s. 9462-9467
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Konferensbidrag (refereegranskat)abstract
- Gray-box identification is prevalent in modeling physical and networked systems. However, due to the non-convex nature of the gray-box identification problem, good initial parameter estimates are crucial for a successful application. In this paper, a new identification method is proposed by exploiting the low-rank and structured Hankel matrix of impulse response. This identification problem is recasted into a difference-of-convex programming problem, which is then solved by the sequential convex programming approach with the associated initialization obtained by nuclear-norm optimization. The presented method aims to achieve the maximum impulse-response fitting while not requiring additional (non-convex) conditions to secure non-singularity of the similarity transformation relating the given state space matrices to the gray-box parameterized ones. This overcomes a persistent shortcoming in a number of recent contributions on this topic, and the new method can be applied for the structured state-space realization even if the involved system parameters are unidentifiable. The method can be used both for directly estimating the gray-box parameters and for providing initial parameter estimates for further iterative search in a conventional gray-box identification setup. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
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| 4. |
- Yu, Chengpu, et al.
(författare)
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Identification of structured state-space models
- 2018
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Ingår i: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 90, s. 54-61
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Tidskriftsartikel (refereegranskat)abstract
- Identification of structured state-space (gray-box) model is popular for modeling physical and network systems. Due to the non-convex nature of the gray-box identification problem, good initial parameter estimates are crucial for successful applications. In this paper, the non-convex gray-box identification problem is reformulated as a structured low-rank matrix factorization problem by exploiting the rank and structured properties of a block Hankel matrix constructed by the system impulse response. To address the low-rank optimization problem, it is first transformed into a difference-of-convex (DC) formulation and then solved using the sequentially convex relaxation method. Compared with the classical gray-box identification methods like the prediction-error method (PEM), the new approach turns out to be more robust against converging to non-global minima, as supported by a simulation study. The developed identification can either be directly used for gray-box identification or provide an initial parameter estimate for the PEM. (C) 2018 Elsevier Ltd. All rights reserved.
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| 5. |
- Yu, Chengpu, et al.
(författare)
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Subspace Identification of Continuous-Time Models Using Generalized Orthonormal Bases
- 2017
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Ingår i: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC). - : IEEE. - 9781509028733
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Konferensbidrag (refereegranskat)abstract
- The continuous-time subspace identification using state-variable filtering has been investigated for a long time. Due to the simple orthogonal basis functions that were adopted by the existing methods, the identification performance is quite sensitive to the selection of the system-dynamic parameter associated with an orthogonal basis. To cope with this problem, a subspace identification method using generalized orthonormal(Takenaka-Malmquist) basis functions is developed, which has the potential to perform better than the existing state-variable filtering methods since the adopted Takenaka-Malmquist basis has more degree of freedom in selecting the system-dynamic parameters. As a price for the flexibility of the generalized orthonormal bases, the transformed state-space model is time-varying or parameter-varying which cannot be identified using traditional subspace identification methods. To this end, a new subspace identification algorithm is developed by exploiting the structural properties of the time-variant system matrices, which is then validated by numerical simulations.
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| 6. |
- Yu, Chengpu, et al.
(författare)
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Subspace Identification of Local Systems in One-Dimensional Homogeneous Networks
- 2018
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 63:4, s. 1126-1131
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Tidskriftsartikel (refereegranskat)abstract
- This note considers the identification of large-scale one-dimensional networks consisting of identical LTI dynamical systems. A subspace identification method is developed that only uses local input-output information and does not rely on knowledge about the local state interaction. The proposed identification method estimates the Markov parameters of a locally lifted system, following the state-space realization of a single subsystem. The Markov-parameter estimation is formulated as a rank minimization problem by exploiting the low-rank property and the two-layer Toeplitz structural property in the data equation, whereas the state-space realization of a single subsystem is formulated as a structured low-rank matrix-factorization problem. The effectiveness of the proposed identification method is demonstrated by simulation examples.
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