Direct identification of continuous-time linear parameter-varying input/output models
05 May 2011-Iet Control Theory and Applications (Institution of Engineering and Technology (IET))-Vol. 5, Iss: 7, pp 878-888
TL;DR: In this paper, the authors proposed a direct identification of CT-LPV systems in an input-output setting, focusing on the case when the noise part of the data generating system is an additive discrete-time (DT) coloured noise process.
Abstract: Controllers in the linear parameter-varying (LPV) framework are commonly designed in continuous time (CT) requiring accurate and low-order CT models of the system. However, identification of CT-LPV models is largely unsolved, representing a gap between the available LPV identification methods and the needs of control synthesis. In order to bridge this gap, direct identification of CT-LPV systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive discrete-time (DT) coloured noise process. To provide consistent model parameter estimates in this setting, a refined instrumental variable (IV) approach is proposed and its properties are analysed based on the prediction-error framework. The benefits of the introduced direct CT-IV approach over identification in the DT case are demonstrated through a representative simulation example inspired by the Rao-Garnier benchmark.
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TL;DR: An adapted version of the simplified refined instrumental variable method is first proposed to estimate the parameters of the fractional model when all the differentiation orders are assumed known, and an optimization approach based on the use of the developed instrumental variable estimator is presented.
188 citations
TL;DR: The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box-Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms.
94 citations
Cites background from "Direct identification of continuous..."
...More recent papers in this general field include [12,8,42,21,48,22,40,34]....
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TL;DR: In this article, the authors discuss the importance and relevance of direct continuous-time system identification and how this relates to the solution for model identification problems in practical applications and discuss the software tools available and illustrate their advantages via simulated and real data examples.
87 citations
TL;DR: The main aim is to discuss the advantages of direct, continuous-time model identification with the help of illustrative examples that are all based on real data from practical applications, and the latest and most sophisticated time domain identification algorithm is used in these examples.
Abstract: The direct identification and estimation of continuous-time models from sampled data is now mature. This paper does not present any new methodology, nor does it compare the performance of existing methods. Its main aim is to discuss the advantages of direct, continuous-time model identification with the help of illustrative examples that are all based on real data from practical applications. Although the specific method of statistical parameter estimation is relatively unimportant in this regard, the latest and most sophisticated time domain identification algorithm that is freely available to the reader is used in these examples in order to ensure that the results reflect the best performance that can be achieved at this time by time-domain identification.
72 citations
TL;DR: In this paper, a kernel-based estimator for the identification of continuous-time linear time-varying systems is presented. But the estimator is not suitable for noisy signals and the model complexity is formulated as an optimization problem with continuous variables.
Abstract: A novel estimator for the identification of continuous-time linear time-varying systems is presented in this paper. The estimator uses kernel-based regression to identify the time-varying coefficients of a linear ordinary differential equation, based on noisy samples of the input and output signals. The estimator adopts a mixed time- and frequency-domain formulation, which allows it to be formulated as the solution of a set of algebraic equations, without relying on finite differences to approximate the time derivatives. Since a kernel-based approach is used, the model complexity selection of the time-varying parameters is formulated as an optimisation problem with continuous variables. Variance and bias expressions of the estimate are derived and validated on a simulation example. Also, it is shown that, in highly noisy environments, the proposed kernel-based estimator provides more reliable results than an ‘Oracle’-based estimator which is deprived of regularisation.
22 citations
References
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Book•
01 Jan 1987
TL;DR: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis and praktische Anwendung der verschiedenen Verfahren zur IdentifIZierung hat.
Abstract: Das Buch behandelt die Systemidentifizierung in dem theoretischen Bereich, der direkte Auswirkungen auf Verstaendnis und praktische Anwendung der verschiedenen Verfahren zur Identifizierung hat. Da ...
20,436 citations
"Direct identification of continuous..." refers background or methods in this paper
...Therefore, similarly to the LTI case, the one-step-ahead prediction error can be expressed and defined as [31]: εθ(tk) = y(tk) − ŷθ(tk), (25)...
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...Assuming that Ho has a stable inverse such that eo(tk) = H o (q)vo(tk), then the classical one-step-ahead predictor can be given a s [31]...
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...Furthermor e, in terms of (6), exactly the same noise assumption is made as in the classical DT Box-Jenkins mo dels (see [31])....
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...} is adopted from the prediction error framework of [31]....
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...Therefore, by using the traditional approach [31], the predictio n of vo(tk) is considered as the conditional expectation ofvo(tk) based on{eo(τ)}τ≤tk−1 which is according to (20): v̂(tk) = v̂(tk | tk−1) = E{vo(tk) | {eo(τ)}τ≤k−1} = ∞ ∑...
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Book•
16 Feb 2013
TL;DR: This well written book is enlarged by the following topics: B-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for theLR and QR algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations and preconditioning techniques.
Abstract: This well written book is enlarged by the following topics:
$B$-splines and their computation, elimination methods for
large sparse systems of linear equations, Lanczos algorithm for
eigenvalue problems, implicit shift techniques for the $LR$ and
$QR$ algorithm, implicit differential equations, differential
algebraic systems, new methods for stiff differential
equations, preconditioning techniques and convergence rate of
the conjugate gradient algorithm and multigrid methods for
boundary value problems. Cf. also the reviews of the German
original editions.
6,270 citations
Book•
05 Oct 1997TL;DR: In this article, the authors introduce linear algebraic Riccati Equations and linear systems with Ha spaces and balance model reduction, and Ha Loop Shaping, and Controller Reduction.
Abstract: 1. Introduction. 2. Linear Algebra. 3. Linear Systems. 4. H2 and Ha Spaces. 5. Internal Stability. 6. Performance Specifications and Limitations. 7. Balanced Model Reduction. 8. Uncertainty and Robustness. 9. Linear Fractional Transformation. 10. m and m- Synthesis. 11. Controller Parameterization. 12. Algebraic Riccati Equations. 13. H2 Optimal Control. 14. Ha Control. 15. Controller Reduction. 16. Ha Loop Shaping. 17. Gap Metric and ...u- Gap Metric. 18. Miscellaneous Topics. Bibliography. Index.
3,471 citations
"Direct identification of continuous..." refers background in this paper
...Commonly LPV controllers are synthesized in continuous time(CT) as stability and performance requirements of the closed loop behavior can be more conveniently expressed in CT, like in a mixed-sensiti vity setting [8]....
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Book•
01 Jan 1978
TL;DR: In this article, the authors present a solution to the Matrix Eigenvalue Problem for linear systems of linear equations, based on linear algebra and linear algebra with nonlinear functions, which they call linear algebraic integration.
Abstract: Error: Its Sources, Propagation, and Analysis. Rootfinding for Nonlinear Equations. Interpolation Theory. Approximation of Functions. Numerical Integration. Numerical Methods for Ordinary Differential Equations. Linear Algebra. Numerical Solution of Systems of Linear Equations. The Matrix Eigenvalue Problem. Appendix. Answers to Selected Problems. Index.
2,608 citations
Book•
01 Sep 2000
TL;DR: A key aspect of the book is the frequent use of real world design examples drawn directly from the authors' industrial experience, represented by over 15 substantial case studies ranging from distillation columns to satellite tracking.
Abstract: From the Publisher:
A key aspect of the book is the frequent use of real world design examples drawn directly from the authors' industrial experience. These are represented by over 15 substantial case studies ranging from distillation columns to satellite tracking. The book is also liberally supported by modern teaching aids available on both an accompanying CD-ROM and Companion Website. Resources to be found there include MATLAB® routines for all examples; extensive PowerPoint lecture notes based on the book; and a totally unique Java Applet-driven "virtual laboratory" that allows readers to interact with the real-world case studies.
1,701 citations
"Direct identification of continuous..." refers background in this paper
...Note that to derive an accurate DT approximation of the system, it is often sufficient in terms of the classical discr etization theory to assume that the sampled free CT signals of the system are restricted to be cons tant in the sampling period [32], which has also been shown in case of LPV systems with static de pendence [9]....
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