| 281. |
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| 282. |
- Ljung, Lennart, 1946-, et al.
(författare)
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System Identification through the Eyes of Model Validation
- 1995
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Ingår i: Proceedings of the 3rd European Control Conference. - Linköping : Linköping University.
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Classical model validation procedures are placed at the focus of our attention. We discuss the principles by which we reach confidence in a model through such validation techniques, and also how the distance to a "true" description can be estimated this way. In particular we stress that model errors must be separated from disturbances in this process, and that consequently correlation tests between the model residuals and past inputs play a crucial role in this process.
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| 283. |
- Ljungberg, Fredrik, 1993-
(författare)
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Estimation of Nonlinear Greybox Models for Marine Applications
- 2020
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- As marine vessels are becoming increasingly autonomous, having accurate simulation models available is turning into an absolute necessity. This holds both for facilitation of development and for achieving satisfactory model-based control. When accurate ship models are sought, it is necessary to account for nonlinear hydrodynamic effects and to deal with environmental disturbances in a correct way. In this thesis, parameter estimators for nonlinear regression models where the regressors are second-order modulus functions are analyzed. This model class is referred to as second-order modulus models and is often used for greybox identification of marine vessels. The primary focus in the thesis is to find consistent estimators and for this an instrumental variable (IV) method is used.First, it is demonstrated that the accuracy of an IV estimator can be improved by conducting experiments where the input signal has a static offset of sufficient amplitude and the instruments are forced to have zero mean. This two-step procedure is shown to give consistent estimators for second-order modulus models in cases where an off-the-shelf applied IV method does not, in particular when measurement uncertainty is taken into account.Moreover, it is shown that the possibility of obtaining consistent parameter estimators for models of this type depends on how process disturbances enter the system and on the amount of prior knowledge about the disturbances’ probability distributions that is available. In cases where the first-order moments are known, the aforementioned approach gives consistent estimators even when disturbances enter the system before the nonlinearity. In order to obtain consistent estimators in cases where the first-order moments are unknown, a framework for estimating the first and second-order moments alongside the model parameters is suggested. The idea is to describe the environmental disturbances as stationary stochastic processes in an inertial frame and to utilize the fact that their effect on a vessel depends on the vessel’s attitude. It is consequently possible to infer information about the environmental disturbances by over time measuring the orientation of a vessel they are affecting. Furthermore, in cases where the process disturbances are of more general character it is shown that supplementary disturbance measurements can be used for achieving consistency.Different scenarios where consistency can be achieved for instrumental variable estimators of second-order modulus models are demonstrated, both in theory and by simulation examples. Finally, estimation results obtained using data from a full-scale marine vessel are presented.
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| 284. |
- Malmström, Magnus, 1994-
(författare)
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Uncertainties in Neural Networks : A System Identification Approach
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In science, technology, and engineering, creating models of the environment to predict future events has always been a key component. The models could be everything from how the friction of a tire depends on the wheels slip to how a pathogen is spread throughout society. As more data becomes available, the use of data-driven black-box models becomes more attractive. In many areas they have shown promising results, but for them to be used widespread in safety-critical applications such as autonomous driving some notion of uncertainty in the prediction is required.An example of such a black-box model is neural networks (NNs). This thesis aims to increase the usefulness of NNs by presenting an method where uncertainty in the prediction is obtained by linearization of the model. In system identification and sensor fusion, under the condition that the model structure is identifiable, this is a commonly used approach to get uncertainty in the prediction from a nonlinear model. If the model structure is not identifiable, such as for NNs, the ambiguities that cause this have to be taken care of in order to make the approach applicable. This is handled in the first part of the thesis where NNs are analyzed from a system identification perspective, and sources of uncertainty are discussed.Another problem with data-driven black-box models is that it is difficult to know how flexible the model needs to be in order to correctly model the true system. One solution to this problem is to use a model that is more flexible than necessary to make sure that the model is flexible enough. But how would that extra flexibility affect the uncertainty in the prediction? This is handled in the later part of the thesis where it is shown that the uncertainty in the prediction is bounded from below by the uncertainty in the prediction of the model with lowest flexibility required for representing true system accurately. In the literature, many other approaches to handle the uncertainty in predictions by NNs have been suggested, of which some are summarized in this work. Furthermore, a simulation and an experimental studies inspired by autonomous driving are conducted. In the simulation study, different sources of uncertainty are investigated, as well as how large the uncertainty in the predictions by NNs are in areas without training data. In the experimental study, the uncertainty in predictions done by different models are investigated. The results show that, compared to existing methods, the linearization method produces similar results for the uncertainty in predictions by NNs.An introduction video is available at https://youtu.be/O4ZcUTGXFN0
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| 285. |
- Markusson, Ola, et al.
(författare)
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Higher order cumulant based parameter estimation in nonlinear time series models
- 2001
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Ingår i: PROCEEDINGS OF THE 2001 AMERICAN CONTROL CONFERENCE. - 0780364953 ; , s. 4888-4889
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Konferensbidrag (refereegranskat)abstract
- Parameter estimation in nonlinear time-series models based on higher order cumulant matching is proposed in this paper. The cumulant estimates are computed from measured and simulated data and a cost function computed from second and fourth order cumulants is used. To simplify the calculations a reduced cost function is suggested using low-dimensional slices of the cumulant functions. The estimation method is illustrated on a numerical example.
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| 286. |
- Markusson, Ola, et al.
(författare)
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Inversion of non-linear stochastic models for the purpose of parameter estimation
- 2001
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Ingår i: International Journal of Control. - 0020-7179 .- 1366-5820. ; 74:18, s. 1783-1795
-
Tidskriftsartikel (refereegranskat)abstract
- Prediction error and maximum likelihood estimation of non-linear stochastic models requires inversion of the model, a step which may require substantial efforts, either in terms of manual calculations or through the use of software capable of symbolic computations. In this paper we show that model inversion can be easily implemented in numerical software such as, e.g. Simulink and Matrix(X), by means of a feedback connection based on the model. It is further shown how the gradients, used for the optimization of the cost function, can be generated by a linear time-varying feedback system associated with the non-linear model. In addition, we derive sufficient conditions for the existence of a stable causal inverse as well as sufficient conditions for the initial transient to decay. These conditions are given in terms of properties for a linear time-varying system associated with the non-linear model. The method is illustrated on numerical examples.
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| 287. |
- Markusson, Ola, et al.
(författare)
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Inversion of nonlinear stochastic models for parameter estimation
- 2000
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. ; , s. 1591-1596
-
Konferensbidrag (refereegranskat)abstract
- Prediction error and maximum likelihood estimation of nonlinear stochastic models requires inversion of the model, a step which may require substantial efforts, either in terms of manual calculations or through the use of software capable of symbolic computations. In this paper we show that model inversion can be easily implemented in numerical software such as, e.g., Simulink and Matrixx, by means of a feedback connection based on the model. We derive sufficient conditions for the existence of a stable causal inverse as well as sufficient conditions for the initial transient to decay. These conditions are given in terms of properties for a linear time-varying system associated with the nonlinear model. The method is illustrated on a numerical example.
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| 288. |
- Markusson, Ola, et al.
(författare)
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Iterative learning control of nonlinear non-minimum phase systems and its application to system and model inversion
- 2001
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Ingår i: PROCEEDINGS OF THE 40TH IEEE CONFERENCE ON DECISION AND CONTROL. - 0780370619 ; , s. 4481-4482
-
Konferensbidrag (refereegranskat)abstract
- In this contribution we present a model based method for reference tracking in the Iterative Learning Control (ILC) framework. The method can be applied to nonlinear, possibly non-minimum phase, systems. The idea is to use the inverse of a linearized model in the ILC update. In the non-minimum phase case, the batch property of ILC is explored by means of non-causal filtering. Apart from reference tracking, this method is useful for system and model inversion - a problem that arises in many disciplines where nonlinear systems and models are involved, e.g. maximum likelihood identification and input design for identification for control. The method is illustrated on a numerical example.
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| 289. |
- Markusson, Ola, 1971-, et al.
(författare)
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Iterative Learning Control of Nonlinear Non-Minimum Phase Systems and its Application to System and Model Inversion
- 2002
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this contribution we place ILC in the realm of numerical optimization. This clarifies the role played by the design variables and how they affect e.g. convergence properties. We give a model based interpretation of these design variables and also a sufficient condition for convergence of ILC which is similar in spirit to the sufficient and necessary condition previously derived for linear systems. This condition shows that the desired performance has to be traded against modelling accuracy. Finally, one of the main benefits of ILC when non-minimum phase systems are concerned, the possibility of non-causal control, is given a comprehensive coverage.
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| 290. |
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