| 1. |
- Bergman, Niclas
(författare)
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Recursive Bayesian Estimation : Navigation and Tracking Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Recursive estimation deals with the problem of extracting information about parameters, or states, of a dynamical system in real time, given noisy measurements of the system output. Recursive estimation plays a central role in many applications of signal processing, system identification and automatic control. In this thesis we study nonlinear and non-Gaussian recursive estimation problems in discrete time. Our interest in these problems stems from the airborne applications of target tracking, and autonomous aircraft navigation using terrain information.In the Bayesian framework of recursive estimation, both the sought parameters and the observations are considered as stochastic processes. The conceptual solution to the estimation problem is found as a recursive expression for the posterior probability density function of the parameters conditioned on the observed measurements. This optimal solution to nonlinear recursive estimation is usually impossible to compute in practice, since it involves several integrals that lack analytical solutions.We phrase the application of terrain navigation in the Bayesian framework, and develop a numerical approximation to the optimal but intractable recursive solution. The designed point-mass filter computes a discretized version of the posterior filter density in a uniform mesh over the interesting region of the parameter space. Both the uniform mesh resolution and the grid point locations are automatically adjusted at each iteration of the algorithm. This Bayesian point-mass solution is shown to yield high navigation performance in a simulated realistic environment.Even though the optimal Bayesian solution is intractable to implement, the performance of the optimal solution is assessable and can be used for comparative evaluation of suboptimal implementations. We derive explicit expressions for the Cramér-Rao bound of general nonlinear filtering, smoothing and prediction problems. We consider both the cases of random and nonrandom modeling of the parameters. The bounds are recursively expressed and are connected to linear recursive estimation. The newly developed Cramér-Rao bounds are applied to the terrain navigation problem, and the point-mass filter is verified to reach the bound in exhaustive simulations.The uniform mesh of the point-mass filter limits it to estimation problems of low dimension. Monte Carlo methods offer an alternative approach to recursive estimation and promise tractable solutions to general high dimensional estimation problems. We provide a review over the active field of statistical Monte Carlo methods. In particular, we study the particle filters for recursive estimation. Three different particle filters are applied to terrain navigation, and evaluated against the Cramér-Rao bound and the point-mass filter. The particle filters utilize an adaptive grid representation of the filter density and are shown to yield a performance equal to the point-mass method.A Markov Chain Monte Carlo (MCMC) method is developed for a highly complex data association problem in target tracking. This algorithm is compared to previously proposed methods and is shown to yield competitive results in a simulation study.
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| 2. |
- Forssell, Urban
(författare)
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Closed-loop Identification : Methods, Theory, and Applications
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification deals with constructing mathematical models of dynamical systems from measured data. Such models have important applications in many technical and nontechnical areas, such as diagnosis, simulation, prediction, and control. The theme in this thesis is to study how the use of closed-loop data for identication of open-loop processes affects dierent identification methods. The focus is on prediction error methods for closed-loop identification and a main resultis that we show that most common methods correspond to diefferent parameterizations of the general prediction error method. This provides a unifying framework for analyzing the statistical properties of the different methods. Here we concentrate on asymptotic variance expressions for the resulting estimates and on explicit characterizations of the bias distribution for the different methods. Furthermore, we present and analyze a new method for closed-loop identification, called the projection method, which allows approximation of the open-loop dynamics in a fixed, user-specified frequency domain norm, even in the case of an unknown, nonlinear regulator.In prediction error identification it is common to use some gradient-type search algorithm for the parameter estimation. A requirement is then that the predictor filters along with their derivatives are stable for all admissible values of the parameters. The standard output error and Box-Jenkins model structures cannot beused if the underlying system is unstable, since the predictor filters will generically be unstable under these circumstances. In the thesis, modified versions of these model structures are derived that are applicable also to unstable systems. Another way to handle the problems associated with output error identification of unstable systems is to implement the search algorithm using noncausal filtering. Several such approaches are also studied and compared.Another topic covered in the thesis is the use of periodic excitation signals for time domain identification of errors-in-variables systems. A number of compensation strategies for the least-squares and total least-squares methods are suggested. The main idea is to use a nonparametric noise model, estimated directly from data, to whiten the noise and to remove the bias in the estimates."Identication for Control" deals specically with the problem of constructing models from data that are good for control. A main idea has been to try to match the identication and control criteria to obtain a control-relevant model fit. The use of closed-loop experiments has been an important tool for achieving this. We study a number of iterative methods for dealing with this problem and show how they can be implemented using the indirect method. Several problems with the iterative schemes are observed and it is argued that performing iterated identification experiments with the current controller in the loop is suboptimal. Related to this is the problem of designing the identification experiment so that the quality of the resulting model is maximized. Here we concentrate on minimizing the variance error and a main result is that we give explicit expressions for the optimal regulator and reference signal spectrum to use in the identification experiment in case both the input and the output variances are constrained
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| 3. |
- Gunnarsson, Johan
(författare)
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Symbolic Methods and Tools for Discrete Event Dynamic Systems
- 1997
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The interest in Discrete Event Dynamic Systems (DEDS) has increased during the last years, due to the lack of methods and tools that are capable of handling the complexity of problems and tasks present in industry today. In this thesis we will consider a framework based on relations over finite domains. The framework is used for modeling, analysis, and synthesis of DEDS.Binary Decision Diagrams (BDDs) are used to represent relations, as well as the operations for modeling, analysis and synthesis of DEDS. To utilized the structure of integers and arithmetic operation, Integer Decision Diagrams (IDDs) are developed and implemented. Polynomials over finite fields are another type of representation that is used for the relational framework. Here Gröbner bases, and Integrated Monomial Diagrams (IMDs) are the tools that are used. IDDs and IMDs are both developed, by the author, to represent integer structures and arithmetic operations efficiently.With tools for efficient relational representation, it possible to improve scalability of DEDS computations, as shown in this thesis by the modeling and analysis of the landing gear controller of the Swedish fighter aircraft JAS 39 Gripen. A relational model, represented by a BDD, is automatically generated from a 1200 lines Pascal implementation, which contains 105 binary variables of which 26 are state variables. Function specifications expressed with temporal algebra, are verified using tools for dynamic analysis, which we also use to compute a polynomial representing the set of all reachable states in the model. The landing gear controller serves as a benchmark test of BDDs and IDDs. The IDDs reduced the computation time by 50%.To explore the ability and applicability of using a polynomial relational representation when doing synthesis, we use a tank system containing actuators (pump and valves) and sensors (the tank level and measurable disturbances). We propose a synthesis method that uses actuator priority, weighting of states, and Gröbner bases to compute explicit control laws for the actuators, fulfilling the control objectives even if one of the actuators (the pump) is defective.Modeling aspects are emphasized further, by comparing the polynomial approach which we have used, with Boolean expressions and established DEDS approaches in the community of automatic control like Ramadge-Wonham, Petri nets, and COCOLOG. We discuss how to handle transformation between signals and events for DEDS and how to modularize DEDS to gain complexity advantages. Model description languages are discussed and desirable features are stated, using the experiences achieved from the modeling of the tank system and the landing gear controller.
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| 4. |
- Helmersson, Anders
(författare)
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Methods for robust gain scheduling
- 1995
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Regulatorer används i många tillämpningar för att förbättra prestanda ochegenskaper hos fordon och farkoster av olika slag, t ex flygplan och raketer.Beroende på olika faktorer, som hastighet och höjd, kan dynamiken ochuppträdandet av dessa farkoster variera. Man vill därför låta regulatorn tahänsyn till dessa variationer genom att ändra sitt uppförande i motsvarandegrad.Regulatorn kan konstrueras på olika sätt. En möjlighet är att styrsignalernaberor linjärt eller proportionellt på regulatorns insignaler, till exempelavvikelser från önskad bana. Regulatorn bestäms av ett antal parametrarsom kan ändras efter de yttre betingelserna (t ex hastighet och höjd för ett flygplan). Denna metod kallas för parameterstyrning.Vid konstruktionen av regulatorn använder man en modell av det systemsom ska styras. En viktig och önskad egenskap hos en regulator är att denska kunna fungera bra även om systemet den ska styra varierar eller avvikerfrån modellen. Ett flygplan beter sig på olika sätt beroende på hur mycketlast den har och hur lasten är placerad. Det är därför önskvärt att användaregulatorer som inte är känsliga för variationer, t ex i last, och som uppförsig bra i olika situationer. En sådan regulator sägs vara robust.Avhandlingen behandlar hur man kan analysera och konstruera regulatorersom är robusta och parameterstyrda. Det visar sig att båda dessaproblem är likartade och att de kan behandlas med samma metoder.
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| 5. |
- Klein, Inger
(författare)
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Automatic Synthesis of Sequential Control Schemes
- 1993
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Of all hard- and software developed for industrial control purposes, the majority is devoted to sequential, or binary valued, control and only a minor part to classical linear control. Typically, the sequential parts of the controller are invoked during startup and shut-down to bring the system into its normal operating region and into some safe standby region, respectively. Despite its importance, fairly little theoretical research has been devoted to this area, and sequential control programs are therefore still created manually without much theoretical support to obtain a systematic approach.We propose a method to create sequential control programs automatically. The main idea is to spend some eort off-line modelling the plant, and from this model generate the control strategy, that is the plan. The plant is modelled using action structures, thereby concentrating on the actions instead of the states of the plant. In general the planning problem shows exponential complexity in the number of state variables. However, by focusing on the actions, we can identify problem classes as well as algorithms such that the planning complexity is reduced to polynomial complexity. We prove that these algorithms are sound, i.e., the generated solution will solve the stated problem, and complete, i.e., if the algorithms fail, then no solution exists. The algorithms generate a plan as a set of actions and a partial order on this set specifying the execution order. The generated plan is proven to be minimal and maximally parallel.For a larger class of problems we propose a method to split the original problem into a number of simpler problems that can each be solved using one of the presented algorithms. It is also shown how a plan can be translated into a GRAFCET chart, and to illustrate these ideas we have implemented a planning tool, i.e., a system that is able to automatically create control schemes. Such a tool can of course also be used on-line if it is fast enough. This possibility opens up completely new applications such as operator supervision and simplied error recovery and restart procedures after a plant fault has occurred.Additionally we analyze reachability for a restricted class of problems. For this class we state a reachability criterion that may be checked using a slightly modified version of one of the above mentioned algorithms.
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| 6. |
- Larsson, Magnus
(författare)
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Behavioral and Structural Model Based Approaches to Discrete Diagnosis
- 1999
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The basic motivation for this thesis is the fact that things go wrong. With the growing complexity of todays engineering systems, the need has arisen for systematic approaches to failure diagnosis, i.e., fault detection and isolation.In the first part of this thesis an approach for modeling and diagnosis of systems that fall in the area of discrete event dynamic systems is proposed. The approach is applicable to systems that at some level of abstraction have an interesting discrete event dynamics that can display faulty behavior. The systems suitable for this approach typically consist of several interacting components where abrupt, butnon-catastrophic, faults can occur in the components.We use a relational framework for discrete event dynamic systems focusing on a conceptually simple representation of the relationship between inputs, outputs and states of a discrete event system. Faults and faulty behavior are modeled locally using the state variables, and the diagnosis problem basically is to infer the possible states of the system using the system model and observations of the real system, i.e., an observer problem. Detectability and isolatability properties are defined and algorithms for analysis are proposed. The transitions necessary and sufficient for detection can automatically be computed from the system model under certain conditions. We also show how to compute the nest possible fault partition.The second part of this thesis addresses the problem of fault propagation between software modules in a large-scale control system with object oriented architecture. There exists a conflict between object-oriented design goals such as encapsulation and modularity, and the possibility to suppress propagating error conditions. When an object detects an error condition, it is not desirable to perform the extensive querying of other objects that would be necessary to decide how close to the real fault the object is and hence whether it should report to the user.The fault propagation manifests itself as many irrelevant error messages and hence causes problems for system operators and service personnel trying to quickly isolate the real fault. A system developer with insight in the internal system design, can, of course, often easily interpret the multitude of error messages from a fault scenario and isolate the root cause. The key observation is that it can often be done using mental high-level models of the system and the mechanics of the fault propagation. We have made an effort to automate this procedure, and propose a fault isolation scheme as an extra layer between the operator and the core control system. In the fault isolation layer, post-processing of the fault information from the system is performed, to achieve clear and concise fault information to the operator without violating encapsulation and modularity.A high-level and informal explanation model for the fault propagation is presented and a taxonomy for error conditions in an object oriented system is proposed. We present algorithms and methods that use the explanation model and the error condition taxonomy together with a structural system model to form a cause-effect relation on the error messages, that can be used to find the most significant error message(s) in a fault scenario.
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| 7. |
- Larsson, Roger, 1968-
(författare)
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Flight Test System Identification
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- With the demand for more advanced fighter aircraft, relying on unstable flight mechanical characteristics to gain flight performance, more focus has been put on model-based system engineering to help with the design work. The flight control system design is one important part that relies on this modeling. Therefore, it has become more important to develop flight mechanical models that are highly accurate in the whole flight envelope. For today’s modern fighter aircraft, the basic flight mechanical characteristics change between linear and nonlinear as well as stable and unstable as an effect of the desired capability of advanced maneuvering at subsonic, transonic and supersonic speeds.This thesis combines the subject of system identification, which is the art of building mathematical models of dynamical systems based on measurements, with aeronautical engineering in order to find methods for identifying flight mechanical characteristics. Here, some challenging aeronautical identification problems, estimating model parameters from flight-testing, are treated.Two aspects are considered. The first is online identification during flight-testing with the intent to aid the engineers in the analysis process when looking at the flight mechanical characteristics. This will also ensure that enough information is available in the resulting test data for post-flight analysis. Here, a frequency domain method is used. An existing method has been developed further by including an Instrumental Variable approach to take care of noisy data including atmospheric turbulence and by a sensor-fusion step to handle varying excitation during an experiment. The method treats linear systems that can be both stable and unstable working under feedback control. An experiment has been performed on a radio-controlled demonstrator aircraft. For this, multisine input signals have been designed and the results show that it is possible to perform more time-efficient flight-testing compared with standard input signals.The other aspect is post-flight identification of nonlinear characteristics. Here the properties of a parameterized observer approach, using a prediction-error method, are investigated. This approach is compared with four other methods for some test cases. It is shown that this parameterized observer approach is the most robust one with respect to noise disturbances and initial offsets. Another attractive property is that no user parameters have to be tuned by the engineers in order to get the best performance.All methods in this thesis have been validated on simulated data where the system is known, and have also been tested on real flight test data. Both of the investigated approaches show promising results.
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| 8. |
- Löfberg, Johan, 1974-
(författare)
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Minimax Approaches to Robust Model Predictive Control
- 2003
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Controlling a system with control and state constraints is one of the most important problems in control theory, but also one of the most challenging. Another important but just as demanding topic is robustness against uncertainties in a controlled system. One of the most successful approaches, both in theory and practice, to control constrained systems is model predictive control (MPC). The basic idea in MPC is to repeatedly solve optimization problems on-line to find an optimal input to the controlled system. In recent years, much effort has been spent to incorporate the robustness problem into this framework.The main part of the thesis revolves around minimax formulations of MPC for uncertain constrained linear discrete-time systems. A minimax strategy in MPC means that worst-case performance with respect to uncertainties is optimized. Unfortunately, many minimax MPC formulations yield intractable optimization problems with exponential complexity.Minimax algorithms for a number of uncertainty models are derived in the thesis. These include systems with bounded external additive disturbances, systems with uncertain gain, and systems described with linear fractional transformations. The central theme in the different algorithms is semidefinite relaxations. This means that the minimax problems are written as uncertain semidefinite programs, and then conservatively approximated using robust optimization theory. The result is an optimization problem with polynomial complexity.The use of semidefinite relaxations enables a framework that allows extensions of the basic algorithms, such as joint minimax control and estimation, and approx- imation of closed-loop minimax MPC using a convex programming framework. Additional topics include development of an efficient optimization algorithm to solve the resulting semidefinite programs and connections between deterministic minimax MPC and stochastic risk-sensitive control.The remaining part of the thesis is devoted to stability issues in MPC for continuous-time nonlinear unconstrained systems. While stability of MPC for un-constrained linear systems essentially is solved with the linear quadratic controller, no such simple solution exists in the nonlinear case. It is shown how tools from modern nonlinear control theory can be used to synthesize finite horizon MPC controllers with guaranteed stability, and more importantly, how some of the tech- nical assumptions in the literature can be dispensed with by using a slightly more complex controller.
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| 9. |
- McKelvey, Tomas
(författare)
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Identification of State-Space Models from Time and Frequency Data
- 1995
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This dissertation considers the identication of linear multivariable systems using finite dimensional time-invariant state-space models.Parametrization of multivariable state-space models is considered. A full parametrization, where all elements in the state-space matrices are parameters, is introduced. A model structure with full parametrization gives two important implications; low sensitivity realizations can be used and the structural issues of multivariable canonical parametrizations are circumvented. Analysis reveals that additional estimated parameters do not increase the variance of the transfer function estimate if the resulting model class is not enlarged.Estimation and validation issues for the case of impulse response data are discussed. Identication techniques based on realization theory are linked to the prediction error method. The combination of these techniques allows for the estimation of high quality models for systems with many oscillative modes. A new model quality measure, Modal Coherence Indicator, is introduced. This indicator gives an independent quality tag for each identified mode and provides information useful for model validation and order estimation.Two applications from the aircraft and space industry are considered. Both problems are concerned with vibrational analysis of mechanical structures. The first application is from an extensive experimental vibrational study of the airframe structure of the Saab 2000 commuter aircraft. The second stems from vibrational analysis of a launcher-satellite separation system. In both applications multi-output discrete time state-space models are estimated, which are then used to derive resonant frequencies and damping ratios.New multivariable frequency domain identification algorithms are also introduced. Assuming primary data consist of uniformly spaced frequency response measurements, an identification algorithm based on realization theory is derived. The algorithm is shown to be robust against bounded noise as well as being consistent. The resulting estimate is shown to be asymptotically normal, and an explicit variance expression is determined. If data originate from an infinite dimensional system, it is shown that the estimated transfer function converges to the transfer function of the truncated balanced realization.Frequency domain subspace based algorithms are also derived and analyzed when the data consist of samples of the Fourier transform of the input and output signals. These algorithms are the frequency domain counterparts of the time domain subspace based algorithms.The frequency domain identification methods developed are applied to measured frequency data from a mechanical truss structure which exhibits many lightly damped oscillative modes. With the new methods, high quality state-space models are estimated both in continuous and discrete time.
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| 10. |
- Ohlsson, Henrik, 1981-
(författare)
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Regularization for Sparseness and Smoothness : Applications in System Identification and Signal Processing
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In system identification, the Akaike Information Criterion (AIC) is a well known method to balance the model fit against model complexity. Regularization here acts as a price on model complexity. In statistics and machine learning, regularization has gained popularity due to modeling methods such as Support Vector Machines (SVM), ridge regression and lasso. But also when using a Bayesian approach to modeling, regularization often implicitly shows up and can be associated with the prior knowledge. Regularization has also had a great impact on many applications, and very much so in clinical imaging. In e.g., breast cancer imaging, the number of sensors is physically restricted which leads to long scantimes. Regularization and sparsity can be used to reduce that. In Magnetic Resonance Imaging (MRI), the number of scans is physically limited and to obtain high resolution images, regularization plays an important role.Regularization shows-up in a variety of different situations and is a well known technique to handle ill-posed problems and to control for overfit. We focus on the use of regularization to obtain sparseness and smoothness and discuss novel developments relevant to system identification and signal processing.In regularization for sparsity a quantity is forced to contain elements equal to zero, or to be sparse. The quantity could e.g., be the regression parameter vectorof a linear regression model and regularization would then result in a tool for variable selection. Sparsity has had a huge impact on neighboring disciplines, such as machine learning and signal processing, but rather limited effect on system identification. One of the major contributions of this thesis is therefore the new developments in system identification using sparsity. In particular, a novel method for the estimation of segmented ARX models using regularization for sparsity is presented. A technique for piecewise-affine system identification is also elaborated on as well as several novel applications in signal processing. Another property that regularization can be used to impose is smoothness. To require the relation between regressors and predictions to be a smooth function is a way to control for overfit. We are here particularly interested in regression problems with regressors constrained to limited regions in the regressor-space e.g., a manifold. For this type of systems we develop a new regression technique, Weight Determination by Manifold Regularization (WDMR). WDMR is inspired byapplications in biology and developments in manifold learning and uses regularization for smoothness to obtain smooth estimates. The use of regularization for smoothness in linear system identification is also discussed.The thesis also presents a real-time functional Magnetic Resonance Imaging (fMRI) bio-feedback setup. The setup has served as proof of concept and been the foundation for several real-time fMRI studies.
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