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The ranking of nodes in a network according to their centrality or ``importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The COVID-19 pandemic has recently rejuvenated the interest in this problem, as the ranking may be used to decide who should be tested, or vaccinated, first, in a population of asymptomatic individuals. In this paper, we review classic methods for node ranking and compare their performance in a benchmark network that considers the community-based structure of society. The outcome of the ranking procedure is then used to decide which individuals should be tested, and possibly quarantined, first. Finally, we also review the extension of these ranking methods to weighted graphs and explore the importance of weights in a contact network by providing a toy model and comparing node rankings for this case in the context of disease spread.

We present a decentralised class of algorithms called Tree-Proof-of-Position (T-PoP). T-PoP algorithms rely on the web of interconnected devices in a smart city to establish how likely it is that an agent is in the position they claim to be. T-PoP operates under adversarial assumptions, by which some agents are incentivised to be dishonest. We present a theoretical formulation for T-PoP and its security properties, and we validate this model through a large number of Monte-Carlo simulations. We specifically focus on two instances of T-PoP and analyse their security and reliability properties under a range of adversarial conditions. Use-cases and applications are discussed towards the end of this paper.

This paper discusses congestion control and inconsistency problems in DAG-based distributed ledgers and proposes an additional filter to mitigate these issues. Unlike traditional blockchains, DAG-based DLTs use a directed acyclic graph structure to organize transactions, allowing higher scalability and efficiency. However, this also introduces challenges in controlling the rate at which blocks are added to the network and preventing the influence of spam attacks. To address these challenges, we propose a filter to limit the tip pool size and to avoid referencing old blocks. Furthermore, we present experimental results to demonstrate the effectiveness of this filter in reducing the negative impacts of various attacks. Our approach offers a lightweight and efficient solution for managing the flow of blocks in DAG-based DLTs, which can enhance the consistency and reliability of these systems. Index

In many sharing-economy applications, as well as in conventional economy applications, one wishes to regulate the behaviour of an ensemble of agents with guarantees on both the regulation of the ensemble in aggregate and the revenue or quality of service associated with each agent. Previous work [Automatica, Volume 108, 108483, arXiv:1807.03256 ] has developed guarantees of unique ergodicity when there are linear filters. Here, we extend the guarantees to systems including non-linear elements, such as non-linear filters.

There has been much recent interest in the regulation of AI. We argue for a view based on civil-rights legislation, built on the notions of equal treatment and equal impact. In a closed-loop view of the AI system and its users, the equal treatment concerns one pass through the loop. Equal impact, in our view, concerns the long-run average behaviour across repeated interactions. In order to establish the existence of the average and its properties, one needs to study the ergodic properties of the closed-loop and its unique stationary measure.

In this paper we present a feedback approach to the design of an attack mitigation policy for DAG-based Distributed Ledgers. We develop a model to analyse the behaviour of the ledger under the so called Tips Inflation Attack and we design a control strategy to counteract this attack strategy. The efficacy of this approach is showcased through a theoretical analysis, in the form of two theorems about the stability properties of the ledger with and without the controller, and extensive Monte Carlo simulations of an agent-based model of the distributed ledger.

In this paper, we describe an approach to guide drivers searching for a parking space (PS). The proposed system suggests a sequence of routes that drivers should traverse in order to maximise the expected likelihood of finding a PS and minimise the travel distance. This system is built on our recent architecture SPToken, which combines both Distributed Ledger Technology (DLT) and Reinforcement Learning (RL) to realise a system for the estimation of an unknown distribution without disturbing the environment. For this, we use a number of virtual tokens that are passed from vehicle to vehicle to enable a massively parallelised RL system that estimates the best route for a given origin-destination (OD) pair, using crowdsourced information from participant vehicles. Additionally, a moving window with reward memory mechanism is included to better cope with non-stationary environments. Simulation results are given to illustrate the efficacy of our system., Comment: 12 pages, 5 figures, 27th ITS World Congress, Hamburg, Germany, 11-15 October 2021

Cyclists travelling in urban areas are particularly at risk of harm from particulate emissions due to their increased breathing rate and proximity to vehicles. In this paper we combine human respiratory models with models of particulate inhalation to estimate the pollution risk an individual is experiencing in real time given the local pollution level and their heart rate for the first time. Using this model as a baseline, we learn a policy that simultaneously optimises the route for a large number of cyclists with diverse origins and destinations, to minimise overall pollution risk and account for the detrimental impacts of congestion. We learn this policy using reinforcement learning techniques on simulated data in different environments with varying distributions of cyclist fitness. These findings establish that individualised routing is effective in reducing pollution risk while cycling, improving the net benefits of active commuting.

Reinforcement learning (RL) algorithms aim to learn optimal decisions in unknown environments through experience of taking actions and observing the rewards gained. In some cases, the environment is not influenced by the actions of the RL agent, in which case the problem can be modeled as a contextual multi-armed bandit and lightweight myopic algorithms can be employed. On the other hand, when the RL agent's actions affect the environment, the problem must be modeled as a Markov decision process and more complex RL algorithms are required which take the future effects of actions into account. Moreover, in practice, it is often unknown from the outset whether or not the agent's actions will impact the environment and it is therefore not possible to determine which RL algorithm is most fitting. In this work, we propose to avoid this difficult decision entirely and incorporate a choice mechanism into our RL framework. Rather than assuming a specific problem structure, we use a probabilistic structure estimation procedure based on a likelihood-ratio (LR) test to make a more informed selection of learning algorithm. We derive a sufficient condition under which myopic policies are optimal, present an LR test for this condition, and derive a bound on the regret of our framework. We provide examples of real-world scenarios where our framework is needed and provide extensive simulations to validate our approach.

The recent COVID-19 outbreak has motivated an extensive development of non-pharmaceutical intervention policies for epidemics containment. While a total lockdown is a viable solution, interesting policies are those allowing some degree of normal functioning of the society, as this allows a continued, albeit reduced, economic activity and lessens the many societal problems associated with a prolonged lockdown. Recent studies have provided evidence that fast periodic alternation of lockdown and normal-functioning days may effectively lead to a good trade-off between outbreak abatement and economic activity. Nevertheless, the correct number of normal days to allocate within each period in such a way to guarantee the desired trade-off is a highly uncertain quantity that cannot be fixed a priori and that must rather be adapted online from measured data. This adaptation task, in turn, is still a largely open problem, and it is the subject of this work. In particular, we study a class of solutions based on hysteresis logic. First, in a rather general setting, we provide general convergence and performance guarantees on the evolution of the decision variable. Then, in a more specific context relevant for epidemic control, we derive a set of results characterizing robustness with respect to uncertainty and giving insight about how a priori knowledge about the controlled process may be used for fine-tuning the control parameters. Finally, we validate the results through numerical simulations tailored on the COVID-19 outbreak.

COVID-19 abatement strategies have risks and uncertainties which could lead to repeating waves of infection. We show—as proof of concept grounded on rigorous mathematical evidence—that periodic, high-frequency alternation of into, and out-of, lockdown effectively mitigates second-wave effects, while allowing continued, albeit reduced, economic activity. Periodicity confers (i) predictability, which is essential for economic sustainability, and (ii) robustness, since lockdown periods are not activated by uncertain measurements over short time scales. In turn—while not eliminating the virus—this fast switching policy is sustainable over time, and it mitigates the infection until a vaccine or treatment becomes available, while alleviating the social costs associated with long lockdowns. Typically, the policy might be in the form of 1-day of work followed by 6-days of lockdown every week (or perhaps 2 days working, 5 days off) and it can be modified at a slow-rate based on measurements filtered over longer time scales. Our results highlight the potential efficacy of high frequency switching interventions in post lockdown mitigation. All code is available on Github athttps://github.com/V4p1d/FPSP_Covid19. A software tool has also been developed so that interested parties can explore the proof-of-concept system.

This paper studies the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition while the system output is selected as a either Dirichlet or Neumann boundary trace. The control strategy takes the form of a finite-dimensional observer-based controller with feedback and observer gains that are computed in order to dominate the state delayed term. For any arbitrarily given value of the state delay, we show the exponential stability of the resulting closed-loop system provided the order of the observer is selected large enough.

The recent uptake in popularity in vehicles with zero tailpipe emissions is a welcome development in the fight against traffic induced airborne pollutants. As vehicle fleets become electrified, and tailpipe emissions become less prevalent, non-tailpipe emissions (from tires and brake disks) will become the dominant source of traffic related emissions, and will in all likelihood become a major concern for human health. This trend is likely to be exacerbated by the heavier weight of electric vehicles, their increased power, and their increased torque capabilities, when compared with traditional vehicles. While the problem of emissions from tire wear is well-known, issues around the process of tire abrasion, its impact on the environment, and modelling and mitigation measures, remain relatively unexplored. Work on this topic has proceeded in several discrete directions including: on-vehicle collection methods; vehicle tire-wear abatement algorithms and controlling the ride characteristics of a vehicle, all with a view to abating tire emissions. Additional approaches include access control mechanisms to manage aggregate tire emissions in a geofenced area with other notable work focussing on understanding the particle size distribution of tire generated PM, the degree to which particles become airborne, and the health impacts of tire emissions. While such efforts are already underway, the problem of developing models to predict the aggregate picture of a network of vehicles at the scale of a city, has yet to be considered. Our objective in this paper is to present one such model, built using ideas from Markov chains. Applications of our modelling approach are given toward the end of this note, both to illustrate the utility of the proposed method, and to illustrate its application as part of a method to collect tire dust particles., Comment: 24 pages, 11 figures

We present the observation that the process of stochastic model predictive control can be formulated in the framework of iterated function systems. The latter has a rich ergodic theory that can be applied to study the system's long-run behavior. We show how such a framework can be realized for specific problems and illustrate the required conditions for the application of relevant theoretical guarantees.

This paper is concerned with the design of a human-in-the-loop system for deployment on a smart pedelec (e-bike). From the control-theoretic perspective, the goal is not only to use the power assistance of the e-bike to reject disturbances along the route but also to manage the possibly competitive interactions between a human and the motor intervention. Managing the competitive/cooperative nature of the interactions is crucial for applications in which we wish to control physical aspects of the cycling behavior (e.g. heart rate and breathing rate). The basis of the control is a pitchfork bifurcation system, modeling the interactions, augmented using ideas from gain-scheduling. In vivo experiments have been conducted, showing the effectiveness of the proposed control strategy., Comment: 7 figures

Testing, tracking and tracing abilities have been identified as pivotal in helping countries to safely reopen activities after the first wave of the COVID-19 virus. Contact tracing apps give the unprecedented possibility to reconstruct graphs of daily contacts, so the question is: who should be tested? As human contact networks are known to exhibit community structure, in this paper we show that the Kemeny constant of a graph can be used to identify and analyze bridges between communities in a graph. Our ‘Kemeny indicator’ is the value of the Kemeny constant in the new graph that is obtained when a node is removed from the original graph. We show that testing individuals who are associated with large values of the Kemeny indicator can help in efficiently intercepting new virus outbreaks, when they are still in their early stage. Extensive simulations provide promising results in early identification and in blocking the possible ‘super-spreaders’ links that transmit disease between different communities.

Within the study of uncertain dynamical systems, iterated random functions are a key tool. There, one samples a family of functions according to a stationary distribution. Here, we introduce an extension, where one sample functions according to a time-varying distribution over the family of functions. For such iterated piecewise-stationary random functions on Polish spaces, we prove a number of results, including a bound on the tracking error.

Cooperative Adaptive Cruise Control (CACC) systems are considered as key potential enablers to improve driving safety and traffic efficiency. They allow for automated vehicle following using wireless communication in addition to onboard sensors. To achieve string stability in CACC platoons, constant time headway (CTH) spacing policies have prevailed in research; namely, vehicle interspacing grows with the speed. While constant distance headway (CDH) spacing policies provide superior potential to increase traffic capacity than CTH, a major drawback is a smaller safety margin at high velocities and string stability cannot be achieved using a one-vehicle look-ahead communication. The hypothesis of this work is to apply CDH only in few driving situations, when traffic throughput is of highest importance and safety requirements can be met due to comparably low velocities. As the most relevant situations where CDH could be applied, we identify starting platoons at signalized intersections. In this paper, we illustrate this idea. Specifically, we compare CTH with CDH regarding its potential to increase the capacity of traffic lights. Starting with the elementary situation of single traffic lights we expand our scope to whole traffic networks including several thousand vehicles in simulation. Using real world data to calibrate and validate vehicle dynamics simulation and traffic simulation, the study discusses the most relevant working parameters of CDH, CTH, and the traffic system in which both are applied., Comment: A short version of this study was published in the Vehicular Technology Section in IEEE Access under the title "A numerical study on constant spacing policies for starting platoons at oversaturated intersections". First version (v1) submitted to IEEE Access on 21-Oct-2021, resubmission (v2) on 31-Jan-2022, acceptance (v3) on 09-Mar-2022

Directed Acylic Graphs (DAGs) are emerging as an attractive alternative to traditional blockchain architectures for distributed ledger technology (DLT). In particular DAG ledgers with stochastic attachment mechanisms potentially offer many advantages over blockchain, including scalability and faster transaction speeds. However, the random nature of the attachment mechanism coupled with the requirement of protection against double-spend transactions leaves open the possibility that not all transactions will be eventually validated. Such transactions are said to be orphaned, and will never be validated. Our principal contribution is to propose a simple modification to the attachment mechanism for the Tangle (the IOTA DAG architecture). This modification ensures that all transactions are validated in finite time, and preserves essential features of the popular Monte-Carlo selection algorithm. In order to demonstrate these results we derive a fluid approximation for the Tangle (in the limit of infinite arrival rate) and prove that this fluid model exhibits the desired behavior. We also present simulations which validate the results for finite arrival rates., Comment: This paper has been published with the title "On the stability of unverified transactions in a DAG-based Distributed Ledger"

This paper describes how Distributed Ledger Technologies can be used to design a class of cyber-physical systems, as well as to enforce social contracts and to orchestrate the behaviour of agents trying to access a shared resource. The first part of the paper analyses the advantages and disadvantages of using Distributed Ledger Technologies architectures to implement certain control systems in an Internet of Things (IoT) setting, and then focuses on a specific type of DLT based on a Directed Acyclic Graph. In this setting we propose a set of delay differential equations to describe the dynamical behaviour of the Tangle, an IoT-inspired Directed Acyclic Graph designed for the cryptocurrency IOTA. The second part proposes an application of Distributed Ledger Technologies as a mechanism for dynamic deposit pricing, wherein the deposit of digital currency is used to orchestrate access to a network of shared resources. The pricing signal is used as a mechanism to enforce the desired level of compliance according to a predetermined set of rules. After presenting an illustrative example, we analyze the control system and provide sufficient conditions for the stability of the network., Comment: This paper has been accepted for publication on the journal IEEE Access, with the title "Distributed Ledger Technology for Smart Cities, the Sharing Economy, and Social Compliance"

The effects of real-time provision of travel-time information on the behaviour of drivers are considered. The model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015] is extended to consider uncertainty in the response of a driver to an interval provided per route. Specifically, it is suggested that one can optimise over all distributions of a random variable associated with the driver's response with the first two moments fixed, and for each route, over the sub-intervals within the minimum and maximum in a certain number of previous realisations of the travel time per the route.

We propose a distributed algorithm to solve a special distributed multi-resource allocation problem with no direct inter-agent communication. We do so by extending a recently introduced additive-increase multiplicative-decrease (AIMD) algorithm, which only uses very little communication between the system and agents. Namely, a control unit broadcasts a one-bit signal to agents whenever one of the allocated resources exceeds capacity. Agents then respond to this signal in a probabilistic manner. In the proposed algorithm, each agent is unaware of the resource allocation of other agents. We also propose a version of the AIMD algorithm for multiple binary resources (e.g., parking spaces). Binary resources are indivisible unit-demand resources, and each agent either allocated one unit of the resource or none. In empirical results, we observe that in both cases, the average allocations converge over time to optimal allocations.

One of the key ideas to make Intelligent Transportation Systems (ITS) work effectively is to deploy advanced communication and cooperative control technologies among the vehicles and road infrastructures. In this spirit, we propose a consensus-based distributed speed advisory system that optimally determines a recommended common speed for a given area in order that the group emissions, or group battery consumptions, are minimised. Our algorithms achieve this in a privacy-aware manner; namely, individual vehicles do not reveal in-vehicle information to other vehicles or to infrastructure. A mobility simulator is used to illustrate the efficacy of the algorithm, and hardware-in-the-loop tests involving a real vehicle are given to illustrate user acceptability and ease of the deployment., Comment: This is a journal paper based on the conference paper "Highway speed limits, optimised consensus, and intelligent speed advisory systems" presented at the 3rd International Conference on Connected Vehicles and Expo (ICCVE 2014) in November 2014. This is the revised version of the paper recently submitted to the IEEE Transactions on Intelligent Transportation Systems for publication

Distributed ledger technology (DLT) can used to store information in such a way that no individual or organisation can compromise its veracity, contrary to a traditional centralised ledger. This nascent technology has received a great deal of attention from both researchers and practitioners in recent years due to the vast array of open questions related to its design and the assortment novel applications it unlocks. In this thesis, we are especially interested in the design of DLTs suitable for application in the domain of the internet of things (IoT), where factors such as efficiency, performance and scalability are of paramount importance. This work confronts the challenges of designing IoT-oriented distributed ledgers through analysis of ledger properties, development of design tools and the design of a number of core protocol components. We begin by introducing a class of DLTs whose data structures consist of directed acyclic graphs (DAGs) and which possess properties that make them particularly well suited to IoT applications. With a focus on the DAG structure, we then present analysis through mathematical modelling and simulations which provides new insights to the properties of this class of ledgers and allows us to propose novel security enhancements. Next, we shift our focus away from the DAG structure itself to another open problem for DAG-based distributed ledgers, that of access control. Specifically, we present a networking approach which removes the need for an expensive and inefficient mechanism known as Proof of Work, solving an open problem for IoT-oriented distributed ledgers. We then draw upon our analysis of the DAG structure to integrate and test our new access control with other core components of the DLT. Finally, we present a mechanism for orchestrating the interaction between users of a DLT and its operators, seeking to improves the usability of DLTs for IoT applications. In the appendix, we present two projects also carried out during this PhD which showcase applications of this technology in the IoT domain. Open Access

Hybride lineare Systeme sind eine Klasse von hybriden Systemen, bei denen die kontinuierliche Zeitentwicklung durch einen Satz von linearen Differentialgleichungen erster Ordnung, und die Sprungdynamik durch einen Satz von linearen Differenzengleichungen erster Ordnung beschrieben werden. Geschaltete lineare Systeme sind eine Unterklasse von hybriden linearen Systemen mit einer stetigen Zeitentwicklung der Systemzustände. Aufgrund der großen Anzahl physikalischer Anwendungen erfuhr die Regelung von hybriden und geschalteten linearen Systemen in den letzten Jahren beträchtliche Aufmerksamkeit. Diese Dissertation stellt neue Beiträge zur Regelung solcher Systeme vor und erweitert einige vorhandene Ergebnisse in diesem Bereich. Diese Arbeit konzentriert sich auf verschiedene Aspekte der Stabilität und Stabilisierung geschalteter linearer Systeme sowie der optimalen Regelung hybrider linearer Systeme. Der größte Teil dieser Arbeit betrifft die Stabilität und Stabilisierung von geschalteten linearen Systemen. Die Darstellung der Ergebnisse bezieht sich in erster Linie auf Bedingungen für die Stabilität autonomer geschalteter linearer Systeme. Stabilisierungsverfahren zielen dann auf den Entwurf einer lokalen Zustandsrückführung für jeden Modus eines geregelten geschalteten linearen Systems, um die Stabilitätskriterien für die Modi des geschlossenen Regelkreises zu befriedigen. Teile dieser Ergebnisse beruhen auf dem Konzept gemeinsamer linker Eigenvektoren und der Zuweisung linker Eigenstruktur. Zu diesem Zweck werden mehrere Verfahren zur Zuweisung der Eigenstruktur von linearen Systemen entwickelt. Anschließend werden diese Techniken zur Charakterisierung exponentieller Stabilität und zur Stabilisierung einer Klasse von geschalteten linearen Systemen mit zustandsabhängigem Schalten unter bestimmten Einschränkungen bezüglich der Schaltmannigfaltigkeiten eingesetzt. Darüber hinaus werden sie zur quadratischen Stabilisierung einer Klasse von beliebig schaltenden linearen Systemen eingesetzt, in der die Dynamikmatrizen des offenen Kreises einen invarianten Untervektorraum gemeinsam haben, der mit einer gemeinsamen quadratischen Lyapunov-Funktion assoziiert werden kann. Ein weiterer Stabilitätsansatz nutzt das Kalman-Yakubovic-Popov-Lemma, um quadratische Stabilität einer Klasse von geschalteten linearen Systemen zu zeigen. Diese Klasse wird von beliebigem Schalten zwischen zwei Modi gekennzeichnet, für welche die Differenz der Dynamikmatrizen von Rang $m \geq 1$ ist, und mit denen eine symmetrische Übertragungsfunktionsmatrix assoziiert werden kann. Diese Ergebnisse erweitern vorhandene Ergebnisse zur quadratischen Stabilität geschalteter linearer Systeme, bei denen die Differenz der Dynamikmatrizen Rang 1 aufweist. Die Dissertation befasst sich auch mit der linear quadratischen Regelung von hybriden linearen Systemen. Hierbei sind die Kostenfunktionen quadratisch, der Zeithorizont und die Anzahl und Reihenfolge des Schaltens gegeben. Einschränkungen sind durch lineare (Un-) Gleichungen im Zustandsraum gegeben. Die Zeitpunkte des Schaltens zwischen unterschiedlichen Dynamiken können entweder vorgegeben oder frei sein. Ein Parametrierungsverfahren in Bezug auf Ausgangs- und Endpunkte der einzelnen Intervalle eines generalisierten Zeitbereichs wird verwendet. Numerische Lösungen werden für solche Aufgaben vorgeschlagen. Hybrid linear systems are a class of hybrid systems where the continuous time evolution is governed by a set of first order linear ordinary differential equations and the jump dynamics are described by a set of first order linear difference equations. Switched linear systems are a subclass of hybrid linear systems with a continuous evolution of the system states. Due to the large number of physical applications, control of hybrid and switched linear systems has received considerable attention over the past years. This dissertation provides novel contributions to the control of such systems and extends some existing results in this area. This work focuses on different problems regarding stability and stabilization of switched linear systems and optimal control of hybrid linear systems. The major part of this thesis concerns stability and stabilization of switched linear systems. The results are primarily presented in terms of conditions for stability of autonomous switched systems. Then, stabilization methods aim at designing a local state feedback for each mode of a controlled switched system to satisfy the stability criteria for the closed loop system modes. Parts of these results rely on the concept of common left eigenvectors and left eigenstructure assignment. To this end, several techniques for eigenstructure assignment in the context of linear systems are developed. Afterwards, these techniques are employed for characterizing exponential stability and for stabilization of a class of switched linear systems with state dependent switching and certain restrictions on the switching manifolds. In addition, they are used for quadratic stabilization of a class of controlled switched linear systems with arbitrary switching signals where the open loop constituent matrices share an invariant subspace to which a common quadratic Lyapunov function can be associated. Another stability approach makes use of the Kalman-Yakubovic-Popov lemma to demonstrate quadratic stability of a class of switched linear systems. This class is characterized by arbitrary switching between two modes, where the difference of the constitute matrices is of rank $m\geq 1$, and to which a symmetric transfer function matrix can be associated. These results extend existing results in quadratic stability of rank-1 difference switched linear systems. The thesis also addresses problems in linear quadratic control of hybrid linear systems. In these problems, cost functions are quadratic, the final time and the number and sequence of switches are given. Constraints are specified by linear (in-)equalities in the state space. Switching between different dynamics may either occur at fixed or free time instances. A parameterization method with respect to initial and end points of each interval in a generalized time domain is employed. Numerical solutions for such problems are suggested.

Ein Konsensussystem besteht aus einer Menge von kommunizierenden Agenten, die sich mittels ausschließlich lokaler Kommunikation auf eine Variable einigen. Einige denkbare Anwendungen für Konsensussysteme sind beispielsweise elektrische Netzwerke (so genannte "smart grids"), drahtlose Sensornetzwerke, soziale Netzwerke, und viele Anwendungen aus dem Bereich unbemannte Flugmaschinen, wie etwa Überwachung, Kartographie und Beobachtung von Ökosystemen. Wenn die Agenten, aus denen das Netzwerk besteht, eine Doppelintegratordynamik besitzen, so spricht man vom Doppelintegratorkonsensussystem. Diese Arbeit beschäftigt sich mit einem Doppelintegratorkonsensussystem in kontinuierlicher Zeit. Es wird angenommen, dass die Agenten ihre Position und Geschwindigkeit entlang von gewichteten Kommunikationsnetzwerken übermitteln können, die verschieden sein dürfen und mittels gewichteter gerichteter Graphen modelliert werden. Das mathematische Modell des Systems hat die Form \begin{equation}\ddot x(t)=-L_xx(t)-\beta L_{\dot x}\dot x(t),\tag{S1}\label{abs:3}\end{equation} wobei $x:\mathbb R^+\rightarrow\mathbb R^n$ und $\dot x:\mathbb R^+\rightarrow \mathbb R^n$ die gesammelten Positionen und Geschwindigkeiten der Agenten repräsentieren, $L_x$ und $L_{\dot x}$ die Laplacematrizen der Kommunikationsgraphen sind und $\beta\in\mathbb R^+\setminus\{0\}$ ein Verstärkungsfaktor ist. Für solche Systeme wird in dieser Arbeit ein Stabilitätskonzept hergeleitet. Das System \ref{abs:3} wird konsensusstabil genannt, wenn alle Geschwindigkeitsunterschiede im System mit laufender Zeit null werden. Es wird asymptotisch konsensusstabil genannt, wenn alle Positionsunterschiede mit laufender Zeit null werden. Die üblicherweise in der Literatur getätigte Annahme, dass die Kommunikationsnetzwerke gleich, also homogen für beide Informationsflüsse sind, ist in vielen Fällen zu stark. Daher wird in dieser Arbeit die Annahme getroffen, dass die Kommunikationsnetzwerke unterschiedlich und unter Umständen sogar nicht verbunden sein können. Notwendige und hinreichende Bedingungen für Konsensusstabilität und asymptotische Konsensusstabilität werden für den Spezialfall hergeleitet, dass die Kommunikationsgraphen gewichtet und ungerichtet sind. Diese Bedingungen werden anschließend auf einige Fälle erweitert, in denen die Graphen gewichtet und gerichtet sind. Zudem betrachten wir die Konvergenzgeschwindigkeit und -wert des Systems. Im Anschluß an die Stabilitätsanalyse wird aufgezeigt, wie das autonome Konsensusystem \ref{abs:3} in ein Regelsystem überführt werden kann, indem ein Teil der Agenten mit einem externen Regler versehen wird. Es ergibt sich das System \begin{equation} \ddot x(t)=-A_x^fx(t)-A_{\dot x}^f\dot x(t)+Bu(t),\tag{S2}\label{abs:4} \end{equation} wobei $x:\mathbb R^+\rightarrow \mathbb R^{n_f}$ und $\dot x:\mathbb R^+\rightarrow \mathbb R^{n_f}$ die Zustände der zu regelnden, ``folgenden'' Agenten sind, $u:\mathbb R^+\rightarrow \mathbb R^{n_l}$ die Stellgröße ist, die von den ``führenden'' Agenten übermittelt wird, $n_f+n_l=n$, und die Matrizen $A_x^f,A_{\dot x}^f\in\mathbb R^{n_f\times n_f}$, $B\in\mathbb R^{n_f\times n_l}$ aus den Laplacematrizen $L_x$, $L_{\dot x}$ hergeleitet werden. Dieses Netzwerk wird als ein so genanntes "leader-follower" Netzwerk bezeichnet. Es wird auf Steuerbarkeit hin untersucht. Notwendige Bedingungen für die Steuerbarkeit von \ref{abs:4} werden sowohl auf graphenteoretischer als auch auf algebraischer Ebene hergeleitet. Es wird aufgezeigt, dass die graphtheoretischen Bedingungen stark von den in den Graphen vorhandenen Symmetrien abhängen., A consensus system is a set of communicating agents that agree on a variable of interest using only local communication. Some possible uses for consensus systems include smart grids, wireless sensor networks, social networks and various applications of unmanned aerial vehicles such as surveillance, mapping and environmental monitoring. If the agents have double integrator dynamics, then the consensus system is called a double integrator consensus system. In this thesis a double integrator consensus system in continuous time is studied. The agents are assumed to be communicating their position and velocity information along some possibly different, weigh\-ted directed communication networks that are modeled by weighted directed graphs. The mathematical model of the system has the form \begin{equation}\ddot x(t)=-L_xx(t)-\beta L_{\dot x}\dot x(t),\tag{S1}\label{abs:1}\end{equation} where $x:\mathbb R^+\rightarrow\mathbb R^n$ and $\dot x:\mathbb R^+\rightarrow \mathbb R^n$ are the collected positions and velocities of the agents, $L_x$ and $L_{\dot x}$ are the Laplacians of the communication graphs and $\beta\in\mathbb R^+\setminus\{0\}$ is a gain. A stability concept for such systems is derived in the thesis. The system \ref{abs:1} is said to be consensus stable if all of its velocity differences approach zero in time, and asymptotically consensus stable, if all of its position differences tend to zero. The standard assumption made in the literature, that the communication networks are the same, i.e. homogeneous, for both information, is too strong in many cases. Thus, the algorithm is investigated under the assumption that the communication graphs may be different and possibly even disconnected. Necessary and sufficient conditions for consensus stability and asymptotic consensus stability are presented in the special case that the communication graphs are weighted and undirected. These conditions are subsequently relaxed to some cases of weighted directed graphs. Moreover, we consider the convergence rate of the system and the final convergence value. Following the stability analysis, it is shown how the autonomous consensus system \ref{abs:1} can be transformed into a control system by introducing an external control input to a subset of the agents. The resulting system is given by \begin{equation} \ddot x(t)=-A_x^fx(t)-A_{\dot x}^f\dot x(t)+Bu(t),\tag{S2}\label{abs:2} \end{equation} where $x:\mathbb R^+\rightarrow \mathbb R^{n_f}$ and $\dot x:\mathbb R^+\rightarrow \mathbb R^{n_f}$ are the states of the controlled, ``follower'' agents, $u:\mathbb R^+\rightarrow \mathbb R^{n_l}$ is the control input provided by the ``leader'' agents, $n_f+n_l=n$, and the matrices $A_x^f,A_{\dot x}^f\in\mathbb R^{n_f\times n_f}$, $B\in\mathbb R^{n_f\times n_l}$ are obtained from the Laplacian matrices $L_x$, $L_{\dot x}$. This network is called a leader-follower network and its controllability is investigated. Necessary conditions for controllability of the system \ref{abs:2} are given on both algebraic and graph-theoretic levels. It is made apparent that the graph-theoretic conditions are highly dependent on the underlying graph symmetries.