| 1. |
- Hjalmarsson, Håkan, et al.
(författare)
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How to Estimate Model Uncertainty in the Case of Under-Modelling
- 1990
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Ingår i: Proceedings of the 1990 American Control Conference. - Linköping : Linköping University. ; , s. 323-324
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In System Identification, traditionally, the uncertainty estimate provided with the model is based on the assumption that the model structure used is capable of achieving a correct system description. This estimate is however not correct unless the parameter estimate is close to a "true" model parameter, that yields white noise residuals. The correct expression is known but more complex. The main difficulty, though, is that it is not easily estimated. We suggest a simple and explicit method for estimating the model uncertainty, applicable also to severe under-modelling. The method is illustrated by an example.
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| 2. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Influence of Model Order on Change Detection in Noise-Free Complex Systems
- 1990
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Ingår i: Proceedings of the 1990 American Control Conference. - Linköping : Linköping University. ; , s. 2388-2393
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In all adaptation problems it is essential to estimate the system's (or signal's) characteristics as quickly as possible. There are several design variables that effect this ability. Forgetting factors in recursive algorithms, band-pass filtering to select interesting frequency ranges, and similar, are of major importance for this problem. Also the model order will affect the speed of adaptation since it influences both the "noise" level arising from unmodelled dynamics and the "variance" that depends on the number of estimated parameters. We discuss in this contribution the role of the model order for adaptation. The conclusion is that provided appropriate regularization is applied there are no disadvantages in the use of (very) high order models other than the computational burden.
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| 3. |
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| 4. |
- Ljung, Lennart, 1946-
(författare)
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A Result of the Mean Square Error Obtained using General Tracking Algorithms
- 1990
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Tracking time-varying properties is of crucial importance in all adaptive algorithms. In this contribution we study a fairly general algorithm for tracking properties of model parameters that can be described in a linear regression form (including AR models and the like). An explicit expression for the mean square error between the estimated and the true (time-varying) parameter is established. For slow adaptation this expression can be arbitrarily well approximated by a much simpler expression. The treatment differs from other related studies using weak convergence theory, averaging, etc. in that the results are not asymptotic in nature and are applicable also to the transient phase as well as over unbounded time intervals.
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| 5. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Adaptation and Tracking in System Identification : A Survey
- 1990
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 26:1, s. 7-21
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Tidskriftsartikel (refereegranskat)abstract
- To track the time-varying dynamics of a system or the time-varying properties of a signal is a fundamental problem in control and signal processing. Many approaches to derive such adaptation algorithms and to analyse their behaviour have been taken. This article gives a survey of basic techniques to derive and analyse algorithms for tracking time-varying systems. Special attention is paid to the study of how different assumptions about the true system's variations affect the algorithm. Several explicit and semi-explicit expressions for the mean square error are derived, which clearly demonstrate the character of the trade-off between tracking ability and noise rejection.
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| 6. |
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| 7. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Model Structure Identifiability and Persistence of Excitation
- 1990
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Ingår i: Proceedings of the 29th IEEE Conference on Decision and Control. ; , s. 3236-3240 vol.6
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Konferensbidrag (refereegranskat)abstract
- An algorithm procedure for determining identifiability of nonlinear systems is presented. It also gives conditions for the control signal to be persistently exciting. The algorithm is based on differential algebraic concepts.
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| 8. |
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| 9. |
- Skeppstedt, Anders, et al.
(författare)
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Construction of Composite Models from Observed Data
- 1990
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Most processes of realistic complexity cannot be described by simple linear relationships. An alternative to creating high order/non-linear models is to develop 'composite models’, i.e. a collection of simple models along with rules concerning when to use which one. In this paper we describe a method for constructing such composite models from observed data. It is assumed that the dynamics of the process changes with some 'operating-point vector’, which is assumed to be a measurable quantity. Based on input-output measurements and measurements of the operating-point vector, a composite model is constructed which consists of piecewise linear models. Different regions of the operating point space thus give different linear dynamics. The dynamics as well as the region boundaries are determined from the data. The basic idea is to utilize a method from recursive identification, which is able to track slow as well as rapid dynamic changes. A classification procedure is then applied to the models produced by this identification procedure, and finally borders are created between the different classified models. Techniques for supervised pattern recognition are used for the latter step. The whole construction procedure is illustrated with an example.
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| 10. |
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