A common strategy to address new scientific challenges consists of abstracting the underlying problem, recasting it to an existing problem formulation and applying an established methodology. In this dissertation, we offer a variation on this familiar academic theme. The setting we will focus on is primarily found within image-acquiring instruments, characterized by producing vast quantities of data, from several hundreds up to more than half a million images per experiment. The challenges that we address throughout this work will mainly consist of (a) reducing dimensionality and (b) denoising, which have a direct and significant impact on the analysis and thus interpretation of these extensive image sets.
We investigate computational methods for two specific imaging instruments: (1) a time-of-flight imaging mass spectrometer, employed in biochemical research to visualize molecular distributions across very small organic tissues, and (2) a mid-infrared imager, utilized in astronomical research to study very large protostars, temperate exoplanets, and objects within our solar system. Despite their considerable promise in acquiring detailed molecular maps and critical astronomical insights, respectively, the practical analysis and interpretation of their image sets face substantial obstacles, namely their dimensionality and the effect of noise. Addressing these challenges may involve drawing on existing computational and storage capacity and harnessing any available prior information or problem-specific structure. Fortunately, analytical solutions to the obstacles across imaging instruments often bear a resemblance to each other, as we distil them to abstract mathematical models and eventually formulate those problems as optimization problems.
The computational methods we are interested in are so-called low-rankmethods, they can simultaneously provide insight in data structure (analysis), as well as reduce the dimensionality of the data and denoise it....

While reinforcement learning (RL) and supervised learning provide powerful approaches for finding optimal controllers for complex systems, ensuring safety remains a critical challenge. In control problems, safety is typically defined as maintaining state and input constraint satisfaction throughout the system’s evolution. The key issue lies in balancing constraint satisfaction with computational efficiency in the presence of inevitable learning errors. This PhD thesis addresses this challenge across linear, piecewise affine (PWA), and nonlinear systems with various constraint structures.

The increasing integration of renewable energy sources into power systems, characterized by their variability and inherent lack of inertia, presents significant challenges for the load frequency control problem, as large frequency fluctuations can cause equipment damage or even blackouts. Additionally, the large geographical size and complexity of today’s power systems require a multi-agent control strategy that is scalable and computationally efficient for real-time control.
This thesis proposes two novel control structures that integrate decentralized Model Predictive Control (MPC) with residual reinforcement learning based on the Deep Deterministic Policy Gradient (DDPG) algorithm. In the first structure, each area is controlled by a decentralized MPC, and a centralized coordinating residual DDPG layer is added on top. In the second structure, the decentralized MPC layer is combined with a distributed coordinating residual DDPG layer. The second structure is more scalable, but limits every DDPG controller to partial system observability. To effectively test and evaluate the novel control strategies, the European Economic Area Electricity Network Benchmark (EEA-ENB) is used.
Both structures share four key ideas: 1) Due to the coupling of areas in the EEA-ENB, the resulting power system is unstable, making it difficult to train the DDPG agent. To overcome this, the decentralized MPC layer enforces baseline stability, enabling the DDPG agent to learn a residual input to improve coordination between areas. 2) The coordinating DDPG layer is trained offline, shifting the computational burden away from online control. 3) By providing a meaningful baseline, decentralized MPC removes the need for the DDPG agent to learn entirely from scratch, which increases the sample efficiency. 4) The baseline allows the DDPG agent to learn in a smaller action space, which reduces exploration difficulties and improves the accuracy.
The proposed structures are compared against the centralized MPC, distributed MPC based on the alternating direction method of multipliers, and decentralized MPC in a four and six-area case study. Simulation results demonstrate that the coordinating residual input from the centralized or distributed DDPG layer significantly reduces the performance gap between decentralized MPC and the optimal centralized MPC solution. The centralized DDPG layer reduces the gap by 69.0% in the four-area case and 76.3% in the six-area case, while the distributed variant achieves reductions of 49.5% and 87.3%, respectively. Although the performance of the developed control structures does not fully match that of distributed MPC, the computational cost is at least 15 times lower. The distributed DDPG variant requires longer offline training time compared to the centralized DDPG method, but improves the scalability. To fully validate their performance and scalability, future work should implement the control structures on the entire EEA-ENB network.

Driven by the rapid integration of Renewable Energy Sources (RESs) and the growing elec- trification of transport, heating, and industry, the Dutch power grid is being fundamentally reshaped. While essential for meeting climate goals, these developments introduce significant operational challenges, including higher uncertainty in power production and congestion risks. Existing approaches for Congestion Management (CM) often neglect the stochastic nature of RESs generation, rely on simplified network representations, or overlook real-world market constraints.
This thesis addresses these gaps by formulating the Dutch market-based CM problem as a Chance-Constrained Model Predictive Control (CC-MPC) framework. A linearized model of the Dutch high-voltage network is employed within a CC-MPC scheme that incorporates flexibility offers through integer decision variables. Uncertainty in RESs generation is cap- tured using an Seasonal AutoRegressive Integrated Moving-Average (SARIMA) model for each production region in the network, enabling a probabilistic treatment of forecast errors. To mitigate conservatism in the chance constraints, a Reinforcement Learning (RL) approach is introduced to adaptively tune the uncertainty model. The resulting stochastic disturbance trajectories are used in a sampling-based approximation of the CC-MPC, optimising conges- tion mitigation decisions under uncertainty.
The proposed methodology is validated using real-world data from the Dutch energy data ex- change platform Energie Data Services Nederland (EDSN), including operational data from Grid Operators Platform for AnCillary Services (GOPACS), the national CM platform. Re- sults demonstrate that the RL-enhanced CC-MPC achieves improved constraint satisfaction compared to other methods. Overall, this work contributes to the current literature by devel- oping a rigorous framework for market-based CM under uncertainty, aimed at ensuring the reliable and cost-effective operation of future renewable-dominated power systems.

Autonomous vehicles offer significant potential for improving traffic efficiency and reducing
fuel consumption, with Model Predictive Control (MPC) being widely used due to its ability
to guarantee constraint satisfaction and safety while providing optimal control performance.
However, car models traditionally used in MPC approaches for vehicle control often overlooks
discrete dynamics like gear changes, which are critical for optimizing vehicle fuel consumption. Advancements have incorporated these discrete dynamics into MPC, resulting in a hybrid model that considers both continuous and discrete dynamics. The incorporation of
the fuel model, along with these discrete dynamics, significantly increases the computational
complexity of the MPC problem, making real-time implementation challenging. To address
this issue, Reinforcement Learning (RL) can be leveraged to simplify the optimization problem by learning policies that determine key discrete components, such as gear selection. This
allows the MPC controller to handle a simpler optimization problem, thereby reducing the
computational burden and enabling real-time control. This research aims to propose a new
approach to integrate RL and MPC for vehicle control, where RL is used to manage gear
transitions and MPC controls the overall vehicle dynamics, offering a computationally efficient solution, while achieving near optimal performance comparable to the conventional
MPC approach.

Spatiotemporal systems are systems whose dynamics depend on time and space and are commonly found in real life. These systems are mathematically modeled using partial differential equations and are also known as distributed-parameter systems. Due to their structure and the high number of variables involved, control and estimation for this class of systems are very challenging. This thesis addresses two problems related to spatiotemporal systems: state estimation and system identification.

Monitoring the states of a control system is important to ensure the behavior of the system is achieving the control objectives. This can be achieved, among others, by using state observers that estimate the states of the systems regularly. First, we present a literature review of observer design methods for distributed parameter systems. In general, the design requires a dimension-reduction approach to implement the observer. From the dimension reduction, the design approaches can be classified into late and early lumping. In the late lumping perspective, model reduction is performed at the end of the observer design. In the early lumping perspective, dimension reduction is applied to the model of the system. We incorporate both approaches in our literature review.

State observer design requires the model of the systems. This thesis also presents a system identification method for distributed-parameter systems. The identification of such systems typically requires spatially dense and regular measurements, followed by selecting sensors that provide significant measurements to the model to reduce the model complexity. However, these requirements may be challenging to fulfill. In case the sensor locations are irregular and sparse in space, we propose the use of lumped-parameter system identification.

For models with a large number of regressors, we propose a method for reducing the number of regressors using a tree representation. The tree is a way to list models with different numbers of regressors. From all possible regressors for the model, the proposed method builds the tree from the simplest models, i.e., models with one regressor. The number of regressors in the models is incrementally increased to one or more models with the best performance. The addition is repeated until the tree contains models with the desired maximum number of regressors.

System identification is typically performed using a complete data set, i.e., for each input sample, there is an associated output sample available. However, there are cases in which some output samples are not recorded in the data set, making the identification data incomplete. This thesis also considers the problem of incomplete data for Takagi-Sugeno (TS) fuzzy system identification using the product space clustering method. This method comprises two steps: fuzzy clustering and rules construction. The first proposed method enables the use of incomplete system identification data to fuzzy c-means clustering algorithm developed for incomplete classification, which yields different estimates for a missing sample. This can be achieved by fusing those different values into a single value. The second proposed method treats missing samples as optimization variables during the identification process. The optimization is repeated until the change of all optimization variables is small.

Recent engineering developments have surrounded us with intelligent devices, which are required to autonomously take rational decisions while interacting with the physical world. These systems are increasingly widespread, interacting and interconnected, thus resulting in decision problems that involve multiple rational agents, generally with conflicting objectives and interrelated operating constraints. Currently relevant examples include autonomous driving, traffic routing, clearance of autonomous bidding markets, power consumption and production scheduling on the electricity grid, control of robotic swarms, and autonomous racing. The mathematical framework for formulating these problems is known as a game. Over the past decade, there has been significant progress in the development of algorithms that determine an action which is simultaneously rational (i.e. optimal) for each agent, namely, a generalized Nash equilibrium (GNE). This solution is particularly favorable as it is self-enforcing, in the sense that no decision maker can improve its payoff by unilaterally deviating from it. However, currently available algorithms for the computation of a GNE present numerous shortcomings, which limit their applicability to real-world non-cooperative decision processes and that we address in this thesis.

First of all, GNE problems typically admit multiple solutions, but currently available algorithms only compute an arbitrary, initialization-dependent GNE. In applications where a predictable and well-defined solution is necessary, it becomes important to select a specific GNE (among potentially infinitely many) that optimizes an arbitrary metric or a secondary, cooperative objective. We develop the first optimal GNE selection algorithms. We compare two different algorithm design methods, both developed under the framework of operator theory: the first, i.e. the hybrid steepest descent method (HSDM), entails a gradient descent of the selection function with vanishing step size combined with a GNE seeking algorithm, while the second requires the solution of a sequence of Variational Inequalities (VIs) with a vanishing regularizing term. Both design methods lead to algorithms that are suitable to distributing the computation between a central node and the agents, and we include ad-hoc algorithms for the particular cases of aggregative and cocoercive games.

Secondly, we consider time-varying games, motivated by the need for algorithms that continuously monitor and control physical multiagent systems. In such games, the agents must track an evolving solution with limited computation time between the problem's updates. This scenario is particularly relevant when the agents are affected by disturbances whose time-scale is comparable to the algorithm convergence rate. The challenge lies in finding algorithms that exhibit fast convergence and a robustness property to external disturbances, both typically associated with a linear convergence rate. We derive and study the asymptotic tracking error of a fully-distributed algorithm (i.e., without a central coordinator) for GNE problems with linear equality constraints. For a time-varying GNE selection problem, we find the HSDM with constant stepsize to be linearly convergent to an approximate solution. We find that the approximation error can be controller by an appropriate choice of the stepsize and number of iterations per time step, and we derive a bound to the asymptotic tracking error.

Finally, again driven by the need of applying GNE seeking algorithms to the control of physical systems, we consider dynamic games, where the decision each agent has to take is a time sequence of inputs to a dynamical system. In this case, the coupling between the agents emerges not only through the objectives and constraints, but also through the system dynamics. Ideally, one should compute the GNE solution by predicting the dynamics over an indefinitely long horizon. This is typically computationally intractable, especially when constraints are present. We then approximate the infinite-horizon control sequence by recomputing at each time instant the solutions to a finite-time equilibrium problem, a method typically known as receding-horizon control (or model predictive control, in the single-agent case). We derive a novel characterization of the infinite horizon objective achieved by the Nash equilibrium trajectory, and we show that one can recover the infinite-horizon performance by including this expression in the agents' objectives as an additive terminal cost. With this result, we conclude asymptotic stability of the steady state under a receding-horizon game-theoretic control action. Compared to the literature, we do not assume stability of the uncontrolled plant, nor we introduce auxiliary constraints. Furthermore, we find that the asymptotic stability of the steady state can be obtained with a more generic terminal cost if the game is potential, as we demonstrate on a practical traffic routing application.

Emergency maneuvers on highways present one of the most complex challenges for automated driving. High speeds pushing the vehicle towards nonlinear regimes, coupled with the necessity of swift decision making, complicates the collision avoidance problem to the extent that even expert human drivers may struggle to safely avoid collisions.
Lack of sufficient and reliable data limits applicability of model-free and data-driven control approaches in hazardous scenarios, opening the door to model-based and optimization based control approaches. However, the unknown behavior of other road users, the sensitivity of the handling limits (e.g., tire saturation) to road conditions, and the amplification of minor steering adjustments on the lateral trajectory due to high speed necessitate the incorporation of nonlinear models in the design. Such nonlinearities should be balanced with the increased complexity and the need for swift responses to hazard....

Deep Learning (DL) has transformed computer vision, leading to significant
progress in areas like autonomous vehicles and industrial automation. However, its application in underwater environments remains challenging due to factors such as light absorption, scattering, and water turbidity, which degrade image quality and hinder DL model performance. This thesis addresses these challenges by enhancing DL-based computer vision techniques for underwater scenarios, with a focus on autonomous robotic litter collection from the seabed. The work targets key limitations such as data scarcity, visual degradation, and scene variability, and proposes domain-informed approaches to enhance model generalization. The contributions cover the full DL pipeline, starting with the design of representative training data that supports object detection in shallow-water conditions, providing a benchmark for training and evaluation of detection algorithms. A multi-robot system is developed that integrates aerial, surface, and underwater vehicles to perform collaborative litter detection and collection. The thesis presents the system design, deployment, and the role of computer vision in the operational workflow. To address image degradation, an automated framework is proposed for selecting image enhancement methods based on task-specific performance metrics. Furthermore, environment-specific neural networks are introduced to handle variability in turbidity and lighting. Generalization to Out-of-Distribution (OOD) data is further addressed through a hybrid classification framework that combines a Convolutional Neural Network (CNN) with a physics-based classifier using the Moving Horizon Estimation (MHE) framework. Their outputs are fused via Dempster-Shafer theory to enable decision-making in unfamiliar scenarios. Finally, domain-informed neural networks are proposed to integrate physics-based knowledge into the DL pipeline via knowledge distillation. This method improves generalization and reduces dependence on large labeled datasets. The proposed methods are validated through simulation and real-world deployments, demonstrating improved performance and adaptability. Together, these contributions provide an integrated framework for deploying DL-based perception systems in challenging underwater environments.

While various tracking algorithms have demonstrated effectiveness in terrestrial and aerial contexts, their performance in underwater settings remains unexplored. Object tracking in underwater videos presents unique challenges due to variable lighting, water turbidity, and unpredictable camera movement, all of which are likely to hinder the performance of traditional detection and tracking methods. Addressing this gap is crucial for applications such as marine biology research, underwater surveillance, and autonomous underwater vehicles.

This thesis first evaluates existing tracking algorithms, SORT, ByteTrack, and Bag-of-Tricks SORT (BoT-SORT), each incorporating motion estimation and linear data assignment methods on a novel underwater video dataset with a moving camera. The thesis then improves on the SORT algorithm by adopting velocity estimation techniques, a formula-based and an optical flow-based, giving rise to two new algorithms, SORT-V and SORT-OF. Furthermore, the thesis proposes a novel tracker that utilises an Interacting Multiple Model filter to estimate the location of the target object. The evaluation focuses on finding a balance between specific metrics, such as tracking accuracy, identity switches, and the number of tracked and lost trajectories. The results indicate that using velocity estimation techniques improves the tracking accuracy by 11% and tracks more objects by nearly halving the number of lost objects. Incorporating a constant acceleration model in the IMM filter gives the best result, with the highest tracking accuracy and with the least number of identity switches, all in real-time computational speed.

In the evolving landscape of energy systems, microgrids have emerged as a key solution for enhancing energy efficiency and sustainability. Capable of operating independently or alongside the main power grid, microgrids integrate renewable energy sources and ensure local energy distribution. This makes them instrumental in reducing dependencies on centralised power supplies and improving resilience against disruptions. This research addresses the unit commitment problem, a mathematical optimisation challenge where the objective is to coordinate a group of energy production units to meet demand at minimal cost. We model the microgrid as a mixed logical dynamical (MLD) system, incorporating both the continuous and discrete variables involved in the microgrid. Model predictive control (MPC) is selected as the control strategy due to its suitability for controlling hybrid systems and its ability to handle complex constraints.

However, the application of MPC is challenged by the need to solve computationally demanding mixed-integer linear programming (MILP) problems at each control iteration, which are combinatorial. To address this challenge, this research proposes integrating a learning-based method to enhance MPC in microgrids. We propose using transformers to learn and predict the binary decisions in MILP problems, thereby reducing the problem to a more tractable linear programming problem. Transformers are chosen for their ability to recognise patterns in sequential data, a key aspect of the decision-making process in MPC. Furthermore, their capability for parallel processing allows for more efficient training and scalability to larger problems, making them highly suitable for handling the dynamic and complex optimisation tasks found in microgrid control. Simulation experiments show that integrating transformers in the decision of the discrete variables reduces the overall computation with only a slight loss of optimality and, therefore, improves the online applicability of MPC in microgrid control.

This PhD thesis advances resource recovery from wastewater by focusing on two key technologies: Purple Phototrophic Bacteria (PPB) raceway reactors and anaerobic digesters (ADs). To address challenges such as process variability, monitoring limitations, and operational inefficiencies, this research employs three complementary approaches: mechanistic modeling, hybrid system identification, and adaptive predictive control. Mechanistic models offer detailed insights into microbial interactions and process dynamics; hybrid system identification develops low-order models for practical data reconciliation and forecasting; and adaptive model predictive control dynamically optimizes operations to enhance performance. Key contributions include a novel mechanistic model for PPB cultivation in raceway reactors, a temperature-dependent extension for the anaerobic digestion model no.1, a hybrid system identification method to approximate complex mechanistic models, and an adaptive hierarchical process-oriented MPC framework for PPB reactors and ADs to manage variable operations and unknown disturbances. These approaches advance wastewater resource recovery in their intended perspectives, providing efficient solutions for both case studies.

Urban rail transit networks are dedicated to providing safe, efficient, and eco-friendly transportation services for passengers. This thesis focuses on innovative model predictive control (MPC) strategies for the integration of passenger flows, timetables, and train speeds in urban rail transit networks. We introduce several innovative MPC frameworks, including bi-level MPC, scenario-based distributed MPC, learning-based MPC, and cooperative distributed MPC. These approaches exhibit significantly improved performance compared to conventional methods.

The railway timetable rescheduling problem is a challenging problem in both industry and academia. It is required to calculate a feasible and relatively good timetable within a limited time to reduce the negative impact of disturbances or disruptions. The railway timetable rescheduling problem is typically formulated as a mixed integer linear programming (MILP) problem, which is difficult to solve due to the existence of the integer variables. To address this problem, many optimization-based studies have been conducted. The main advantage of using optimization-based methods is that they are easy to implement and more straightforward. However, the main disadvantage is that most optimization-based methods cannot reach the time requirements for large railway timetable rescheduling problems. There are also some researches using reinforcement learning techniques to solve this problem. By using reinforcement learning, the time requirement could be fulfilled.

In this thesis, an algorithm that combines both reinforcement learning and optimization approaches is proposed to solve the railway timetable rescheduling problem. In the beginning, the reinforcement learning environment is constructed from the railway timetable rescheduling problem. By selecting the independent integer variables as the action, the constraints involving the integer variables are satisfied. After that, a value-based reinforcement learning algorithm is implemented to determine the independent integer variables of the MILP problem. Then, the complete solution of the integer variables could be derived from these independent integer variables. With the solution of integer variables, the MILP problem could be transformed into a linear programming problem, which could be solved efficiently.

Several case studies are conducted in this thesis based on part of the Dutch railway network from Utrecht to 's-Hertogenbosch. The simulation results show that the proposed method makes a great improvement compared with the baseline regarding reducing the total delay of the system. Meanwhile, the reinforcement learning-based method also has an obvious advantage in terms of running time.

Quadrupedal robots possess the ability to move freely in the world and perform a variety of actions that would be unsafe or impractical for humans to perform. In the SNOW project, a quadrupedal robot is tasked with aiding firefighters in rescue missions during house fires by locating humans and assessing their health. Pushing away obstacles that cannot be circumvented otherwise is one of the many capabilities a quadrupedal robot should possess to be of most use in such missions. We develop a proof of concept by solving two problems sequentially: which stance to take on prior to the push and how to perform the push.

The process of stance selection starts with generating a certain amount of stances. Stances are generated starting from a preselected stance appropriate to the goal location and deviating from the 12 joint angles with a normal distribution. All generated stances are ran through a number of filters, which rely on solving for the forward and inverse kinematics of the robot. These filters check if the initial position is sensible and balanced and if the projected final position is close to the goal and balanced. The inverse kinematics are solved using Adaptive-Network-Based Fuzzy Inference Systems (ANFIS), which results in accurate estimations within a time frame that can be used in real-time applications. The final stance is selected by comparing the total displacement of all joint angles per stance, where the lowest total displacement is considered optimal.

The push is controlled by a nonlinear model predictive controller. We strive for a stable push, where the contact between the pusher and the object sticks, by keeping the movement of the end-effector within the motion cone. The motion cone denotes all twists the object can have without slipping at the contact with the pusher and is constructed using the limit surface to model the interaction between the object and the support surface and the generalized friction cone to model the interaction between the pusher and the object. We find that the motion cone predicts stick and slip with an accuracy slightly higher than 80%. Our controller steers accurately to all goals that lie within the motion cone and moves the object with a twist on the edge of the motion cone if the goal location lies outside of the motion cone. The robot remains balanced throughout the pushing motion in the vast majority of cases, but is more at risk of tipping over when pushing heavier objects.

Ambitions to limit climate change are incentivizing the expansion of renewable energy. In particular, offshore wind energy is expected to grow rapidly. To harness the full potential of existing as well as prospected offshore wind farms, the limited capacity of the internal cable network of the offshore wind farm, called the collector system, should be efficiently used.

The operation of the collector system during cable outages presents significant potential in this regard. Currently, during these outages, a conservative approach is taken that under-utilizes the capacity of the collector system and consequently limits power production excessively. The available headroom of the system can be unlocked by optimizing the power routing and turbine setpoints. This optimization problem is the topic of the MSc Thesis, carried out
within Vattenfall.

Two novel optimization-based rerouting and setpoint decision frameworks are developed for collector systems with arbitrary topologies: an open-loop control strategy and a receding horizon control strategy.

The open-loop control strategy assumes that the network can only be reconfigured at the beginning of the outage. It is formulated as a mixed-integer linear programming problem, in which the cables are modeled as binary control variables and the setpoints as continuous control variables.

The receding horizon control strategy is deployed in real time, leveraging cable temperature measurements and power forecasts to derive optimal control actions dynamically. Dynamic thermal rating is applied, which entails that the power flows are constrained based on the cables’ temperatures rather than on a static rating. The resulting control strategy is formulated as a mixed-integer quadratically constrained programming problem.

A case study is performed to compare the performance of the developed strategies to existing strategies. Simulations concerning seven occurred cable outages at an offshore wind farm show an average increase in power production with respect to the industry control strategy of 0.82% for the open-loop control strategy and 4.2% for the receding horizon control strategy.

The renewable generation capacity, particularly solar and wind power installations, has increased steadily in the Netherlands over the course of recent years. Due to the local, small-scale nature of these power plants (compared to conventional power plants), a large share of this generation capacity is installed into the medium- and low-voltage distribution grids. This trend acts as the source of several challenges for distribution system operators (DSOs) such as Stedin Netbeheer B.V. (a DSO in the Netherlands, supporting this project). One of the main problems is the fact that voltage limit violations, particularly upper voltage limit violations, become more frequent.
Conventional voltage control schemes assume a unidirectional power flow (i.e., consumption only) in distribution grids and are unable to keep the limits in case a large share of generation capacity is installed. This is further complicated by the fact that underground cable networks, typical in Western European electricity distribution grids, have lines with large R/X ratios, which reduces the effectiveness of reactive power injection-based voltage control methods.
This MSc project intends to solve the issue of voltage limit violations with a model predictive control (MPC) policy. The considered control actions coordinated by the model predictive controller are the switching of the on-load tap changer (OLTC) mechanism mounted to the primary substation’s transformer, setpoint adjustments of the low-level OLTC control relay, and the active power curtailment of larger photovoltaic plants. A linear, sensitivity-matrix-based model is used for the grid’s state prediction; and the sensitivity values are re-calculated at each sampling time step of the MPC. To avoid the curtailment of photovoltaic (PV) plants when not justified, a conditional curtailment logic is incorporated into the MPC policy: PV plants are only allowed to be curtailed if their local voltage magnitude is above a tuneable threshold. This logic is described and incorporated into the model predictive controller’s optimization problem with the help of binary variables and mixed-integer linear (MIL) constraints. The benefit of incorporating knowledge about future disturbances (load, generation, and external grid voltage profiles) is also tested, in order to assess the potential benefit DSOs could get from forecasting these quantities.
A case study was conducted in which the considered controllers were tested on a section of a Stedin grid that carries the characteristics of a typical Western European medium voltage distribution grid: large R/X ratios and a large installed PV generation capacity both in the form of household generation and larger PV plants. All controllers were simulated in 4 different test cases: a typical summer day, a summer day with the external grid’s overvoltage, a summer day with 2 out of 3 large PV plants not operating, and a typical winter day. All test cases have the control goals of mitigating limit violations and ensuring that the nodal voltage magnitudes are as close as possible to the nominal 1 per unit throughout the day. The winter day test case has the additional goal of avoiding excessive curtailment as PV energy is worth considerably more during these days. All profile data is based on real Stedin measurements. The designed model predictive control policies are compared to two simple control schemes: current compounding, i.e. when the primary substation’s automatic voltage control relay’s setpoint is adjusted based on the active power delivery through the substation’s transformer, and another scheme when current compounding is combined with local active power curtailment controllers for large PV plants. The most important metrics used for comparison are voltage root mean square error (RMSE), the total voltage limit violation area, the percentage of curtailed PV energy, and the number of tap changes over the considered day. The simulations were carried out using Python and DIgSILENT PowerFactory.
The simulation results show that the MPC policy can perform better than the simple control schemes but only when exact knowledge of future profiles is available. In this case, the MPC results in lower voltage RMSE, smaller violation areas, and lower curtailment percentage values, at the expense of using more tap changes in all 4 test cases. In 3 of the 4 test cases, MPC was completely able to eliminate voltage limit violations, showing clearly the advantages of good quality forecasts on future disturbances. Since this exact knowledge about the near future fluctuations is quite ideal, more realistic MPC policies were also tested with no future knowledge and tightened voltage constraints. These simulations brought mixed results when compared with the simple schemes, performing better in terms of voltage RMSE, but worse in terms of the total voltage limit violation area.

This thesis addresses the Learning-Based Control (LBC) of unknown partially observable systems in the Linear Quadratic (LQ) paradigm. In this setting of learning-based LQ control, the control action influences not only the control performance but also the rate at which the system is being learnt, causing a conflict between learning and control (exploration and exploitation), which is particularly challenging to address. This thesis aims to develop a novel LBC algorithm for unknown partially observable systems in the LQG setting that is computationally efficient and can guarantee an optimal exploration-exploitation trade-off, quantified by a metric called regret. The regret quantifies the cumulative performance gap between the LBC policy and the ideal controller having full knowledge of the true system dynamics. The contributions in this thesis involve a novel LBC algorithm deployed in a two-phase structure. The first phase involves injecting Gaussian input signals to obtain an initial system model. The subsequent second phase deploys the proposed LBC strategy in an episodic setting, where the model is updated for each episode, and the resulting updated LQG controller is applied with additive Gaussian signals for exploration. In addition, the thesis establishes strong theoretical guarantees on optimal regret growth.

Nowadays, the high demand for road transportation often reaches a point where it exceeds the capacity of freeway traffic networks, resulting in congestion. Freeway traffic congestion is a major social problem, as it is the reason for increased time delays, higher accident risk and environmental pollution. There is, therefore, the need for a sustainable solution that can be implemented on the existing road infrastructure. Freeway traffic control is considered as such a solution. It uses different control measures, in order to improve the performance of the freeway traffic network, by influencing the drivers’ behaviour.

The Variable Speed Limits (VSLs) are a traffic control measure that aims to increase traffic safety, improve traffic flow and reduce the environmental pollution. Towards the improvement of the freeway traffic flow, easy-to-implement VSL control algorithms are used as mainline metering control approach.

Two easy-to-implement VSL algorithms are reported, namely the Mainstream Traffic Flow Control (MTFC) and the Logic-Based control algorithm for Variable Speed Limits (LB-VSL). The algorithms are usually implemented in an non-adaptive framework. The main contribution of this thesis is that it proposes an adaptive framework for both algorithms, in which the critical density of the freeway traffic network at bottleneck’s location is estimated on-line. This estimated critical density is used to adjust the controllers’ parameters in real-time.

Three different estimation methods for the bottleneck’s critical density are studied, namely the Parameter Estimation (Parameterschatter) method, the Simple Derivative Estimation (SDE) and the Kalman-Filter-based derivative Estimation (KFE) methods. All three methods focus on the real-time estimation of the derivative of the Fundamental Diagram (FD), in order to produce estimations of the critical density.

A case study is performed to evaluate the performance of the three algorithms. A hypothetical 12 km long freeway stretch is used, which contains two VSLs installations and a lane-drop bottleneck. In the first part of the case study an accident scenario is studied, which decreases the critical density at the bottleneck’s location. The second part of the case study evaluates the three adaptive easy-to-implement VSL algorithms under the assumption of a decrease of the critical density across the whole network, due to bad weather conditions.

The microscope is an essential tool for biologists. Since the late 16th century, it has given researchers a better understanding of cell processes and greatly advanced healthcare. In this century, Single molecule localization microscopy (SMLM) has revolutionized optical microscopy by breaking the optical diffraction limit. Sparsely activating emitters in a sample labeled with fluorophores, the object can be reconstructed by estimating their positions using the system point spread function (PSF). These localization algorithms are the state of the art
in optical imaging, using unbiased estimators to reach the theoretical minimum uncertainty, or Cramér-Rao lower bound (CRLB).
While SMLM works well when emitters are sparsely activated, overlap of the emitter images is inevitable for thick or densely labeled samples. When SMLM is used on such images, the estimates become biased and the algorithm cannot find the correct number of emitters. Most techniques also make a deterministic estimate and are incapable of representing the uncertainty of estimates for dense samples.
A three-dimensional, Bayesian multiple emitter fitting algorithm is constructed using reversible jump Markov chain Monte Carlo (RJMCMC). While following the structure of Bayesian multiple-emitter fitting (BAMF), novel RJMCMC moves are designed to sample the parameters. The algorithm also jumps through models, estimating the number of emitters. It asymptotically samples from the posterior, revealing uncertainties in three-dimensional imaging that other techniques are incapable of imaging.
The algorithm was tested with astigmatic and biplane imaging. It has proven capable of consistently finding the correct model when a prior on emitter intensity is used. When separating two emitters, posterior density reconstruction revealed non-Gaussian emitter position uncertainties. Upon further investigation, the posterior density was found to be multimodal, with
both modes representative of the data and indistinguishable in terms of likelihood. This shows the algorithm can quantify three-dimensional PSF degeneracy and can become a vital tool for researchers to analyze their imaging setup. We also expect it to be especially effective when combined with modulation-enhanced localization microscopy (meLM) techniques.