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.
Models are commonly used to simulate events and processes, and can be constructed from measured data using system identification. The common way is to model the system from input to output, but in this thesis we want to obtain the inverse of the system. Power amplifiers (PAs) used in communication devices can be nonlinear, and this causes interference in adjacent transmitting channels. A prefilter, called predistorter, can be used to invert the effects of the PA, such that the combination of predistorter and PA reconstructs an amplified version of the input signal. In this thesis, the predistortion problem has been investigated for outphasing power amplifiers, where the input signal is decomposed into two branches that are amplified separately by highly efficient nonlinear amplifiers and then recombined. We have formulated a model structure describing the imperfections in an outphasing abbrPA and the matching ideal predistorter. The predistorter can be estimated from measured data in different ways. Here, the initially nonconvex optimization problem has been developed into a convex problem. The predistorters have been evaluated in measurements. The goal with the inverse models in this thesis is to use them in cascade with the systems to reconstruct the original input. It is shown that the problems of identifying a model of a preinverse and a postinverse are fundamentally different. It turns out that the true inverse is not necessarily the best one when noise is present, and that other models and structures can lead to better inversion results. To construct a predistorter (for a PA, for example), a model of the inverse is used, and different methods can be used for the estimation. One common method is to estimate a postinverse, and then using it as a preinverse, making it straightforward to try out different model structures. Another is to construct a model of the system and then use it to estimate a preinverse in a second step. This method identifies the inverse in the setup it will be used, but leads to a complicated optimization problem. A third option is to model the forward system and then invert it. This method can be understood using standard identification theory in contrast to the ones above, but the model is tuned for the forward system, not the inverse. Models obtained using the various methods capture different properties of the system, and a more detailed analysis of the methods is presented for linear time-invariant systems and linear approximations of block-oriented systems. The theory is also illustrated in examples. When a preinverse is used, the input to the system will be changed, and typically the input data will be different than the original input. This is why the estimation of preinverses is more complicated than for postinverses, and one set of experimental data is not enough. Here, we have shown that identifying a preinverse in series with the system in repeated experiments can improve the inversion performance.
Numerical algorithms for efficiently solving optimal control problems are important for commonly used advanced control strategies, such as model predictive control (MPC), but can also be useful for advanced estimation techniques, such as moving horizon estimation (MHE). In MPC, the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line, and in MHE the estimated states are obtained by solving an optimization problem that often can be formulated as a CFTOC problem. Common types of optimization methods for solving CFTOC problems are interior-point (IP) methods, sequential quadratic programming (SQP) methods and active-set (AS) methods. In these types of methods, the main computational effort is often the computation of the second-order search directions. This boils down to solving a sequence of systems of equations that correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performing second-order methods for CFTOC problems rely on efficient numerical algorithms for solving UFTOC problems. Developing such algorithms is one of the main focuses in this thesis. When the solution to a CFTOC problem is computed using an AS type method, the aforementioned system of equations is only changed by a low-rank modification between two AS iterations. In this thesis, it is shown how to exploit these structured modifications while still exploiting structure in the UFTOC problem using the Riccati recursion. Furthermore, direct (non-iterative) parallel algorithms for computing the search directions in IP, SQP and AS methods are proposed in the thesis. These algorithms exploit, and retain, the sparse structure of the UFTOC problem such that no dense system of equations needs to be solved serially as in many other algorithms. The proposed algorithms can be applied recursively to obtain logarithmic computational complexity growth in the prediction horizon length. For the case with linear MPC problems, an alternative approach to solving the CFTOC problem on-line is to use multiparametric quadratic programming (mp-QP), where the corresponding CFTOC problem can be solved explicitly off-line. This is referred to as explicit MPC. One of the main limitations with mp-QP is the amount of memory that is required to store the parametric solution. In this thesis, an algorithm for decreasing the required amount of memory is proposed. The aim is to make mp-QP and explicit MPC more useful in practical applications, such as embedded systems with limited memory resources. The proposed algorithm exploits the structure from the QP problem in the parametric solution in order to reduce the memory footprint of general mp-QP solutions, and in particular, of explicit MPC solutions. The algorithm can be used directly in mp-QP solvers, or as a post-processing step to an existing solution.
Flight control design for modern fighter aircraft is a challenging task. Aircraft are dynamical systems, which naturally contain a variety of constraints and nonlinearities such as, e.g., maximum permissible load factor, angle of attack and control surface deflections. Taking these limitations into account in the design of control systems is becoming increasingly important as the performance and complexity of the aircraft is constantly increasing. The aeronautical industry has traditionally applied feedforward, anti-windup or similar techniques and different ad hoc engineering solutions to handle constraints on the aircraft. However these approaches often rely on engineering experience and insight rather than a theoretical foundation, and can often require a tremendous amount of time to tune. In this thesis we investigate model predictive control as an alternative design tool to handle the constraints that arises in the flight control design. We derive a simple reference tracking MPC algorithm for linear systems that build on the dual mode formulation with guaranteed stability and low complexity suitable for implementation in real time safety critical systems. To reduce the computational burden of nonlinear model predictive control we propose a method to handle the nonlinear constraints, using a set of dynamically generated local inner polytopic approximations. The main benefit of the proposed method is that while computationally cheap it still can guarantee recursive feasibility and convergence. An alternative to deriving MPC algorithms with guaranteed stability properties is to analyze the closed loop stability, post design. Here we focus on deriving a tool based on Mixed Integer Linear Programming for analysis of the closed loop stability and robust stability of linear systems controlled with MPC controllers. To test the performance of model predictive control for a real world example we design and implement a standard MPC controller in the development simulator for the JAS 39 Gripen aircraft at Saab Aeronautics. This part of the thesis focuses on practical and tuning aspects of designing MPC controllers for fighter aircraft. Finally we have compared the MPC design with an alternative approach to maneuver limiting using a command governor.
Presents mathematical tools and techniques for solving change detection problems in wide domains like signal processing, controlled systems and monitoring. The book covers a wide class of stochastic processes, including scalar independent observations and multidimensional dependent ARMA.
Target tracking is a mature topic with over half a century of mainly military and aviation research. The field has lately expanded into a range of civilian applications due to the development of cheap sensors and improved computational power. With the rise of new applications, new challenges emerge, and with better hardware there is an opportunity to employ more elaborated algorithms. There are five main contributions to the field of target tracking in this thesis. Contributions I-IV concern the development of non-conventional models for target tracking and the resulting estimation methods. Contribution V concerns a reformulation for improved performance. To show the functionality and applicability of the contributions, all proposed methods are applied to and verified on experimental data related to tracking of animals or other objects in nature. In Contribution I, sparse Gaussian processes are proposed to model behaviours of targets that are caused by influences from the environment, such as wind or obstacles. The influences are learned online as a part of the state estimation using an extended Kalman filter. The method is also adapted to handle time-varying influences and to identify dynamic systems. It is shown to improve accuracy over the nearly constant velocity and acceleration models in simulation. The method is also evaluated in a sea ice tracking application using data from a radar on Svalbard. In Contribution II, a state-space model is derived that incorporates observations with uncertain timestamps. An example of such observations could be traces left by a target. Estimation accuracy is shown to be better than the alternative of disregarding the observation. The position of an orienteering sprinter is improved using the control points as additional observations. In Contribution III, targets that are confined to a certain space, such as animals in captivity, are modelled to avoid collision with the boundaries by turning. The proposed model forces the predictions to remain inside the confined space compared to conventional models that may suffer from infeasible predictions. In particular the model improves robustness against occlusions. The model is successfully used to track dolphins in a dolphinarium as they swim in a basin with occluded sections. In Contribution IV, an extension to the jump Markov model is proposed that incorporates observations of the mode that are state-independent. Normally, the mode is estimated by comparing actual and predicted observations of the state. However, sensor signals may provide additional information directly dependent on the mode. Such information from a video recorded by biologists is used to estimate take-off times and directions of birds captured in circular cages. The method is shown to compare well with a more time-consuming manual method. In Contribution V, a reformulation of the labelled multi-Bernoulli filter is used to exploit a structure of the algorithm to attain a more efficient implementation.Modern target tracking algorithms are often very demanding, so sound approximations and clever implementations are needed to obtain reasonable computational performance. The filter is integrated in a full framework for tracking sea ice, from pre-processing to presentation of results. Målföljning (eng. target tracking) är ett välutforskat ämne med en historia som sträcker sig tillbaka till åtminstone 30-talet. Då tävlade en handfull nationer om att snabbast kunna upptäcka fienden innan det var för sent. Traditionellt sett har målföljning fortsatt att vara starkt förknippat med militära tillämpningar och flygfart. Det är först på senare år som billiga och kommersiellt tillgängliga sensorer har öppnat upp för en mängd betydligt fredligare användningsområden. Målföljning skulle kunna beskrivas som lokalisering av främmande objekt genom att samla in data från sensorer. Den här avhandlingen behandlar framförallt målföljning av olika sorters djur där data samlas in med videokameror. Det finns två bakomliggande syften. Det ena handlar om att underlätta forskning för biologer och det andra handlar om att skapa tekniska lösningar för att underlätta skyddet av sällsynta djur. Även målföljning av drivis där data samlas in med radar behandlas. Trots den vitt skilda tillämpningen är många metoder desamma. Syftet är att hantera drivis i norra ishavet där detektion och målföljning är viktiga komponenter för att undvika kollisioner. Biologer lägger ofta en ansenlig mängd tid på att samla in, annotera och sortera data. Det är tid som kan spenderas på mer givande forskningsaktiviteter. Med videokamera, bildbehandling och moderna algoritmer för målföljning är det möjligt att i viss mån automatisera datainsamlingen. Med automatisering kan mer information samlas in än med traditionella metoder och längre experiment kan ofta genomföras. Ytterligare en fördel är att man kan minska påverkan på djuren. Parkvakterna i många nationalparker kämpar dagligen med intrång från tjuvjägare. De har ytterst begränsade resurser och utsätter sina liv för stor fara. Bestånden minskar fortfarande för många djurarter som går en mörk framtid till mötes. För att vända trenden behövs stora insatser på många fronter samtidigt. Målföljning kan bidra med att på ett kostnadseffektivt sätt tillhandahålla övervakning av nationalparker. Kännedom om var djuren befinner sig underlättar koordinering av parkvakternas insatser för att skydda djuren. Målföljning kan ske med ett flertal olika sensorer, såsom radarer, fast uppsatta och luftburna videokameror, mikrofoner som lyssnar efter djurläten och även vittnesmål från parkvakterna. All insamlad information bidrar till att skapa en helhetsbild av situationen i nationalparken om den används rätt. Ishantering är ett viktigt område för oljeindustrin för att garantera säkerhet och undvika allvarliga olyckor. Målet är att upptäcka och spåra is som flyter i havet och om nödvändigt vidta åtgärder för att undvika kollision. Målet är att i förlängningen sätta upp ett stort nätverk av olika sensorer och databaser för att få en heltäckande bild av det aktuella läget. Flera källor diskuteras, såsom mark- och fartygsradarer av olika slag, satelliter, drönare med kameror och väderdatabaser. Att skapa fullständiga och användbara lösningar för biologer, parkvakter och oljeindustrin är väldigt ambitiösa mål. I avhandlingen presenteras bakomliggande teori för målföljning varvat med författarens egna forskningsbidrag och lösningar för en handfull specifika problem och tillämpningar. Det första projektet som presenteras är ett samarbete med Kolmårdens djurpark. Biologer i djurparken studerar delfiners beteende i fångenskap. I dagsläget markerar studenter för hand i video var delfinerna befinner sig i bassängen. Med målföljning samlas djurens positioner in automatiskt utan mänsklig inblandning. Det främsta bidraget i forskningen är utvecklingen av en modell för hur delfinerna rör sig i bassängen. Det andra projektet som presenteras är ett samarbete med biologer vid Lunds universitet som studerar beteendet hos flyttfåglar. I en metod från 60-talet mäts fåglars rörelser i en tratt. Från repor i tratten som orsakats vid fåglarnas lyftförsök analyserar man riktningarna för lyftförsöken. Med videokamera och målföljning samlas djurens positioner in och enskilda lyftförsök detekteras automatiskt. Det främsta bidraget i forskningen är en metod för att bättre utnyttja information från videon till att detektera lyftförsöken. Det tredje projektet som presenteras är ett samarbete med Smarta Savanner. En idé som utforskas är möjligheten att använda parkvakternas vittnesmål om spår från noshörningar för att förbättra målföljningen. Å ena sidan är data från videokameror och radarer väldigt noggranna i tid, men relativt osäkra i de uppmätta positionerna. Å andra sidan kan positionen för ett spår mätas noggrant samtidigt som det ofta är svårt att avgöra när noshörningen var på platsen. Genom att utnyttja informationen från båda källorna kan noshörningars förflyttningar i parken kartläggas bättre. Den bakomliggande teorin för observationer med osäker tid inom målföljning är relativt outforskad. Det främsta bidraget i forskningen är utvecklingen av en metod för att utnyttja sådana observationer. Enkla simulerade fall används för att analysera metoden. Metoden utvärderas även i en tillämpning för att förbättra den satellitbaserade positionsbestämningen av en orienterare genom att noggrant mäta positionen på kontrollerna. Det fjärde projektet som presenteras är ett samarbete med Norges teknisk-naturvitenskapelige universitet (NTNU) och Norut i Norge som samlat in radardata på Svalbard. Det främsta bidraget är utvecklandet av en metod som lär sig hur lokala strömmar och vindar påverkar drivisen för att bättre kunna förutspå rörelser.Ett annat bidrag i forskningen är en förenkling av formuleringen och implementationen av en modern algoritm för målföljning. Projekten, som alla har flera likheter och skillnader med varandra, kan gemensamt sammanfattas med att de spårar rörelser, eller vandringar, i naturen.
Identification and System Parameter Estimation 1982 covers the proceedings of the Sixth International Federation of Automatic Control (IFAC) Symposium. The book also serves as a tribute to Dr. Naum S. Rajbman. The text covers issues concerning identification and estimation, such as increasing interrelationships between identification/estimation and other aspects of system theory, including control theory, signal processing, experimental design, numerical mathematics, pattern recognition, and information theory. The book also provides coverage regarding the application and problems faced by several engineering and scientific fields that use identification and estimation, such as biological systems, traffic control, geophysics, aeronautics, robotics, economics, and power systems. Researchers from all scientific fields will find this book a great reference material, since it presents topics that concern various disciplines.
Many practical applications, such as search and rescue operations and environmental monitoring, involve the use of mobile sensor platforms. The workload of the sensor operators is becoming overwhelming, as both the number of sensors and their complexity are increasing. This thesis addresses the problem of automating sensor systems to support the operators. This is often referred to as sensor management. By planning trajectories for the sensor platforms and exploiting sensor characteristics, the accuracy of the resulting state estimates can be improved. The considered sensor management problems are formulated in the framework of stochastic optimal control, where prior knowledge, sensor models, and environment models can be incorporated. The core challenge lies in making decisions based on the predicted utility of future measurements. In the special case of linear Gaussian measurement and motion models, the estimation performance is independent of the actual measurements. This reduces the problem of computing sensing trajectories to a deterministic optimal control problem, for which standard numerical optimization techniques can be applied. A theorem is formulated that makes it possible to reformulate a class of nonconvex optimization problems with matrix-valued variables as convex optimization problems. This theorem is then used to prove that globally optimal sensing trajectories can be computed using off-the-shelf optimization tools. As in many other fields, nonlinearities make sensor management problems more complicated. Two approaches are derived to handle the randomness inherent in the nonlinear problem of tracking a maneuvering target using a mobile range-bearing sensor with limited field of view. The first approach uses deterministic sampling to predict several candidates of future target trajectories that are taken into account when planning the sensing trajectory. This significantly increases the tracking performance compared to a conventional approach that neglects the uncertainty in the future target trajectory. The second approach is a method to find the optimal range between the sensor and the target. Given the size of the sensor's field of view and an assumption of the maximum acceleration of the target, the optimal range is determined as the one that minimizes the tracking error while satisfying a user-defined constraint on the probability of losing track of the target. While optimization for tracking of a single target may be difficult, planning for jointly maintaining track of discovered targets and searching for yet undetected targets is even more challenging. Conventional approaches are typically based on a traditional tracking method with separate handling of undetected targets. Here, it is shown that the Poisson multi-Bernoulli mixture (PMBM) filter provides a theoretical foundation for a unified search and track method, as it not only provides state estimates of discovered targets, but also maintains an explicit representation of where undetected targets may be located. Furthermore, in an effort to decrease the computational complexity, a version of the PMBM filter which uses a grid-based intensity to represent undetected targets is derived.
During the last decades, motion planning for autonomous systems has become an important area of research. The high interest is not the least due to the development of systems such as self-driving cars, unmanned aerial vehicles and robotic manipulators. The objective in optimal motion planning problems is to find feasible motion plans that also optimize a performance measure. From a control perspective, the problem is an instance of an optimal control problem. This thesis addresses optimal motion planning problems for complex dynamical systems that operate in unstructured environments, where no prior reference such as road-lane information is available. Some example scenarios are autonomous docking of vessels in harbors and autonomous parking of self-driving tractor-trailer vehicles at loading sites. The focus is to develop optimal motion planning algorithms that can reliably be applied to these types of problems. This is achieved by combining recent ideas from automatic control, numerical optimization and robotics. The first contribution is a systematic approach for computing local solutions to motion planning problems in challenging unstructured environments. The solutions are computed by combining homotopy methods and direct optimal control techniques. The general principle is to define a homotopy that transforms, or preferably relaxes, the original problem to an easily solved problem. The approach is demonstrated in motion planning problems in 2D and 3D environments, where the presented method outperforms a state-of-the-art asymptotically optimal motion planner based on random sampling. The second contribution is an optimization-based framework for automatic generation of motion primitives for lattice-based motion planners. Given a family of systems, the user only needs to specify which principle types of motions that are relevant for the considered system family. Based on the selected principle motions and a selected system instance, the framework computes a library of motion primitives by simultaneously optimizing the motions and the terminal states. The final contribution of this thesis is a motion planning framework that combines the strengths of sampling-based planners with direct optimal control in a novel way. The sampling-based planner is applied to the problem in a first step using a discretized search space, where the system dynamics and objective function are chosen to coincide with those used in a second step based on optimal control. This combination ensures that the sampling-based motion planner provides a feasible motion plan which is highly suitable as warm-start to the optimal control step. Furthermore, the second step is modified such that it also can be applied in a receding-horizon fashion, where the proposed combination of methods is used to provide theoretical guarantees in terms of recursive feasibility, worst-case objective function value and convergence to the terminal state. The proposed motion planning framework is successfully applied to several problems in challenging unstructured environments for tractor-trailer vehicles. The framework is also applied and tailored for maritime navigation for vessels in archipelagos and harbors, where it is able to compute energy-efficient trajectories which complies with the international regulations for preventing collisions at sea.
Nonlinear filtering is an important standard tool for information and sensor fusion applications, e.g., localization, navigation, and tracking. It is an essential component in surveillance systems and of increasing importance for standard consumer products, such as cellular phones with localization, car navigation systems, and augmented reality. This thesis addresses several issues related to nonlinear filtering, including performance analysis of filtering and detection, algorithm analysis, and various implementation details. The most commonly used measure of filtering performance is the root mean square error (RMSE), which is bounded from below by the Cramér-Rao lower bound (CRLB). This thesis presents a methodology to determine the effect different noise distributions have on the CRLB. This leads up to an analysis of the intrinsic accuracy (IA), the informativeness of a noise distribution. For linear systems the resulting expressions are direct and can be used to determine whether a problem is feasible or not, and to indicate the efficacy of nonlinear methods such as the particle filter (PF). A similar analysis is used for change detection performance analysis, which once again shows the importance of IA. A problem with the RMSE evaluation is that it captures only one aspect of the resulting estimate and the distribution of the estimates can differ substantially. To solve this problem, the Kullback divergence has been evaluated demonstrating the shortcomings of pure RMSE evaluation. Two estimation algorithms have been analyzed in more detail; the Rao-Blackwellized particle filter (RBPF) by some authors referred to as the marginalized particle filter (MPF) and the unscented Kalman filter (UKF). The RBPF analysis leads to a new way of presenting the algorithm, thereby making it easier to implement. In addition the presentation can possibly give new intuition for the RBPF as being a stochastic Kalman filter bank. In the analysis of the UKF the focus is on the unscented transform (UT). The results include several simulation studies and a comparison with the Gauss approximation of the first and second order in the limit case. This thesis presents an implementation of a parallelized PF and outlines an object-oriented framework for filtering. The PF has been implemented on a graphics processing unit (GPU), i.e., a graphics card. The GPU is a inexpensive parallel computational resource available with most modern computers and is rarely used to its full potential. Being able to implement the PF in parallel makes new applications, where speed and good performance are important, possible. The object-oriented filtering framework provides the flexibility and performance needed for large scale Monte Carlo simulations using modern software design methodology. It can also be used to help to efficiently turn a prototype into a finished product.
