This thesis studies decentralised multi-robot navigation through dense pedestrian crowds. In such environments, robots must do more than avoid immediate collisions: they must make consistent qualitative decisions about how to pass pedestrians and how to yield or proceed in close robot-robot encounters. These decisions are difficult to represent in a purely reactive controller, yet enumerating all possible interaction patterns is too expensive for online planning in dense scenes.

The proposed method addresses this problem with a three-layer topology-inspired planner. First, deterministic pedestrian predictions are converted into a space-time density field, and a time-expanded A* search computes a coarse route that biases each robot away from high-density regions. Second, a local interaction layer selects the nearby agent-pedestrian and agent-agent events that matter for the current replanning window and searches the resulting sequence space with a bounded best-first procedure. Third, the selected sequence is converted into signed winding-number targets and realised by a short-horizon velocity-sampling controller. The method is decentralised: each robot runs the same planner locally, while the same execution-level safety layer is applied to all
methods in the comparison.

The planner is evaluated in simulation against ORCA, the Social Force model, Dynamic Channel, Socially Competent Navigation, and a decentralised model predictive control (MPC) baseline across several crowd densities and motion patterns. In the random-crowd comparison, the proposed method obtains the lowest collision rate at the highest tested density and reaches goals with competitive time to goal, while requiring substantially less computation time than the MPC baseline. The results indicate that separating route-level guidance, qualitative interaction search, and continuous realisation can make dense crowd navigation safer than purely reactive planning and cheaper than full optimisation-based control. The remaining limitations are the deterministic pedestrian predictions, simplified holonomic-disc dynamics, and hand-designed search and scoring rules, which motivate future work on uncertainty, richer robot dynamics, and more principled topological search. ... Read more

Modern power systems are being fundamentally reshaped by the increasing integration of renewable energy sources, such as solar and wind power generation. Their inherent variability poses significant challenges for real-time grid control. In particular, advanced control strategies, including model predictive control, require multi-step forecasts at temporal resolutions relevant to the specific control application, which in this work is on the order of seconds. However, commonly available meteorological datasets are often temporally sparse, creating a pronounced mismatch between data availability and control requirements. To address this challenge, this thesis investigates the use of physics-informed neural networks to forecast photovoltaic (PV) power generation in spatially distributed PV systems at temporal resolutions on the order of seconds under temporal data sparsity.

The proposed PINN incorporates partial physical knowledge of atmospheric processes through a spatiotemporal cloud motion equation, enabling physically plausible generalization to unseen time steps and conditions. To generate multi-step forecasts at temporal resolutions on the order of seconds, a recursive forecasting framework is developed. In addition, an improved training strategy is proposed in which the model is trained using its own recursively generated forecasts, thereby reducing the mismatch between training and inference. Finally, a novel correlation-based collocation point sampling strategy is developed to generate physically plausible and statistically representative collocation points, thereby supporting effective physics-based regularization.

The proposed methods are evaluated through two complementary case studies. In a case study based on a selected region in France, the PINN with the improved training strategy demonstrates a clear advantage under challenging atmospheric conditions compared to a persistence model, which assumes constant behavior over the forecast horizon. It also achieves superior data efficiency relative to purely data-driven neural networks and improved computational efficiency over a physics-only model during inference. The proposed collocation point sampling strategy also consistently outperforms uniform sampling.

In addition, a real-world case study based on a measurement site in Hawaii validates the forecasting framework under a realistic PV deployment scenario in which available data are not only temporally sparse but also satellite-derived. Because such data provide only an approximate, temporally and spatially smoothed representation of the true atmospheric conditions affecting the PV system, this setting introduces an additional data-reality mismatch. Nevertheless, the framework remains capable of producing meaningful forecasts at temporal resolutions on the order of seconds, establishing its practical applicability for PV systems worldwide without local measurement infrastructure.
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Optimisation problems are all around us and play a critical role in the outcomes of various sectors of society including scheduling, logistics, network design, and resource allocation. In this thesis, we look at a subset of problems where some or all the choices to be made can only take on values belonging to a discrete set of values – a limitation which increases the difficulty of finding a solution in most cases. We handle this thesis in two parts: first zooming in on a particular class of problems – scheduling – and then on a particular solution method – decision diagrams.

In Part I of this dissertation, we consider the problem of scheduling in manufacturing systems. This popular discrete optimisation problem has been studied extensively; however, advancements in modern manufacturing systems present new challenges and opportunities. A major driver of the changes in manufacturing systems is the integration of the physical processes with computation, networking, and automated control capabilities. Thus, the domain of activities that can directly be decided upon and actuated from software has expanded. We look at one such activity in Chapter 3 namely,
sequence-dependent maintenance and propose solution methods that directly integrate maintenance and production planning.

Part II of this thesis looks into decision diagrams as a solution method for discrete optimisation problems. Decision diagrams have existed since the 1950s and were originally introduced as a means to represent boolean functions. Since then they have been used in different fields such as in circuit verification, knowledge representation, and most recently, operations research. While decision diagrams have already been shown to be very promising methods for solving optimisation problems, we push the field forward as follows. In Chapter 5, we propose a decision diagram model for the kind of scheduling problems tackled in Part I of this thesis. We further perform a comparative study of the consequences of heuristic decisions made during the decision diagram compilation process in Chapter 6 and integrate reinforcement learning with decision-diagram-based branch-and-bound in Chapter 7. In Chapter 8 we go further into considering uncertainty in optimisation problems. We focus on the paradigm of finding the best solution while accepting some level of risk, i.e., chance constrained optimisation and present a chance constrained decision diagram formulation. We further provide theoretical guarantees for instances with normally distributed variables.

The contributions of this thesis cover different aspects of solving discrete optimisation problems with a focus on scheduling and logistic applications. The hope is that these advances further the adoption of state of the art research in solving optimisation problems in real-world contexts. ... Read more

This dissertation advances Model Predictive Control (MPC) by addressing two major challenges: computational complexity and model uncertainty. The research focuses on distributed control and learning-based approaches to facilitate MPC for hybrid systems, large-scale networks, and systems with limited model knowledge.

To reduce computational burden, new distributed MPC methods for piecewise affine systems are developed, providing efficient convex optimisation-based solutions with guarantees on consistency and feasibility. Learning-based policies are also integrated with MPC, shifting computationally intensive tasks offline and enabling efficient control of hybrid systems and autonomous vehicles.

To address uncertainty, reinforcement learning (RL) is combined with MPC to learn uncertain controller components from data. Novel distributed MPC-RL frameworks are proposed for networked systems. Furthermore, centralised MPC-RL controllers are proposed for applications such as greenhouse climate control and energy systems. The results demonstrate that distributed and learning-based MPC can significantly improve scalability, efficiency, and performance in complex real-world control problems. ... Read more

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. ... Read more

The evolution of communication and computing technologies of the recent decades has enabled the rapid development and scaling of networks of systems. Consequently, modern networks of systems present complexities and geographical extents for which traditional monitoring, planning, and control paradigms based on centralized, or even human-driven, operation are not sufficient anymore to guarantee efficient and safe operation. For such systems, more sophisticated control strategies are required for nominal functioning and further extension. While the availability of information, given by real-time communication, and the computing power, generally accessible for large applications, are no longer a fundamentally limiting factor in modern networks, the same cannot be stated for the control technologies behind their operation. The achievement of complete non-centralization of control decisions and actions, as well as the satisfaction of complex requirements for safe network operations, preservation, and restoration, are among the main drivers of the future development of networks. Pursuing the achievement of these advanced specifications, of profound societal relevance, and the necessity of improving performance and efficiency are at the basis of current research in the field of systems and control of networks. This thesis approaches some of these topics and consists of two main parts.... ... Read more

This thesis develops a hierarchy of Bayesian estimation methods for Wiener-type state-space models, motivated by autonomous underwater vehicle (AUV) bathymetric mapping and related robotic perception problems. The focus is on a class of models in which a known linear dynamical process is observed through an unknown, possibly nonlinear output map whose parameters must be inferred from noisy input-output data. In this setting, the observation model is driven by latent, stochastic system states. The central objective is to design parameter estimators that are both statistically accurate and computationally tractable, enabling their embedding within navigation and mapping pipelines.

The work begins with a maximum a posteriori (MAP) estimator for identifying an unknown output map, formulated as a linear time-varying (LTV) observation-model identification problem. In this setting, the MAP estimation problem is posed over the entire state-parameter trajectory and shown to be non-convex. A semidefinite-programming (SDP) relaxation based on linear matrix inequalities (LMIs) is then derived to obtain a conservative but tractable approximation, whose solution serves as a warm start for quasi-Newton re!nement. Numerical experiments validate the efficacy of the proposed method in terms of estimation accuracy and computational efficiency.... ... Read more

This dissertation develops a circuit-theoretic methodology for modeling economic systems grounded in first principles. Like electrical circuits, economic systems can be understood as networks consisting of many interacting parts whose collective behavior emerges from their interactions. Circuit theory translates physical first principles into standard components, topological rules, and graphical representations for modeling complex dynamical systems. This dissertation applies these principles to economics by developing a methodology in which economic agents are represented by electrical components and economic systems are constructed as networks of these components.

The theoretical foundation of the methodology is an economic-engineering analogy, which describes economic dynamics in terms of mechanical behavior. Since mechanical and electrical systems can be represented through equivalent analogies, this dissertation adopts an equivalent electrical representation of the economic engineering theory. This allows complex networks of interacting economic agents to be modeled and analyzed using the principles of circuit theory and to be represented by analogous circuit diagrams. The advantage of this electrical representation is that circuit theory provides scalable tools for constructing, simulating, and analyzing interconnected dynamical systems. These tools are leveraged in this dissertation to develop the proposed modeling methodology.

The methodology is developed in two main steps. The first step introduces an economic circuit theory. Economic agents are modeled using generalized circuit elements that satisfy constitutive economic relations analogous to the laws governing resistors, inductors, and capacitors. Economic interactions are represented as network connections through which goods, analogous to currents, and incentives, analogous to voltages, are exchanged. Circuit diagrams provide both graphical and computational representations of economic systems, allowing standard circuit simulation tools such as LTspice to be used directly to simulate economic dynamics.

The second step focuses on scalability. While economic circuit theory provides a systematic way to describe interactions, large and highly interconnected economic systems quickly become difficult to manage when modeled only with elementary circuit elements. To address this, the dissertation extends economic circuit theory into a multiport network methodology. This allows complex economic systems to be constructed from modular subsystems with well-defined interfaces, while preserving interpretability and scalability.

The dissertation demonstrates the applicability of the methodology through several examples, ranging from textbook models to contemporary practical problems. A Robinson–Crusoe economy illustrates how classical microeconomic reasoning can be represented and simulated using circuit diagrams. A supply chain model shows how frequency-domain analysis, central to engineering practice, reveals resonance and oscillatory effects in inventory behavior. An electricity market with storage demonstrates how structural changes in a market alter system dynamics. Finally, a modular macroeconomic model illustrates how the methodology can scale to systems with many interacting sectors, while preserving interpretability and allowing shocks to be traced through the network.

Beyond the dissertation, the methodology has already been applied in a range of MSc theses across domains such as energy markets, industrial competition, financial planning, and macroeconomic modeling. These applications highlight the accessibility of the methodology, particularly for students with an engineering background, and its potential to become a practical tool for research, teaching, and policy analysis.

The methodology introduces several elements from engineering modeling practice into economics: explicit dynamics, modular construction, graphical representation, and scalable system analysis. Because the models can be drawn as circuit-style diagrams and executed in standard simulation environments such as LTspice, the methodology makes it possible to explore economic dynamics computationally using established engineering tools. Taken together, these elements provide a systematic way to examine how economic behavior emerges from agent interactions and how system-wide dynamics are shaped by the underlying network structure.
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In the current age of emerging autonomous and artificial-intelligence-driven machines, sequential decision making constitutes one of the theoretical fundaments at the core of intelligent agency. As these systems are increasingly deployed in real-world engineering applications (e.g., autonomous vehicles and drones, as well as smart energy grids and greenhouses), there is a growing need for the control architectures governing these agents to meet, aside from traditional performance requirements, also interpretability and safety criteria, while encouraging adaptability and scalability. Classical model-based methodologies, such as Model Predictive Control (MPC), can in general provide rigorous frameworks that integrate a priori knowledge (e.g., via explicit, though often approximate, prediction models) and can handle constraints to enforce safety, yet their performance is tightly coupled with the accuracy of the underlying model and expert manual tuning of its parameters. Conversely, purely model-free approaches, such as deep Reinforcement Learning (RL), offer remarkable data-driven adaptation, but often lack interpretability and reliable constraint handling required to provide formal guarantees.
This work expands on the current state-of-the-art results that combine these two distinct approaches into a single framework. While not always straightforward, it is well known that endowing these decision-making processes with model-based knowledge can not only enhance their performance but also benefit their interpretability and analysis: model-based RL, also known as Approximate Dynamic Programming (ADP), is perhaps the most renowned machine learning paradigm to craft these intelligent predictive agents. This dissertation aims to look at RL from a different perspective. Instead of as an alternative to model-based control, RL is used as a performance-enhancing mechanism operating within rigorously defined safety requirements. Concurrently, this thesis establishes MPC as a unifying and scalable foundation block for learning-based control and optimisation for constrained, uncertain, and distributed decision-making systems...... ... Read more

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.... ... Read more

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. ... Read more

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. ... Read more

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. ... Read more

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. ... Read more

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.... ... Read more

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.
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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. ... Read more

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. ... Read more

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.
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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. ... Read more