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The purpose of system identification is to construct mathematical models of dynamical system from experimental data. With the current trend of dynamical systems encountered in engineering growing ever more complex, an important task is to efficiently build models of these systems. Modelling the complete dynamics of these systems is in general not possible or even desired. However, often, these systems can be modelled as simpler linear systems interconnected in a dynamic network. Then, the task of estimating the whole network or a subset of the network can be broken down into subproblems of estimating one simple system, called module, embedded within the dynamic network. The prediction error method (PEM) is a benchmark in parametric system identification. The main advantage with PEM is that for Gaussian noise, it corresponds to the so called maximum likelihood (ML) estimator and is asymptotically efficient. One drawback is that the cost function is in general nonconvex and a gradient based search over the parameters has to be carried out, rendering a good starting point crucial. Therefore, other methods such as subspace or instrumental variable methods are required to initialize the search. In this thesis, an alternative method, called model order reduction Steiglitz-McBride (MORSM) is proposed. As MORSM is also motivated by ML arguments, it may also be used on its own and will in some cases provide asymptotically efficient estimates. The method is computationally attractive since it is composed of a sequence of least squares steps. It also treats the part of the network of no direct interest nonparametrically, simplifying model order selection for the user. A different approach is taken in the second proposed method to identify a module embedded in a dynamic network. Here, the impulse response of the part of the network of no direct interest is modelled as a realization of a Gaussian process. The mean and covariance of the Gaussian process is parameterized by a set of parameters called hyperparameters that needs to be estimated together with the parameters of the module of interest. Using an empirical Bayes approach, all parameters are estimated by maximizing the marginal likelihood of the data. The maximization is carried out by using an iterative expectation/conditional-maximization scheme, which alternates so called expectation steps with a series of conditional-maximization steps. When only the module input and output sensors are used, the expectation step admits an analytical expression. The conditional-maximization steps reduces to solving smaller optimization problems, which either admit a closed form solution, or can be efficiently solved by using gradient descent strategies. Therefore, the overall optimization turns out computationally efficient. Using markov chain monte carlo techniques, the method is extended to incorporate additional sensors. Apart from the choice of identification method, the set of chosen signals to use in the identification will determine the covariance of the estimated modules. To chose these signals, well known expressions for the covariance matrix could, together with signal constraints, be formulated as an optimization problem and solved. However, this approach does neither tell us why a certain choice of signals is optimal nor what will happen if some properties change. The expressions developed in this part of the thesis have a different flavor in that they aim to reformulate the covariance expressions into a form amenable for interpretation. These expressions illustrate how different properties of the identification problem affects the achievable accuracy. In particular, how the power of the input and noise signals, as well as model structure, affect the covariance. / Systemidentifiering används för att skatta en modell av ett dynamiskt system genom att anpassa modellens parametrar utifrån experimentell mätdata inhämtad från systemet som ska modelleras. Systemen som modelleras tenderar att växa sig så omfattande i skala och så komplexa att direkt modellering varken är genomförbar eller önskad. I många fall går det komplexa systemet att beskriva som en komposition av enklare linära system (moduler) sammakopplade i något vi kallar dynamiska nätverk. Uppgiften att modellera hela eller delar av nätverket kan därmed brytas ner till deluppgiften att modellera en modul i det dynamiska nätverket. Det vanligaste sättet att skatta parametrarna hos en model är genom att minimera det så kallade prediktionsfelet. Den här typen av metod har nyligen anpassats för att identifiera moduler i dynamiska nätverk. Metoden åtnjuter goda egenskaper vad det gäller det modelfel som härrör från stokastisk störningar under experimentet och i de fall där störningarna är normalfördelade sammanfaller metoden med maximum likelihood-metoden. En nackdel med metoden är att functionen som minimeras vanligen är inte är konvex och därmed riskerar metoden att fastna i ett lokalt minimum. Det är därför essentiellt med en bra startpunkt. Andra metoder krävs därmed för att hitta en startpunkt, till exempel kan instrumentvariabelmetoder användas. I den här avhandlingen föreslås en alternativ metod kallad MORSM. MORSM är motiverad med argument hämtade från maximum likelihood och är också asymptotiskt effektiv i vissa fall. MORSM består av steg som kan lösas med minstakvadratmetoden och är därmed beräkningsmässigt attraktiv. Den del av nätverket som är utan intresse skattas enbart ickeparametriskt vilket underlättar valet av modellordning för användaren. En annan utgångspunkt tas i den andra metoden som föreslås för att skatta en modul inbäddad i ett dynamiskt nätverk. Impulssvaret från den del av nätverket som är utan intresse modelleras som realisation av en Gaussisk process. Medelvärdet och kovariansen hos den Gaussiska processen parametriseras av en mängd parametrar kallade hyperparametrar vilka skattas tillsammans med parametrarna för modulen. Parametrarna skattas genom att maximera den marginella likelihood funktionen. Optimeringen utförs iterativt med ECM, en variant av förväntan och maximering algoritmen (EM). Algoritmen har två steg. E-steget har en analytisk lösning medan CM-steget reduceras till delproblem som antingen har analytisk lösning eller har låg dimensionalitet och därmed kan lösas med gradientbaserade metoder. Den övergripande optimeringen är därmed beräkningsmässigt attraktiv. Med hjälp av MCMC tekniker generaliseras metoden till att inkludera ytterligare sensorer vars impulssvar också modelleras som Gaussiska processer. Förutom valet av metod så påverkar valet av signaler vilken nogrannhet eller kovarians den skattade modulen har. Klassiska uttryck för kovariansmatrisen kan användas för att optimera valet av signaler. Dock så ger dessa uttryck ingen insikt i varför valet av vissa signaler är optimalt eller vad som skulle hända om förutsättningarna vore annorlunda. Uttrycken som framställs i den här delen av avhandlingen har ett annat syfte. De försöker i stället uttrycka kovariansen i termer som kan ge insikt i vad som påverkar den nogrannhet som kan uppnås. Mer specifikt uttrycks kovariansen med bland annat avseende på insignalernas spektra, brussignalernas spektra samt modellstruktur. / <p>QC 20170614</p>

This thesis treats the identification of Volterra models of the human smooth pursuit system from eye-tracking data. Smooth pursuit movements are gaze movements used in tracking of moving targets and controlled by a complex biological network involving the eyes and brain. Because of the neural control of smooth pursuit, these movements are affected by a number of neurological and mental conditions, such as Parkinson's disease. Therefore, by constructing mathematical models of the smooth pursuit system from eye-tracking data of the patient, it may be possible to identify symptoms of the disease and quantify them. While the smooth pursuit dynamics are typically linear in healthy subjects, this is not necessarily true in disease or under influence of drugs. The Volterra model is a classical black-box model for dynamical systems with smooth nonlinearities that does not require much a priori information about the plant and thus suitable for modeling the smooth pursuit system. The contribution of this thesis is mainly covered by the four appended papers. Papers I–III treat the problem of reducing the number of parameters in Volterra models with the kernels parametrized in Laguerre functional basis (Volterra–Laguerre models), when utilizing them to capture the signal form of smooth pursuit movements. Specifically, a Volterra–Laguerre model is obtained by means of sparse estimation and principal component analysis in Paper I, and a Wiener model approach is used in Paper II. In Paper III, the same model as in Paper I is considered to examine the feasibility of smooth pursuit eye tracking for biometric purposes. Paper IV is concerned with a Volterra–Laguerre model that includes an explicit time delay. An approach to the joint estimation of the time delay and the finite-dimensional part of the Volterra model is proposed and applied to time-delay compensation in eye-tracking data.

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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. In this thesis, the objective is not only to find feasible solutions to a motion planning problem, but solutions that also optimize some kind of performance measure. From a control perspective, the resulting problem is an instance of an optimal control problem. In this thesis, the focus is to further develop optimal control algorithms such that they be can used to obtain improved solutions to motion planning problems. This is achieved by combining ideas from automatic control, numerical optimization and robotics. First, a systematic approach for computing local solutions to motion planning problems in challenging environments is presented. The solutions are computed by combining homotopy methods and numerical 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 both a state-of-the-art numerical optimal control method based on standard initialization strategies and a state-of-the-art optimizing sampling-based planner based on random sampling. Second, a framework for automatically generating motion primitives for lattice-based motion planners is proposed. 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 algorithm not only automatically optimizes the motions connecting pre-defined boundary conditions, but also simultaneously optimizes the terminal state constraints as well. In addition to handling static a priori known system parameters such as platform dimensions, the framework also allows for fast automatic re-optimization of motion primitives if the system parameters change while the system is in use. Furthermore, the proposed framework is extended to also allow for an optimization of discretization parameters, that are are used by the lattice-based motion planner to define a state-space discretization. This enables an optimized selection of these parameters for a specific system instance. Finally, a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems is presented. The main idea is to combine the strengths of sampling-based path planners and numerical optimal control. The lattice-based path planner is applied to the problem in a first step using a discretized search space, where system dynamics and objective function are chosen to coincide with those used in a second numerical optimal control step. This novel tight combination of a sampling-based path planner and numerical optimal control makes, in a structured way, benefit of the former method’s ability to solve combinatorial parts of the problem and the latter method’s ability to obtain locally optimal solutions not constrained to a discretized search space. The proposed approach is shown in several practically relevant path planning problems to provide improvements in terms of computation time, numerical reliability, and objective function value.

One of the most common advanced control strategies used in industry today is Model Predictive Control (MPC), and some reasons for its success are that it can handle multivariable systems and constraints on states and control inputs in a structured way. At each time-step in the MPC control loop the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem on-line. There exist several optimization methods to solve the CFTOC problem, where two common types are interior-point (IP) methods and active-set (AS) methods. In both these types of methods, the main computational effort is known to be the computation of the search directions, which boils down to solving a sequence of Newton-system-like equations. These systems of equations correspond to unconstrained finite-time optimal control (UFTOC) problems. Hence, high-performance IP and AS methods for CFTOC problems rely on efficient algorithms for solving the UFTOC problems. The solution to a UFTOC problem is computed by solving the corresponding Karush-Kuhn-Tucker (KKT) system, which is often done using generic sparsity exploiting algorithms or Riccati recursions. When an AS method is used to compute the solution to the CFTOC problem, the system of equations that is solved to obtain the solution to a UFTOC problem is only changed by a low-rank modification of the system of equations in the previous iteration. This structured change is often exploited in AS methods to improve performance in terms of computation time. Traditionally, this has not been possible to exploit when Riccati recursions are used to solve the UFTOC problems, but in this thesis, an algorithm for performing low-rank modifications of the Riccati recursion is presented. In recent years, parallel hardware has become more commonly available, and the use of parallel algorithms for solving the CFTOC problem and the underlying UFTOC problem has increased. Some existing parallel algorithms for computing the solution to this type of problems obtain the solution iteratively, and these methods may require many iterations to converge. Some other parallel algorithms compute the solution directly (non-iteratively) by solving parts of the system of equations in parallel, followed by a serial solution of a dense system of equations without the sparse structure of the MPC problem. In this thesis, two parallel algorithms that compute the solution directly (non-iteratively) in parallel are presented. These algorithms can be used in both IP and AS methods, and they exploit the sparse structure of the MPC problem such that no dense system of equations needs to be solved serially. Furthermore, one of the proposed parallel algorithms exploits the special structure of the MPC problem even in the parallel computations, which improves performance in terms of computation time even more. By using these algorithms, it is possible to obtain logarithmic complexity growth in the prediction horizon length.

The control-theoretic notion of controllability captures the ability to guide a systems behavior toward a desired state with a suitable choice of inputs. Controllability of complex networks such as traffic networks, gene regulatory networks, power grids etc. brings many opportunities. It could for instance enable improved efficiency in the functioning of a network or lead to that entirely new applicative possibilities emerge. However, when control theory is applied to complex networks like these, several challenges arise. This thesis consider some of these challenges, in particular we investigate how control inputs should be placed in order to render a given network controllable at a minimum cost, taking as cost function either the number of control inputs or the energy that they must exert. We assume that each control input targets only one node (called a driver node) and is either unconstrained or unilateral. A unilateral control input is one that can assume either positive or negative values but not both. Motivated by the many applications where unilateral controls are common, we reformulate classical controllability results for this particular case into a more computationally-efficient form that enables a large scale analysis. We show that the unilateral controllability problem is to a high degree structural and derive theoretical lower bounds on the minimal number of unilateral control inputs from topological properties of the network, similar to the bounds that exists for the minimal number of unconstrained control inputs. Moreover, an algorithm is developed that constructs a near minimal number of control inputs for a given network. When evaluated on various categories of random networks as well as a number of real-world networks, the algorithm often achieves the theoretical lower bounds. A network can be controllable in theory but not in practice when completely unreasonable amounts of control energy are required to steer it in some direction. For unconstrained control inputs we show that the control energy depends on the time constants of the modes of the network, and that the closer the eigenvalues are to the imaginary axis of the complex plane, the less energy is required for control. We also investigate the problem of placing driver nodes such that the control energy requirements are minimized (assuming that theoretical controllability is not an issue). For the special case with networks having all purely imaginary eigenvalues, several constructive algorithms for driver node placement are developed. In order to understand what determines the control energy in the general case with arbitrary eigenvalues, we define two centrality measures for the nodes based on energy flow considerations: the first centrality reflects the network impact of a node and the second the ability to control it indirectly. It turns out that whether a node is suitable as driver node or not largely depends on these two qualities. By combining the centralities into node rankings we obtain driver node placements that significantly reduce the control energy requirements and thereby improve the “practical degree of controllability”. / <p>Minor corrections are made in the electronic version of the thesis (Abstract). / Mindre korreigeringar är gjorda i den elektroniska versionen av avhandlingen (i Abstract).</p>

Mines, construction sites, road construction and quarries are examples of applications where construction equipment are used. In a production chain consisting of several construction machines working together, the work needs to be optimised and coordinated to achieve an environmental friendly, energy efficient and productive production. Recent rapid development within positioning services, telematics and human machine interfaces (HMI) opens up for control of individual machines and optimisation of transport missions where several construction machines co-operate. The production chain on a work site can be split up in different sub-tasks of which some can be transport missions. Taking off in a transport mission where one wheel loader ("loader" hereinafter) and two articulated haulers ("haulers" hereinafter) co-operate to transport material at a set production rate [ton/h], a method for fuel optimal control is developed. On the mission level, optimal cycle times for individual sub-tasks such as wheel loader loading, hauler transport and hauler return, are established through the usage of Pareto fronts. The haulers Pareto fronts are built through the development of a Dynamic Programming (DP) algorithm that trades fuel consumption versus cycle time for a road stretch by means of a time penalty constant. Through varying the time penalty constant n number of times, discrete fuel consumption - cycle time values can be achieved, forming the Pareto front. At a later stage, the same DP algorithm is used to generate fuel optimal vehicle speed and gear trajectories that are used as control signals for the haulers. Input to the DP algorithm is the distance to be travelled, road inclination, rolling resistance coefficient and a max speed limit to avoid unrealistic optimisation results. Thus, a method to describe the road and detect the road related data is needed to enable the optimisation. A map module is built utilising an extended Kalman Filter, Rauch-Tung-Striebel smoother and sensor fusion to merge data and estimate parameters not observable by sensors. The map module uses a model of the vehicle, sensor signals from a GPS or GNSS sensor and machine sensors to establish a map of the road. The wheel loader Pareto front is based on data developed in previous research combined with Volvo in-house data. The developed optimisation algorithms are implemented on a PC and in an interactive computer tablet based system. A human machine interface is created for the tablet, guiding the operators to follow the optimal control signals, which is speed for the haulers and cycle time for the loader. To evaluate the performance of the system it is tested in real working conditions. The contributions develop algorithms, set up a demo mission control system and carry out experiments. Altogether rendering in a platform that can be used as a base for a future design of an off-road transport mission control system.

In this thesis, we address a number of challenges in cluster analysis. We begin by investigating one of the oldest and most challenging problems: determining the number of clusters, k. For this problem, we propose a novel solution that, unlike previous techniques, delivers both the number of clusters and the clusters in one-shot (in contrast, conventional techniques run a given clustering algorithm several times for different values of k, and/or for several initialization with the same k). The second challenge we treat is the drawback, briefly mentioned above, of many conventional iterative clustering algorithms: how should they be initialized? We propose an initialization scheme that is applicable to multiple iterative clustering techniques that are widely used in practice (e.g., spectral clustering, EM-based, k-means). Numerical simulations demonstrate a significant improvement compared to many state-of-the-art initialization techniques. Third, we consider the computation of pairwise similarities between datapoints. A matrix of such similarities (the similarity matrix) constitutes the backbone of many clustering as well as unsupervised learning algorithms. In particular, for a given similarity metric, we propose a similarity transformation that promotes high similarity between the points within the cluster and deceases the similarity within the cluster overlapping regions. The transformation is particularly well-suited for many clustering and dimensionality reduction techniques, which we demonstrate in extensive numerical experiments. Finally, we investigate the application of clustering algorithms to image and video datasets (also known as superpixel segmentation). We propose a segmentation algorithm that significantly outperforms current state-of-the-art algorithms; both in terms of runtime as well as standard accuracy metrics. Based on this algorithm, we develop a tool for fast and accurate image annotation. Our findings show that our annotation technique accelerates the annotation processes by up to 20 times, without compromising the quality. This indicates a big opportunity to significantly speed up all AI computer vision tasks, since image annotation forms a crucial step in creating training data. / Den här avhandlingen behandlar en rad utmaningar inom klusteranalys. Till att börja med undersöker vi ett av de äldsta och mest utmanande problemen: att bestämma antalet kluster k utifrån data. Vi föreslår en ny algoritm som, till skillnad från tidigare algoritmer, ger antalet kluster (samt själva klustren) från enbart en körning. (Tidigare algoritmer kräver att dessa algoritmer körs flera gånger för olika värden på k, eller från olika startpunkter för samma värde på k.) Den andra utmaningen vi behandlar är hur de idag vanligast förekommande klusteringsalgoritmerna (e.g., spektral-, EM-baserad-, samt k-means-klustering) bör initialiseras. Vi föreslår en initialiseringsmetod, och demonstrerar i numeriska simulationer att denna ger signifikant bättre resultat jämfört med de nuvarande bästa metoderna. Som tredje del i avhandlingen studerar vi konstruktionen av mått på parvis likhet mellan datapunkter. En matris bestående av sådana likheter ligger till grund för många klusteringsalgoritmer, samt metoder för oövervakad inlärning inom maskininlärning. Mer specifikt så demonstrerar vi hur en likhetstransformation kan tillämpas på ett givet likhetsmått för att främja likhet mellan datapunkter inom samma kluster och undertrycka likhet för punkter som ligger i områden där kluster överlappar. Transformationen vi föreslår är speciellt lämpad för klusterings- och dimensionsreduceringsalgoritmer, vilket vi demonstrerar i omfattande numeriska experiment. Till sist studerar vi tillämpningar av klusteringsalgoritmer på bild- och videodata. Vi föreslår en segmenteringsalgoritm med signifikant bättre prestanda än de nuvarande bästa algoritmerna; både i termer av beräkningskomplexitet samt precision. Vidare så utvecklar vi en mjukvara baserad på vår algoritm för snabb och precis bildsegmentering. Våra studier visar att bildsegmentering och -annotering kan utföras upp till 20 gånger snabbare än med nuvarande mjukvaror, utan att vi kompromissar på kvalit´en. Detta pekar mot stora möjligheter att snabba upp många applikationer inom datorseende, eftersom segmenterad bilddata ligger till grund som träningsdata för många algoritmer.