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An optimal randomized strategy for design of balanced, normalized mass transport plans is developed. It replaces -- but specializes to -- the deterministic, regularized optimal transport (OT) strategy, which yields only a certainty-equivalent plan. The incompletely specified -- and therefore uncertain -- transport plan is acknowledged to be a random process. Therefore, hierarchical fully probabilistic design (HFPD) is adopted, yielding an optimal hyperprior supported on the set of possible transport plans, and consistent with prior mean constraints on the marginals of the uncertain plan. This Bayesian resetting of the design problem for transport plans -- which we call HFPD-OT -- confers new opportunities. These include (i) a strategy for the generation of a random sample of joint transport plans; (ii) randomized marginal contracts for individual source-target pairs; and (iii) consistent measures of uncertainty in the plan and its contracts. An application in algorithmic fairness is outlined, where HFPD-OT enables the recruitment of a more diverse subset of contracts -- than is possible in classical OT -- into the delivery of an expected plan. Also, it permits fairness proxies to be endowed with uncertainty quantifiers., Comment: 27 pages, 26 figures

As consumer flexibility becomes expected, it is important that the market mechanisms which attain that flexibility are perceived as fair. We set out fairness issues in energy markets today, and propose a market design to address them. Consumption is categorised as either essential or flexible with different prices and reliability levels for each. Prices are generated by an Automatic Market Maker (AMM) based on instantaneous scarcity and resource is allocated using a novel Fair Play algorithm. We empirically show the performance of the system over 1 year for 101 UK households and benchmark its performance against more classical approaches., Comment: Under review for inclusion in Special Issue of Applied Energy on `(R)Evolution of Electricity Markets: Designing Smart Electricity Markets for a Decarbonized World'

Controlled charging of electric vehicles, EVs, is a major potential source of flexibility to facilitate the integration of variable renewable energy and reduce the need for stationary energy storage. To offer system services from EVs, fleet aggregators must address the uncertainty of individual driving and charging behaviour. This paper introduces a means of forecasting the service volume available from EVs by considering several EV batteries as one conceptual battery with aggregate power and energy boundaries. This avoids the impossible task of predicting individual driving behaviour by taking advantage of the law of large numbers. The forecastability of the boundaries is demonstrated in a multiple linear regression model which achieves an $R^2$ of 0.7 for a fleet of 1,000 EVs. A two-stage stochastic model predictive control algorithm is used to schedule reserve services on a day-ahead basis addressing risk trade-offs by including Conditional Value-at-Risk in the objective function. A case study with 1.2 million domestic EV charge records from Great Britain shows that increasing fleet size improves prediction accuracy, thereby increasing reserve revenues and decreasing effective charging costs. For fleet sizes of 400 or above, charging cost reductions plateau at 60\%, with an average of 1.8kW of reserve provided per vehicle.

We present a novel class of proof-of-position algorithms: Tree-Proof-of-Position (T-PoP). This algorithm is decentralised, collaborative and can be computed in a privacy preserving manner, such that agents do not need to reveal their position publicly. We make no assumptions of honest behaviour in the system, and consider varying ways in which agents may misbehave. Our algorithm is therefore resilient to highly adversarial scenarios. This makes it suitable for a wide class of applications, namely those in which trust in a centralised infrastructure may not be assumed, or high security risk scenarios. Our algorithm has a worst case quadratic runtime, making it suitable for hardware constrained IoT applications. We also provide a mathematical model that summarises T-PoP's performance for varying operating conditions. We then simulate T-PoP's behaviour with a large number of agent-based simulations, which are in complete agreement with our mathematical model, thus demonstrating its validity. T-PoP can achieve high levels of reliability and security by tuning its operating conditions, both in high and low density environments. Finally, we also present a mathematical model to probabilistically detect platooning attacks.

Vaccination campaigns have both direct and indirect effects that act to control an infectious disease as it spreads through a population. Indirect effects arise when vaccinated individuals block disease transmission in any infection chains they are part of, and this in turn can benefit both vaccinated and unvaccinated individuals. Indirect effects are difficult to quantify in practice, but here, working with the Susceptible-Infected-Recovered (SIR) model, they are analytically calculated in important cases, through pivoting on the Final Size formula for epidemics. Their relationship to herd immunity is also clarified. Furthermore, we identify the important distinction between quantifying indirect effects of vaccination at the "population level" versus the "per capita" individual level, which often results in radically different conclusions. As an important example, the analysis unpacks why population-level indirect effect can appear significantly larger than its per capita analogue. In addition, we consider a recently proposed epidemiological non-pharamaceutical intervention used over COVID-19, referred to as "shielding", and study its impact in our mathematical analysis. The shielding scheme is extended by inclusion of limited vaccination.

Reinforcement Learning (RL) is a powerful method for controlling dynamic systems, but its learning mechanism can lead to unpredictable actions that undermine the safety of critical systems. Here, we propose RL with Adaptive Control Regularization (RL-ACR), an algorithm that enables safe RL exploration by combining the RL policy with a policy regularizer that hard-codes safety constraints. We perform policy combination via a "focus network," which determines the appropriate combination depending on the state -- relying more on the safe policy regularizer for less-exploited states while allowing unbiased convergence for well-exploited states. In a series of critical control applications, we demonstrate that RL-ACR ensures safety during training while achieving the performance standards of model-free RL approaches that disregard safety.

With the advent of the AI Act and other regulations, there is now an urgent need for algorithms that repair unfairness in training data. In this paper, we define fairness in terms of conditional independence between protected attributes ($S$) and features ($X$), given unprotected attributes ($U$). We address the important setting in which torrents of archival data need to be repaired, using only a small proportion of these data, which are $S|U$-labelled (the research data). We use the latter to design optimal transport (OT)-based repair plans on interpolated supports. This allows {\em off-sample}, labelled, archival data to be repaired, subject to stationarity assumptions. It also significantly reduces the size of the supports of the OT plans, with correspondingly large savings in the cost of their design and of their {\em sequential\/} application to the off-sample data. We provide detailed experimental results with simulated and benchmark real data (the Adult data set). Our performance figures demonstrate effective repair -- in the sense of quenching conditional dependence -- of large quantities of off-sample, labelled (archival) data.

We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove asymptotic convergence of our algorithms to a unique optimal solution. New insights obtained from the convergence proof are highlighted. An example from electrical vehicle charging in a smart city context is outlined, in which the prior zero-constraints prevent energy from being transported from some providers to some vehicles., Comment: Submitted for publication

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

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.

The goal of this paper is to introduce a new theoretical framework for Optimal Transport (OT), using the terminology and techniques of Fully Probabilistic Design (FPD). Optimal Transport is the canonical method for comparing probability measures and has been successfully applied in a wide range of areas (computer vision Rubner et al. [2004], computer graphics Solomon et al. [2015], natural language processing Kusner et al. [2015], etc.). However, we argue that the current OT framework suffers from two shortcomings: first, it is hard to induce generic constraints and probabilistic knowledge in the OT problem; second, the current formalism does not address the question of uncertainty in the marginals, lacking therefore the mechanisms to design robust solutions. By viewing the OT problem as the optimal design of a probability density function with marginal constraints, we prove that OT is an instance of the more generic FPD framework. In this new setting, we can furnish the OT framework with the necessary mechanisms for processing probabilistic constraints and deriving uncertainty quantifiers, hence establishing a new extended framework, called FPD-OT. Our main contribution in this paper is to establish the connection between OT and FPD, providing new theoretical insights for both. This will lay the foundations for the application of FPD-OT in a subsequent work, notably in processing more sophisticated knowledge constraints, as well as in designing robust solutions in the case of uncertain marginals., Comment: Keywords: Optimal Transport, Fully Probabilistic Design, Convex optimization

The AIMD algorithm, which underpins the Transmission Control Protocol (TCP) for transporting data packets in communication networks, is perhaps the most successful control algorithm ever deployed. Recently, its use has been extended beyond communication networks, and successful applications of the AIMD algorithm have been reported in transportation, energy, and mathematical biology. A very recent development in the use of AIMD is its application in solving large-scale optimization and distributed control problems without the need for inter-agent communication. In this context, an interesting problem arises when multiple AIMD networks that are coupled in some sense (usually through a nonlinearity). The purpose of this note is to prove that such systems in certain settings inherit the ergodic properties of individual AIMD networks. This result has important consequences for the convergence of the aforementioned optimization algorithms. The arguments in the paper also correct conceptual and technical errors in [1].

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. This behaviour can often be modelled as observations of an unknown dynamical system with an unobserved state. When the training data for the subgroups are not controlled carefully, however, under-representation bias arises. To counter under-representation bias, we introduce two natural notions of fairness in time-series forecasting problems: subgroup fairness and instantaneous fairness. These notions extend predictive parity to the learning of dynamical systems. We also show globally convergent methods for the fairness-constrained learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. We also show that by exploiting sparsity in the convexifications, we can reduce the run time of our methods considerably. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate the efficacy of our methods., Comment: Journal version of Zhou et al. [arXiv:2006.07315, AAAI 2021]

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.

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.

Over two thirds of women of all ages in the UK have experienced some form of sexual harassment in a public space. Recent tragic incidents involving female pedestrians have highlighted some of the personal safety issues that women still face in cities today. There exist many popular location-based safety applications as a result of this; however, these applications tend to take a reactive approach where action is taken only after an incident has occurred. This paper proposes a preventative approach to the problem by creating safer public environments through societal incentivisation. The proposed system, called "Herd Routes", improves the safety of female pedestrians by generating busier pedestrian routes as a result of route incentivisation. A novel application of distributed ledgers is proposed to provide security and trust, a record of system users' locations and IDs, and a platform for token exchange. A proof-of-concept was developed using the simulation package SUMO (Simulation of Urban Mobility), and a smartphone app. was built in Android Studio so that pedestrian Hardware-in-the-Loop testing could be carried out to validate the technical feasibility and desirability of the system. With positive results from the initial testing of the proof-of-concept, further development could significantly contribute towards creating safer pedestrian routes through cities, and tackle the societal change that is required to improve female pedestrian safety in the long term.

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

We describe an architecture for a decentralised data market for applications in which agents are incentivised to collaborate to crowd-source their data. The architecture is designed to reward data that furthers the market's collective goal, and distributes reward fairly to all those that contribute with their data. We show that the architecture is resilient to Sybil, wormhole, and data poisoning attacks. In order to evaluate the resilience of the architecture, we characterise its breakdown points for various adversarial threat models in an automotive use case., Comment: 13 pages, 7 figures

As Covid-19 remains a cause of concern, especially due to its mutations, wearing masks correctly and efficiently remains a priority in order to limit the spread of the disease. In this paper we present a wearable smart-mask prototype using concepts from Internet of Things, Control Theory and Distributed Ledger Technologies. Its purpose is to encourage people to comply with social distancing norms, through the use of incentives. The smart mask is designed to monitor Carbon Dioxide and Total Volatile Organic Compounds concentrations. The detected data is appended to a DAG-based DLT, named the IOTA Tangle. The IOTA Tangle ensures that the data is secure and immutable and acts as a communication backbone for the incentive mechanism. A hardware-in-the-loop simulation, based on indoor positioning, is developed to validate the effectiveness of the designed prototype.

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.

An outstanding problem in the design of distributed ledgers concerns policies that govern the manner in which users interact with the network. Network usability is crucial to the mainstream adoption of distributed ledgers, particularly for enterprise applications in which most users do not wish to operate full node. For DAG-based ledgers such as IOTA, we propose a user-node interaction mechanism that is designed to ensure the risk of a user experiencing a poor quality of service is low. Our mechanism involves users selecting nodes to issue their transactions to the ledger based on quality of service indicators advertised by the nodes. Simulation results are presented to illustrate the efficacy of the proposed policies.

This is a Masters Thesis completed at University College Dublin, Ireland in 2017 which involved augmenting an off-the-shelf electric bike with sensors to enable new services to be delivered to cyclists in cities. The application of primary interest was to control the cyclist's ventilation rate based on the concentration of local air pollutants. Detailed modelling and system design is presented for our Cyberphysical system which consisted of a modified BTwin e-bike, Cycle Analyst sensors, the cyclist themselves, a Bluetooth connected smartphone and our algorithms. Control algorithms to regulate the proportion of power the cyclist provided as a proxy for their ventilation rate were proposed and validated in a basic way, which were later proven significantly further in Further Work (see IEEE Transactions on Intelligent Transportation Systems paper: https://ieeexplore.ieee.org/abstract/document/8357977). The basic idea was to provide more electrical assistance to cyclists in areas of high air pollution to reduce the cyclist ventilation rate and thereby the amount of air pollutants inhaled. This presents an interesting control challenge due to the human-in-the-loop characteristics and the potential for impactful real life applications. A background literature review is provided on energy as it relates to cycling and some other applications are also discussed. A link to a video which demonstrates the system is provided, and also to a blog published by IBM Research about the system.

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.

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.

In power systems, one wishes to regulate the aggregate demand of an ensemble of distributed energy resources (DERs), such as controllable loads and battery energy storage systems. We suggest a notion of predictability and fairness, which suggests that the long-term averages of prices or incentives offered should be independent of the initial states of the operators of the DER, the aggregator, and the power grid. We show that this notion cannot be guaranteed with many traditional controllers used by the load aggregator, including the usual proportional-integral (PI) controller. We show that even considering the non-linearity of the alternating-current model, this notion of predictability and fairness can be guaranteed for incrementally input-to-state stable (iISS) controllers, under mild assumptions.

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

This paper is concerned with the regulation control of a one-dimensional reaction-diffusion equation in the presence of a state-delay in the reaction term. The objective is to achieve the PI regulation of the right Dirichlet trace with a command selected as the left Dirichlet trace. The control design strategy consists of the design of a PI controller on a finite dimensional truncated model obtained by spectral reduction. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the proposed control design procedure achieves both the exponential stabilization of the original infinite-dimensional system as well as the setpoint regulation of the right Dirichlet trace., Comment: Accepted for publication in Automatica

Access control is a fundamental component of the design of distributed ledgers, influencing many aspects of their design, such as fairness, efficiency, traditional notions of network security, and adversarial attacks such as Denial-of-Service (DoS) attacks. In this work, we consider the security of a recently proposed access control protocol for Directed Acyclic Graph-based distributed ledgers. We present a number of attack scenarios and potential vulnerabilities of the protocol and introduce a number of additional features which enhance its resilience. Specifically, a blacklisting algorithm, which is based on a reputation-weighted threshold, is introduced to handle both spamming and multi-rate malicious attackers. The introduction of a solidification request component is also introduced to ensure the fairness and consistency of network in the presence of attacks. Finally, a timestamp component is also introduced to maintain the consistency of the network in the presence of multi-rate attackers. Simulations to illustrate the efficacy and robustness of the revised protocol are also described., Comment: Submitted for consideration for publication in IEEE IoT Journal

The ranking of nodes in a network according to their ``importance'' is a classic problem that has attracted the interest of different scientific communities in the last decades. The current COVID-19 pandemic has recently rejuvenated the interest in this problem, as it is related to the selection of which individuals should be tested in a population of asymptomatic individuals, or which individuals should be vaccinated first. Motivated by the COVID-19 spreading dynamics, in this paper we review the most popular methods for node ranking in undirected unweighted graphs, and compare their performance in a benchmark realistic network, that takes into account the community-based structure of society. Also, we generalize a classic benchmark network originally proposed by Newman for ranking nodes in unweighted graphs, to show how ranks change in the weighted case.

It is well known that two-sided markets are unfair in a number of ways. For instance, female workers at Uber earn less than their male colleagues per mile driven. Similar observations have been made for other minority subgroups in other two-sided markets. Here, we suggest a novel market-clearing mechanism for two-sided markets, which promotes equalisation of the pay per hour worked across multiple subgroups, as well as within each subgroup. In the process, we introduce a novel notion of subgroup fairness (which we call Inter-fairness), which can be combined with other notions of fairness within each subgroup (called Intra-fairness), and the utility for the customers (Customer-Care) in the objective of the market-clearing problem. While the novel non-linear terms in the objective complicate market clearing by making the problem non-convex, we show that a certain non-convex augmented Lagrangian relaxation can be approximated to any precision in time polynomial in the number of market participants using semi-definite programming. This makes it possible to implement the market-clearing mechanism efficiently. On the example of driver-ride assignment in an Uber-like system, we demonstrate the efficacy and scalability of the approach, and trade-offs between Inter- and Intra-fairness.

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

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.

There has been much recent interest in two-sided markets and dynamics thereof. In a rather a general discrete-time feedback model, which we show conditions that assure that for each agent, there exists the limit of a long-run average allocation of a resource to the agent, which is independent of any initial conditions. We call this property the unique ergodicity. Our model encompasses two-sided markets and more complicated interconnections of workers and customers, such as in a supply chain. It allows for non-linearity of the response functions of market participants. Finally, it allows for uncertainty in the response of market participants by considering a set of the possible responses to either price or other signals and a measure to sample from these.

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.

This paper describes the use of Distributed Ledger Technologies as a mean to enforce social contracts and to orchestrate the behaviour of agents in a smart city environment. Specifically, we present a scheme to price personalised risk in sharing economy applications. We provide proofs for the convergence of the proposed stochastic system and we validate our approach through the use of extensive Monte Carlo simulations.

We present order reduction results for linear time invariant descriptor systems. Results are given for both forced and unforced systems as well methods for constructing the reduced order systems. Our results establish a precise connection between classical and new results on this topic, and lead to an elementary construction of quasi-Weierstrass forms for a descriptor system. Examples are given to illustrate the usefulness of our results., Comment: None

Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of constructive methods for their selection. For certain classes of time-delay systems for which such constructive methods are lacking, it was shown that Lyapunov-Krasovskii functionals that are also allowed to depend on the time-derivative of the state-trajectory are efficient tools for the study of the stability properties. However, in such an approach the initial condition needs to be assumed absolutely continuous with a square integrable weak derivative. In addition, the stability results hold for initial conditions that are evaluated based on the magnitude of both the initial condition and its time-derivative. The main objective of this paper is to show that, for certain classes of time-delay systems, the aforementioned stability results can actually be extended to initial conditions that are only assumed continuous and that are evaluated in uniform norm.

I-nteract is a cyber-physical system that enables real-time interaction with both virtual and real artifacts to design 3D models for additive manufacturing by leveraging on mixed reality technologies. This paper presents novel advances in the development of the interaction platform I-nteract to generate 3D models using both constructive solid geometry and artificial intelligence. The system also enables the user to adjust the dimensions of the 3D models with respect to their physical workspace. The effectiveness of the system is demonstrated by generating 3D models of furniture (e.g., chairs and tables) and fitting them into the physical space in a mixed reality environment.

We consider the design of distributed algorithms that govern the manner in which agents contribute to a social sensing platform. Specifically, we are interested in situations where fairness among the agents contributing to the platform is needed. A notable example are platforms operated by public bodies, where fairness is a legal requirement. The design of such distributed systems is challenging due to the fact that we wish to simultaneously realise an efficient social sensing platform, but also deliver a predefined quality of service to the agents (for example, a fair opportunity to contribute to the platform). In this paper, we introduce iterated function systems (IFS) as a tool for the design and analysis of systems of this kind. We show how the IFS framework can be used to realise systems that deliver a predictable quality of service to agents, can be used to underpin contracts governing the interaction of agents with the social sensing platform, and which are efficient. To illustrate our design via a use case, we consider a large, high-density network of participating parked vehicles. When awoken by an administrative centre, this network proceeds to search for moving missing entities of interest using RFID-based techniques. We regulate which vehicles are actively searching for the moving entity of interest at any point in time. In doing so, we seek to equalise vehicular energy consumption across the network. This is illustrated through simulations of a search for a missing Alzheimer's patient in Melbourne, Australia. Experimental results are presented to illustrate the efficacy of our system and the predictability of access of agents to the platform independent of initial conditions., Comment: 18 pages, 6 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 change in Kemeny constant when a node or edge is removed from the 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 possible "super-spreaders" links that transmit disease between different communities.

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. When the amounts of training data for the subgroups are not controlled carefully, under-representation bias arises. We introduce two natural notions of subgroup fairness and instantaneous fairness to address such under-representation bias in time-series forecasting problems. In particular, we consider the subgroup-fair and instant-fair learning of a linear dynamical system (LDS) from multiple trajectories of varying lengths, and the associated forecasting problems. We provide globally convergent methods for the learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate both the beneficial impact of fairness considerations on statistical performance and encouraging effects of exploiting sparsity on run time.

In the Internet of Things (IoT) domain, devices need a platform to transact seamlessly without a trusted intermediary. Although Distributed Ledger Technologies (DLTs) could provide such a platform, blockchains, such as Bitcoin, were not designed with IoT networks in mind, hence are often unsuitable for such applications: they offer poor transaction throughput and confirmation times, put stress on constrained computing and storage resources, and require high transaction fees. In this work, we consider a class of IoT-friendly DLTs based on directed acyclic graphs, rather than a blockchain, and with a reputation system in the place of Proof of Work (PoW). However, without PoW, implementation of these DLTs requires an access control algorithm to manage the rate at which nodes can add new transactions to the ledger. We model the access control problem and present an algorithm that is fair, efficient and secure. Our algorithm represents a new design paradigm for DLTs in which concepts from networking are applied to the DLT setting for the first time. For example, our algorithm uses distributed rate setting which is similar in nature to transmission control used in the Internet. However, our solution features novel adaptations to cope with the adversarial environment of DLTs in which no individual agent can be trusted. Our algorithm guarantees utilisation of resources, consistency, fairness, and resilience against attackers. All of this is achieved efficiently and with regard for the limitations of IoT devices. We perform extensive simulations to validate these claims.

This paper deals with the exponential input-to-state stabilization with respect to boundary disturbances of a class of diagonal infinite-dimensional systems via delay boundary control. The considered input delays are uncertain and time-varying. The proposed control strategy consists of a constant-delay predictor feedback controller designed on a truncated finite-dimensional model capturing the unstable modes of the original infinite-dimensional system. We show that the resulting closed-loop system is exponentially input-to-state stable with fading memory of both additive boundary input perturbations and disturbances in the computation of the predictor feedback., Comment: Published in Systems & Control Letters

This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design strategy consists of a constant-delay predictor feedback designed based on the known nominal value of the control input delay and is synthesized on a finite-dimensional truncated model capturing the unstable modes of the original infinite-dimensional system. By using a small-gain argument, we show that the resulting closed-loop system is exponentially stable provided that the variations of the delay around its nominal value are small enough. The proposed proof actually applies to any distributed-parameter system associated with an unbounded operator that 1) generates a $C_0$-semigroup on a weighted space of square integrable functions over a compact interval; and 2) is self-adjoint with compact resolvent., Comment: Accepted for publication in Automatica as a brief paper

This paper presents I-nteract, a cyber-physical system that enables real-time interaction with real and virtual objects in a mixed augmented reality environment to design 3D models for additive manufacturing. The system has been developed using mixed reality technologies such as HoloLens, for augmenting visual feedback, and haptic gloves, for augmenting haptic force feedback. The efficacy of the system has been demonstrated by generating 3D model using a novel scanning method to 3D print a customized orthopedic cast for human arm, by estimating spring rates of compression springs, and by simulating interaction with a virtual spring using hand.

In several social choice problems, agents collectively make decisions over the allocation of multiple divisible and heterogeneous resources with capacity constraints to maximize utilitarian social welfare. The agents are constrained through computational or communication resources or privacy considerations. In this paper, we analyze the convergence of a recently proposed distributed solution that allocates such resources to agents with minimal communication. It is based on the randomized additive-increase and multiplicative-decrease (AIMD) algorithm. The agents are not required to exchange information with each other, but little with a central agent that keeps track of the aggregate resource allocated at a time. We formulate the time-averaged allocations over finite window size and model the system as a Markov chain with place-dependent probabilities. Furthermore, we show that the time-averaged allocations vector converges to a unique invariant measure, and also, the ergodic property holds.

This paper is concerned with the point torque boundary feedback stabilization of a damped Euler-Bernoulli beam model in the presence of a time-varying state-delay. First, a finite-dimensional truncated model is derived by spectral reduction. Then, for a given stabilizing state-feedback of the delay-free truncated model, an LMI-based sufficient condition on the maximum amplitude of the state-delay is employed to guarantee the stability of the closed-loop state-delayed truncated model. Second, we assess the exponential stability of the resulting closed-loop infinite-dimensional system under the assumption that the number of modes of the original infinite-dimensional system captured by the truncated model has been selected large enough. Finally, we consider in our control design the possible presence of a distributed perturbation, as well as additive boundary perturbations in the control inputs. In this case, we derive for the closed-loop system an exponential input-to-state estimate with fading memory of the distributed and boundary disturbances., Comment: Preprint

This paper discusses the boundary feedback stabilization of a reaction-diffusion equation with Robin boundary conditions and in the presence of a time-varying state-delay. The proposed control design strategy is based on a finite-dimensional truncated model obtained via a spectral decomposition. By an adequate selection of the number of modes of the original infinite-dimensional system, we show that the design performed on the finite-dimensional truncated model achieves the exponential stabilization of the original infinite-dimensional system. In the presence of distributed disturbances, we show that the closed-loop system is exponentially input-to-state stable with fading memory., Comment: Published in Automatica as a brief paper

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

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.