Data centers, including edge data centers strategically positioned for critical applications, constitute vital components of today's technological infrastructure. Traditional data centers serve as centralized hubs supporting services like cloud computing, while edge centers, located nearer to end-users, play a pivotal role in applications such as augmented and virtual reality. These centers collectively ensure the efficient operation of digital services, providing necessary computing resources and minimizing delays for an optimal user experience. Addressing the dynamic challenges of these environments, effective cooling control strategies are imperative to mitigate energy consumption and optimize performance. Inadequate cooling not only impacts equipment functionality but also results in energy wastage, emphasizing the importance of tailored approaches to meet the dynamic demands of data center operations. The challenges in data center cooling, stemming from the dynamic workload and evolving computing demands, underscore the significance of developing model-based cooling control strategies. Traditional cooling methods may struggle to adapt, causing ineffective temperature regulation and potential hotspots. Intelligent cooling control strategies, rooted in models that dynamically adjust cooling resources based on real-time data and workload fluctuations, offer a solution. These model-based strategies enhance cooling efficiency, ensuring consistent temperature regulation while minimizing energy consumption. This approach becomes pivotal in supporting the sustainability and cost-effectiveness of data center operations amidst increasing computational demands. This licentiate thesis comprises three results that lead to solving the model-based data centers cooling controlproblems. The first result involves adaptive decoupling of multivariable systems,utilizing the extremum-seeking approach to dynamically adjust cooling resources based on real-time data, ensuring optimal efficiency. The second result focuses on online estimation of PID controllers and plant dynamics, enhancing precision and effectiveness through real-time adaptation to changing conditions within the dynamic landscape ofdata centers. The third result specifically applies empirical transfer function estimation for model fitting in a data center cooling model. These results provide guidance and insights to address cooling control design challenges that will be the future focus of this research.

Sustained use of critical infrastructure, such as electrical power and water distribution networks, requires efficient management and control. Facilitated by the advancements in computational devices and non-proprietary communication technology, such as the Internet, the efficient operation of critical infrastructure relies on network decomposition into interconnected subsystems, thus forming networked control systems. However, the use of public and pervasive communication channels leaves these systems vulnerable to cyber attacks. Consequently, the critical infrastructure is put at risk of suffering operation disruption and even physical damage that would inflict financial costs as well as pose a hazard to human health. Therefore, security is crucial to the sustained efficient operation of critical infrastructure. This thesis develops a framework for evaluating and improving the security of networked control systems in the face of cyberattacks. The considered security problem involves two strategic agents, namely a malicious adversary and a defender, pursuing their specific and conflicting goals. The defender aims to efficiently allocate defense resources with the purpose of detecting malicious activities. Meanwhile, the malicious adversary simultaneously conducts cyber attacks and remains stealthy to the defender. We tackle the security problem by proposing a game-theoretic framework and characterizing its main components: the payoff function, the action space, and the available information for each agent. Especially, the payoff function is characterized based on the output-to-output gain security metric that fully explores the worst-case attack impact. Then, we investigate the properties of the game and how to efficiently compute its equilibrium. Given the combinatorial nature of the defender’s actions, one important challenge is to alleviate the computational burden. To overcome this challenge, the thesis contributes several system- and graph-theoretic conditions that enable the defender to shrink the action space, efficiently allocating the defense resources. The effectiveness of the proposed framework is validated through numerical examples.

Learning flow functions of continuous-time control systems is considered in this thesis. The flow function is the operator mapping initial states and control inputs to the state trajectories, and the problem is to find a suitable neural network architecture to learn this infinite-dimensional operator from measurements of state trajectories. The main motivation is the construction of continuous-time simulation models for such systems. The contribution is threefold. We first study the design of neural network architectures for this problem, when the control inputs have a certain discrete-time structure, inspired by the classes of control inputs commonly used in applications. We provide a mathematical formulation of the problem and show that, under the considered input class, the flow function can be represented exactly in discrete time. Based on this representation, we propose a discrete-time recurrent neural network architecture. We evaluate the architecture experimentally on data from models of two nonlinear oscillators, namely the Van der Pol oscillator and the FitzHugh-Nagumo oscillator. In both cases, we show that we can train models which closely reproduce the trajectories of the two systems. Secondly, we consider an application to spiking systems. Conductance-based models of biological neurons are the prototypical examples of this type of system. Because of their multi-timescale dynamics and high-frequency response, continuous-time representations which are efficient to simulate are desirable. We formulate a framework for surrogate modelling of spiking systems from trajectory data, based on learning the flow function of the system. The framework is demonstrated on data from models of a single biological neuron and of the interconnection of two neurons. The results show that we are able to accurately replicate the spiking behaviour. Finally, we prove an universal approximation theorem for the proposed recurrent neural network architecture. First, general conditions are given on the flow function and the control inputs which guarantee that the architecture is able to approximate the flow function of any control system with arbitrary accuracy. Then, we specialise to systems with dynamics given by a controlled ordinary differential equation, showing that the conditions are satisfied whenever the equation has a continuously differentiable right-hand side, for the control input classes of interest. / Denna avhandling studerar maskininlärningsmetoder för tidskontinuerliga reglersystem. Vi utgår från en abstrakt systemrepresentation med en lösningsoperator, som avbildar systemets initialtillstånd och insignal på motsvarande tillståndstrajektorian. Målet är att undersöka inlärning av tidskontinuerliga simuleringsmodeller utifrån tillståndsmätningar. Avhandlingen består av tre huvudbidrag. Vi undersöker först arkitekturer baserade på neurala nätverk, för klasser av insignaler som är brukliga i tillämpningar och har en viss tidsdiskret struktur. Vi formulerar problemet matematiskt, och visar att lösningsoperatorn kan representeras exakt av ett tidsdiskret system. Detta leder till en arkitektur baserad på ett återkopplande neuralt nätverk (RNN), som vi utförligt beskriver, analyserar och validerar med hjälp av data från två modeller av icke-linjära oscillatorer, nämligen Van der Pol oscillatorn och FitzHugh-Nagumo oscillatorn. I båda fall visar vi att vi kan träna modeller som noggrant reproducerar systemens lösningsbanor. Därefter studerar vi en tillämpning på system vars tillståndstrajektorier kännetecknas av förekomsten av snabba oscillationer i form av impulser, såsom modeller av biologiska neuroner. Denna klass av system karakteriseras av ett flerskaligt och högfrekvent tidssvar, vilket gör det önskvärt att ta fram tidskontinuerliga modeller som är lätta att simulera. Vi lägger fram ett ramverk för inlärning av surrogatmodeller av sådana system från data. Ramverket demonstreras med hjälp av data från en modell av en biologisk neuron och en modell av två kopplade biologiska neuroner, och resultaten visar att våra modeller noggrant reproducerar systemens beteende. Slutligen tar vi fram ett bevis för ett approximationsteorem för inlärning av lösningsoperatorer av tidskontinuerliga system. Vi visar att den RNN- arkitektur som vi har tagit fram kan approximera godtyckliga reglersystem under vissa villkor som vi först formulerar abstrakt. Sedan bevisar att reglersystem som beskrivs av ordinära differentialekvationer uppfyller dessa villkor, vilket betyder att de kan approximeras av den studerade arkitekturen. / <p>QC 20240220</p>

As robots become increasingly prevalent in society, it is essential to prescribe complex high-level tasks to them. Tasks prescribed over temporal logics present two main challenges: generating trajectories that satisfy the logical formula and tracking those trajectories that depend on the logical formula. This thesis aims to address these challenges. Firstly, we use Prescribed Performance Control (PPC) to solve the cooperative manipulation problem based on constraints defined by an Signal Temporal Logic (STL) formula. Secondly, we design a planning algorithm that generates spatio-temporal trees and searches for trajectories that satisfy an STL formula for cooperating agents. Finally, we utilise gradient-based methods to shape trajectories that satisfy an STL formula for multiple cooperating agents. Our approach is based on integration of tools from the areas of multi-agent systems, optimisation theory, cooperative object manipulation and motion planning. More specifically, in the second chapter we start by focusing on solving the problem of cooperative manipulation of an object specified by an STL formula. To achieve this, we utilise the PPC methodology, which enforces the desired transient and steady-state performance on the object trajectory to satisfy the STL formula. Specifically, we propose a method that translates the problem of satisfying an STL task into the problem of state evolution within a custom-defined time-varying funnel, which is then used to design a decentralised control strategy for robotic agents. The strategy guarantees compliance with the funnel, and each agent calculates its own control signal, without utilising any information on the dynamic terms of the agents or object. We provide experimental validation of our approach using two manipulator arms cooperatively manipulating an object based on a specified STL formula. In the next chapter, we present a novel motion planning algorithm for two autonomous agents working together to accomplish coupled tasks expressed as STL constraints. The proposed algorithm is a cooperative sampling-based approach that builds two spatio-temporal trees incrementally, one for each agent. This is achieved by sampling points in an extended space, which is a compact subset of the time domain and physical space of the agents. The algorithm constructs the trees by checking if newly sampled points form edges in time and space that satisfy certain parts of the coupled task. As a result, the constructed trees represent time-varying trajectoriesin the agents’ state space that satisfy the task. The algorithm is distributed and inherits the properties of probabilistic completeness and computational efficiency from the original sampling-based procedures. And in the final chapter, we present a distributed algorithm that can generate continuous trajectories for multiagent systems based on an STL formula. The STL formula is designed over functions that are coupled to the states of neighbouringagents. The algorithm is distributed, meaning that each agent independently com-putes its own trajectory by only communicating with its immediate neighbours. The approach is verified through various simulated scenarios. / <p>QC 20230403</p>

To be able to analyze certain classes of non-linear systems, it is necessary to try to represent them as linear parameter varying systems or even as linear fractional representations. For linear parameter varying systems and linear fractional representations of systems there exists many advanced analysis methods such as IQC-analysis and μ-analysis. This means that an important intermediate step in all this is to generate a linear parameter varying model that describes these non-linear system sufficiently well. The first contribution in this thesis is a novel method that tries, through nonlinear programming and a quasi-Newton framework, to generate a linear parameter varying model given linearized state space models. The idea behind the method is to preserve the input-output relations of the given linearized systems and, in an H2-measure, find the best one. To handle uncertainties in data an extension of the proposed method is presented. It is shown how the computationally hard robust optimization approach to the uncertain case can be approximated using a problem specific regularization. The second contribution in this thesis is a method for synthesizing output-feedback H2 controllers of arbitrary order. This method also uses non-linear programming and a quasi-Newton framework to achieve this. One great benefit with this method is that it also possible to impose structure in the controller. Both of the methods described above tries to solve non-linear and non-convex problems, which means that the problem of finding a good initial estimate is an important problem. For both methods an initialization procedure is proposed to try to find an initial estimate. The methods are evaluated on several examples and show promising results. A contributing factor is that significant effort has been spent on utilizing the structure of the optimization problems to make the methods efficient.

Engineering sciences deal with the problem of optimal design in the face of uncertainty. In particular, control engineering is concerned about designing policies/laws/algorithms that sequentially take decisions given unreliable data. This thesis addresses two particular instances of optimal sequential decision making for two different problems. The first problem is known as the H∞-norm (or l2-gain, for LTI systems) estimation problem, which is a fundamental quantity in control design through the small gain theorem. Given an unknown system, the goal is to find the maximum l2-gain which, in a model-free approach, involves solving a sequential input design problem. The H∞-norm estimation problem (or simply "gain estimation problem") is cast as the composition of a multi-armed bandit problem generating data, and an optimal estimation problem given that data. It is shown that the separation of the gain estimation problem into these two sub-problems is optimal in a mean-square sense, as the expected estimation error asymptotically matches the Cramér-Rao lower bound. In the second part of the thesis, we address the problem of risk-coherent optimal control design for disturbance rejection under uncertainty, where optimality is studied from an H2 and an H∞ sense. We consider a parametric model for the plant and the noise spectrum, where the modeling error between the model and the real system is uncertain. This uncertainty is condensed in a probability density function over the different realizations of the parameters defining the model. We use this information to design a controller that minimizes the risk of falling into poor closed-loop performance within a financial theory of risk framework. A systematic approach for the design of H2- and H∞-optimal controllers is proposed in terms of a quadratically-constrained linear program and a semi-definite program, respectively. An interesting application to H2-optimal design under covert attacks is also developed. / <p>QC 20190411</p>

Autonomous driving is a disrupting technology that is expected to reshape transportation systems. The benefits of autonomous vehicles include, but are not limited to, safer transportation, increased economic growth, and broader access to mobility services. Industry and academia are currently researching a variety of topics related to autonomous driving, however, the focus seems to be on passenger vehicles. As a consequence, heavy-duty vehicles, which are a significant share of transportation systems, are overlooked, and the challenges associated with these vehicles are neglected. This thesis studies motion planning algorithms for heavy-duty vehicles. Motion planning is a fundamental part of autonomous vehicles, it is tasked with finding the correct sequence of actions that take the vehicle towards its goal. This work focuses on particular aspects that distinguish heavy-duty vehicles from passenger vehicles, and that call for novel developments within motion planning algorithms. We start by addressing the problem of finding shortest paths for a vehicle in obstacle-free environments. This problem has been studied since the fifties, but the addressed vehicle models are often simplistic. We propose a novel algorithm that is able to plan paths respecting complex vehicle actuator constraints associated with the slow dynamics of heavy vehicles. Using the previous method, we tackle the motion planning problem in environments populated with obstacles. Lattice-based motion planners, a popular choice for this type of scenario, come with drawbacks related to the sub-optimality of solution paths, and the discretization of the goal state. We propose a novel path optimization method, which is able to significantly reduce both problems. The resulting optimized paths contain less oscillatory behavior and arrive precisely at arbitrary non-discretized goal states. We then study the problem of bus driving in urban environments. It is shown how this type of driving is fundamentally different than that of other vehicles, due to the chassis configuration with large overhangs. To successfully maneuver buses, distinct driving objectives need to be used in planning algorithms. Moreover, a novel environment classification scheme must be introduced. The result is a motion planning algorithm that is able to mimic professional bus driver behavior, resulting in safer driving and increased vehicle maneuverability. / <p>QC 20190603</p>

Autonomous vehicle technology is shaping the future of road transportation. This technology promises safer, greener, and more efficient means of transportation for everyone. Autonomous vehicles are expected to have their first big impact in closed environments, such as mining areas, ports, and construction sites, where heavy-duty vehicles (HDVs) operate. Although research for autonomous systems has boomed in recent years, there are still many challenges associated with them. This thesis addresses lateral motion control for autonomous HDVs using model predictive control (MPC). First, the autonomous vehicle architecture and, in particular, the control module architecture are introduced. The control module receives the current vehicle states and a trajectory to follow, and requests a velocity and a steering-wheel angle to the vehicle actuators. Moreover, the control module needs to handle system delays, maintain certain error bounds, respect actuation constraints, and provide a safe and comfortable ride. Second, a linear robust model predictive controller for disturbed discrete-time nonlinear systems is presented. The optimization problem includes the initial nominal state of the system, which allows to guarantee robust exponential stability of the disturbance invariant set for the discrete-time nonlinear system. The controller effectiveness is demonstrated through simulations of an autonomous vehicle lateral control application. Finally, the controller limitations and possible improvements are discussed with the help of a more constrained autonomous vehicle example. Third, a path following reference aware MPC (RA-MPC) for autonomous vehicles is presented. The controller makes use of the linear time-varying MPC framework, and considers control input rates and accelerations to account for limitations on the vehicle steering dynamics and to provide a safe and comfortable ride. Moreover, the controller includes a method to systematically handle references generated by motion planners which can consider different algorithms and vehicle models from the controller. The controller is verified through simulations and through experiments with a Scania construction truck. The experiments show an average lateral error to path of around 7 cm, not exceeding 27 cm on dry roads. Finally, the nonlinear curvature response of the vehicle is studied and the MPC prediction model is modified to account for it. The standard kinematic bicycle model does not describe accurately the lateral motion of the vehicle. Therefore, by extending the model with a nonlinear function that maps the curvature response of the vehicle to a given request, a better prediction of the vehicle's movement is achieved. The modified model is used together with the RA-MPC and verified through simulations and experiments with a Scania construction truck, where the improvements of the more accurate model are verified. The experiments show an average lateral error to path of around 5 cm, not exceeding 20 cm on wet roads. / Autonoma fordon förväntas få en stor inverkan på framtidens transporter av gods och personer. En teknologi som lovar säkrare, grönare och effektivare transporter till alla. Den typ av verksamhet som autonoma fordon först förväntas få ett större genomslag inom är transporter i avskilda områden, så som gruvområden, hamnar och byggplatser. Även om forskning kopplat till autonoma system har exploderat under den senaste åren kvarstår fortfarande ett flertal frågeställningar. Denna avhandling fokuserar på lateral rörelsestyrning av tunga autonoma fordon med modellprediktiva regulatorer (MPC). Avhandlingen består av fyra huvuddelar. I först delen introduceras det autonoma fordonets systemarkitektur, med fokus på regulatormodulen. Regulatormodulen genererar hastighet och rattvinkel referenser till fordonets hastighetaktuator och rattvinkelaktuator baserat på fordonets nuvarande tillstånd samt den givna referensbanan som fordonet skall följa. Regulatormodulen behöver dessutom hantera fördröjningar i systemet, säkerställa att systemet inte överskrider givna felmarginaler, hantera aktuator och systembegränsningar, och sist men inte minst framföra fordonet på ett säkert och komfortabelt sätt. I andra delen presenteras en robust modellprediktiv regulator för ett tidsdiskret olinjärt system med störningar. I  optimeringsproblemet inkluderas systemets nominella initialtillstånd, detta möjliggör garanterad robust exponentiell stabilitet för det tidsdiskreta olinjära systemets störningsinvarianta tillståndsmängd. Regulatorns prestanda visas genom simuleringar av ett autonomt fordon där regulatorn kontrollerar fordonets laterala rörelse. Begränsningar och potentiella förbättringar av regulatorn diskuteras utifrån exempel med ökade begränsningar. I tredje delen presenteras en referens medveten modellprediktiv regulator (RA-MPC), en regulator utvecklad för att styra ett autonomt fordon längs en given referensbana. Regulator baseras på en linjärt tidsvarierande MPC och begränsningar i fordonets styrdynamik hanteras genom att beräkna dessa baserat på in insignalernas, referensbana, värden och derivator. Genom att beakta begränsningarna på detta sätt möjliggörs en komfortabel och säker körning. En systematisk metod för att hantera referensbanor som genererats av rörelseplanerare baseras på algoritmer och modeller som skiljer sig från de som används i regulatorn presenteras också. Den metoden är även implementerad i regulatorn. Regulatorn har utvärderats med såväl simuleringar som tester. Testerna har genomförts i en Scania lastbil av anläggningstyp. Experimenten visade på en lateral avvikelse från referensbana på 7 cm i genomsnitt och en maximal avvikelse på 27 cm då fordonet kördes på torr asfalt. I den sista delen studeras olinjär respons i fordonets kurvaturreglering och hur detta kan hanteras i MPC’ns prediktions modell av fordonet presenteras också. En prediktions modell baserad på en standard kinematisk cykelmodell beskriver inte fordonets laterala rörelse tillräckligt bra för det studerade systemet. Dock, genom att utvidga modellen med en funktion som mappar fordonets respons mot en given kurvaturbegäran kan noggrannhet av fordonets rörelse förbättras. Modellen tillsammans med RA-MPC utvärderades genom simuleringar och tester. Testerna har genomförts i en Scania lastbil av anläggningstyp. Utvärderingen visade att den introducerade modellen gav en förbättrad precision. Experimenten visade på en lateral avvikelse från referensbanan på 5 cm i genomsnitt och en maximal avvikelse på 20 cm då fordonet kördes på våt asfalt. / <p>QC 20200819</p>

In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these efficiently and to have good upper bounds on worst-case solution time. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving such QPs is active-set methods, where a sequence of linear systems of equations is solved.  The primary contribution of this thesis is a method which determines which sequence of subproblems a popular class of such active-set algorithms need to solve, for every possible QP instance that might arise from a given linear MPC problem (i.e, for every possible state and reference signal). By knowing these sequences, worst-case bounds on how many iterations, floating-point operations and, ultimately, the maximum solution time, these active-set algorithms require to compute a solution can be determined, which is of importance when, e.g, linear MPC is used in safety-critical applications.  After establishing this complexity certification method, its applicability is extended by showing how it can be used indirectly to certify the complexity of another, efficient, type of active-set QP algorithm which reformulates the QP as a nonnegative least-squares method.  Finally, the proposed complexity certification method is extended further to situations when enhancements to the active-set algorithms are used, namely, when they are terminated early (to save computations) and when outer proximal-point iterations are performed (to improve numerical stability).

Aeroplanes that are aerodynamically stable in longitudinal dynamics at subsonic velocities suffer from reduced manoeuvrability at supersonic velocities. By using a closed-loop automatic control system, an aeroplane that is unstable at subsonic velocities can be stabilized, allowing for both safe subsonic flight characteristics and high manoeuvrability at supersonic velocities. However, the closed-loop system might be sensitive to uncertain parameter values in the dynamic model used for control system design. This Master’s Thesis explores how robust stability with respect to parametric uncertainties can be analyzed for closed-loop controlled, aerodynamically unstable aeroplanes by using μ-analysis and Linear Parameter Varying modelling, implemented in Matlab and Simulink.