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- Barenthin Syberg, Märta, 1979-
(författare)
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Complexity Issues, Validation and Input Design for Control in System Identification
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control. To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems. Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory. The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared.
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| 2. |
- Barenthin, Märta, 1979-
(författare)
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On input design in system identification for control
- 2006
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- There are many aspects to consider when designing system identification experiments in control applications. Input design is one important issue. This thesis considers input design both for identification of linear time-invariant models and for stability validation. Models obtained from system identification experiments are uncertain due to noise present in measurements. The input spectrum can be used to shape the model quality. A key tool in input design is to introduce a linear parametrization of the spectrum. With this parametrization a number of optimal input design problems can be formulated as convex optimization programs. An Achilles' heel in input design is that the solution depends on the system itself, and this problem can be handled by iterative procedures where the input design is based on a model of the system. Benefits of optimal input design are quantified for typical industrial applications. The result shows that the experiment time can be substantially shortened and that the input power can be reduced. Another contribution of the thesis is a procedure where input design is connected to robust control. For a certain system structure with uncertain parameters, it is shown that the existence of a feedback controller that guarantees a given performance specification can be formulated as a convex optimization program. Furthermore, a method for input design for multivariable systems is proposed. The constraint on the model quality is transformed to a linear matrix inequality using a separation of graphs theorem. The result indicates that in order to obtain a model suitable for control design, it is important to increase the power of the input in the low-gain direction of the system relative to the power in the high-gain direction. A critical issue when validating closed-loop stability is to obtain an accurate estimate of the maximum gain of the system. This problem boils down to finding the input signal that maximizes the gain. Procedures for gain estimation of nonlinear systems are proposed and compared. One approach uses a model of the system to design the optimal input. In other approaches, no model is required, and the system itself determines the optimal input sequence in repeated experiments.
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| 3. |
- Jacobsson, Krister, 1976-
(författare)
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Dynamic modeling of Internet congestion control
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The Transmission Control Protocol (TCP) has successfully governed the Internet congestion control for two decades. It is by now, however, widely recognized that TCP has started to reach its limits and that new congestion control protocols are needed in the near future. This has spurred an intensive research effort searching for new congestion control designs that meet the demands of a future Internet scaled up in size, capacity and heterogeneity. In this thesis we derive network fluid flow models suitable for analysis and synthesis of window based congestion control protocols such as TCP. In window based congestion control the transmission rate of a sender is regulated by: (1) the adjustment of the so called window, which is an upper bound on the number of packets that are allowed to be sent before receiving an acknowledgment packet (ACK) from the receiver side, and (2) the rate of the returning ACKs. From a dynamical perspective, this constitutes a cascaded control structure with an outer and an inner loop. The first contribution of this thesis is a novel dynamical characterization and an analysis of the inner loop, generic to all window based schemes and formed by the interaction between the, so called, ACK-clocking mechanism and the network. The model is based on a fundamental integral equation relating the instantaneous flow rate and the window dynamics. It is verified in simulations and testbed experiments that the model accurately predicts dynamical behavior in terms of system stability, previously unknown oscillatory behavior and even fast phenomenon such as traffic burstiness patterns present in the system. It is demonstrated that this model is more accurate than many of the existing models in the literature. In the second contribution we consider the outer loop and present a detailed fluid model of a generic window based congestion control protocol using queuing delay as congestion notification. The model accounts for the relations between the actual packets in flight and the window size, the window control, the estimator dynamics as well as sampling effects that may be present in an end-to-end congestion control algorithm. The framework facilitates modeling of a quite large class of protocols. The third contribution is a closed loop analysis of the recently proposed congestion control protocol FAST TCP. This contribution also serves as a demonstration of the developed modeling framework. It is shown and verified in experiments that the delay configuration is critical to the stability of the system. A conclusion from the analysis is that the gain of the ACK-clocking mechanism dramatically increases with the delay heterogeneity for the case of an equal resource allocation policy. Since this strongly affects the stability properties of the system, this is alarming for all window based congestion control protocols striving towards proportional fairness. While these results are interesting as such, perhaps the most important contribution is the developed stability analysis technique.
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| 4. |
- Mårtensson, Jonas, 1976-
(författare)
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Geometric analysis of stochastic model errors in system identification
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Models of dynamical systems are important in many disciplines of science, ranging from physics and traditional mechanical and electrical engineering to life sciences, computer science and economics. Engineers, for example, use models for development, analysis and control of complex technical systems. Dynamical models can be derived from physical insights, for example some known laws of nature, (which are models themselves), or, as considered here, by fitting unknown model parameters to measurements from an experiment. The latter approach is what we call system identification. A model is always (at best) an approximation of the true system, and for a model to be useful, we need some characterization of how large the model error is. In this thesis we consider model errors originating from stochastic (random) disturbances that the system was subject to during the experiment. Stochastic model errors, known as variance-errors, are usually analyzed under the assumption of an infinite number of data. In this context the variance-error can be expressed as a (complicated) function of the spectra (and cross-spectra) of the disturbances and the excitation signals, a description of the true system, and the model structure (i.e., the parametrization of the model). The primary contribution of this thesis is an alternative geometric interpretation of this expression. This geometric approach consists in viewing the asymptotic variance as an orthogonal projection on a vector space that to a large extent is defined from the model structure. This approach is useful in several ways. Primarily, it facilitates structural analysis of how, for example, model structure and model order, and possible feedback mechanisms, affect the variance-error. Moreover, simple upper bounds on the variance-error can be obtained, which are independent of the employed model structure. The accuracy of estimated poles and zeros of linear time-invariant systems can also be analyzed using results closely related to the approach described above. One fundamental conclusion is that the accuracy of estimates of unstable poles and zeros is little affected by the model order, while the accuracy deteriorates fast with the model order for stable poles and zeros. The geometric approach has also shown potential in input design, which treats how the excitation signal (input signal) should be chosen to yield informative experiments. For example, we show cases when the input signal can be chosen so that the variance-error does not depend on the model order or the model structure. Perhaps the most important contribution of this thesis, and of the geometric approach, is the analysis method as such. Hopefully the methodology presented in this work will be useful in future research on the accuracy of identified models; in particular non-linear models and models with multiple inputs and outputs, for which there are relatively few results at present.
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