Kernel - based continous - time systems identification: methods and tools

2012/2013Questa tesi ha lo scopo di formalizzare un nuovo filone teorico, che deriva dall’algebra degli operatori lineari integrali di Fredholm-Volterra agenti su spazi di Hilbert, per la sintesi di stimatori dello stato e parametrici per sistemi dinamici a tempo continuo sfruttando le misure ingressi/uscite, soggetti a perturbazione tempo-varianti. In maniera da ottenere stime non-asintotiche di sistemi dinamici a tempo continuo, i metodi classici tipicamente aumentano la dimensione del vettore delle variabili di decisione con le condizioni iniziali incognite di stati non misurati. Tuttavia, questo porta ad un accrescimento della complessitá dell’algoritmo. Recentemente, diversi metodi di stima algebrici sono stati sviluppati, sfruttando un approccio algebrico piuttosto che da una prospettiva statistica o teorica. Mentre le forti fondamenta teoriche e le proprietá di convergenza non asintotiche rappresentano caratteristiche notevoli per questi metodi, il principale inconveniente é che l’implementazione pratica produce una dinamica internamente instabile. Quindi, la progettazione di metodi di stima per questi tipi di sistemi é un argomento importante ed emergente. L’obiettivo di questo lavoro é quello di presentare alcuni risultati recenti, considerando diversi aspetti e affrontando alcuni dei problemi che emergono quando si progettano algoritmi di identificazione. Lo scopo é sviluppare un’architettura di stima con proprietá di convergenza molto veloci e internamente stabile. Seguendo un ordine logico, prima di tutto verrá progettato l’algoritmo di identificazione proponendo una nuova architettura basata sui kernel, utilizzando l’algebra degli operatori lineari integrali di Fredholm-Volterra. Inoltre, la metodologia proposta sará affrontata in maniera da progettare stimatori per sistemi dinamici a tempo continuo con proprietá di convergenza molto veloci, caratterizzati da gradi relativi limitati e possibilmente affetti da perturbazioni strutturate. Piú nello specifico, il progetto di adeguati kernel di operatori lineari integrali non-anticipativi dará origine a stimatori caratterizzati da proprietá di convergenza idealmente "non- asintotiche".Le analisi delle proprietá dei kernel verrá affrontata e due classi di funzioni kernel ammissibili saranno introdotte: una per il problema di stima parametrica e uno per il problema di stima dello stato. Gli operatori che verranno indotti da tali funzioni kernel proposte, ammettono realizzazione spazio-stato implementabile (cioé a dimensione finita e internamente stabile). Allo scopo di dare maggior completezza, l’analisi del bias dello stimatore proposto verrá esaminata, derivando le proprietá asintotiche dell’algoritmo di identificazione e dimostrando che le funzioni kernel possono essere pro- gettate tenendo in debito conto i risultati ottenuti in questa analisi.This thesis is aimed at the formalization of a new theoretical framework, arising from the algebra of Fredholm-Volterra linear integral operators acting on Hilbert spaces, for the synthesis of non-asymptotic state and parameter estimators for continuous-time dynamical systems from input-output measurements subject to time-varying perturbations. In order to achieve non-asymptotic estimates of continuous-time dynamical systems, classical methods usually augment the vector of decision variables with the unknown initial conditions of the non measured states. However, this comes at the price of an increase of complexity for the algorithm. Recently, several algebraic estimation methods have been developed, arising from an algebraic setting rather than from a statistical or a systems-theoretic perspective. While the strong theoretical foundations and the non-asymptotic convergence property represent oustanding features of these methods, the major drawback is that the practical implementation ends up with an internally unstable dynamic. Therefore, the design of estimation methods for these kind of systems is an important and emergent topic. The goal of this work is to present some recent results, considering different frameworks and facing some of the issues emerging when dealing with the design of identification algorithms. The target is to develop a comprehensive estimation architecture with fast convergence properties and internally stable. Following a logical order, first of all we design the identification algorithm by proposing a novel kernel-based architecture, by means of the algebra of Fredholm-Volterra linear integral operators. Besides, the proposed methodology is addressed in order to design estimators with very fast convergence properties for continuous-time dynamic systems characterized by bounded relative degree and possibly affected by structured perturbations. More specifically, the design of suitable kernels of non-anticipative linear integral operators gives rise to estimators characterized by convergence properties ideally “non-asymptotic". The analysis of the properties of the kernels guaranteeing such a fast convergence is addressed and two classes of admissible kernel functions are introduced: one for the parameter estimation problem and one for the state estimation problem. The operators induced by the proposed kernels admit implementable (i.e., finite-dimensional and internally stable) state- space realizations. For the sake of completeness, the bias analysis of the proposed estimator is addressed, deriving the asymptotic properties of the identification algorithm and demonstrating that the kernel functions can be designed taking in account the results obtained with this analysis.XXVI Ciclo198

Towards handling temporal dependence in concept drift streams.

Modern technological advancements have led to the production of an incomprehensible amount of data from a wide array of devices. A constant supply of new data provides an invaluable opportunity for access to qualitative and quantitative insights. Organisations recognise that, in today's modern era, data provides a means of mitigating risk and loss whilst maximising effciency and profit. However, processing this data is not without its challenges. Much of this data is produced in an online environment. Realtime stream data is unbound in size, variety and velocity. Data may arrive complete or with missing attributes, and data availability and persistence is limited to a small window of time. Classification methods and techniques that process offline data are not applicable to online data streams. Instead, new online classification methods have been developed. Research concerning the problematic and prevalent issue of concept drift has produced a considerable number of methods that allow online classifiers to adapt to changes in the stream distribution. However, recent research suggests that the presence of temporal dependence can cause misleading evaluation when accuracy is used as the core metric. This thesis investigates temporal dependence and its negative effcts upon the classification of concept drift data. First, this thesis proposes a novel method for coping with temporal dependence during the classification of real-time data streams, where concept drift is present. Results indicate that a statistical based, selective resetting approach can reduce the impact of temporal dependence in concept drift streams without significant loss in predictive accuracy. Secondly, a new ensemble based method, KTUE, that adopts the Kappa-Temporal statistic for vote weighting is suggested. Results show that this method is capable of outperforming some state-of-the-art ensemble methods in both temporally dependent and non-temporally dependent environments. Finally, this research proposes a novel algorithm for the simulation of temporally dependent concept drift data, which aims to help address the lack of established datasets available for evaluation. Experimental results show that temporal dependence can be injected into fabricated data streams using existing generation methods

Resource Allocation in Distributed Service Networks

The past few years have witnessed significant growth in the use of distributed network analytics involving agile code, data and computational resources. In many such networked systems, for example, Internet of Things (IoT), a large number of smart devices, sensors, processing and storage resources are widely distributed in a geographic region. These devices and resources distributed over a physical space are collectively called a distributed service network. Efficient resource allocation in such high performance service networks remains one of the most critical problems. In this thesis, we model and optimize the allocation of resources in a distributed service network. This thesis contributes to two different types of service networks: caching, and spatial networks; and develops new techniques that optimize the overall performance of these services. First, we propose a new method to compute an upper bound on hit probability for all non-anticipative caching policies in a distributed caching system. We find our bound to be tighter than state-of-the-art upper bounds for a variety of content request arrival processes. We then develop a utility based framework for content placement in a cache network for efficient and fair allocation of caching resources. We develop provably optimal distributed algorithms that operate at each network cache to maximize the overall network utility. Next, we develop and evaluate assignment policies that allocate resources to users with a goal to minimize the expected distance traveled by a user request, where both resources and users are located on a line. Lastly, we design and evaluate resource proximity aware user-request allocation policies with a goal to reduce the implementation cost associated with moving a request/job to/from its allocated resource while balancing the number of requests allocated to a resource. Depending on the topology, our proposed policies achieve a 8% - 99% decrease in implementation cost as compared to the state-of-the-art

A new approach for asynchronous distributed rate control of elastic sessions in integrated packet networks

We develop a new class of asynchronous distributed algorithms for the explicit rate control of elastic sessions in an integrated packet network. Sessions can request for minimum guaranteed rate allocations (e.g., minimum cell rates in the ATM context), and, under this constraint, we seek to allocate the max-min fair rates to the sessions. We capture the integrated network context by permitting the link bandwidths available to elastic sessions to be stochastically time varying. The available capacity of each link is viewed as some statistic of this stochastic process [e.g., a fraction of the mean, or a large deviations-based equivalent service capacity (ESC)]. The ESC is obtained so as to satisfy an overflow probability constraint on the buffer length. For fixed available capacity at each link, we show that the vector of max-min fair rates can be computed from the root of a certain vector equation. A distributed asynchronous stochastic approximation technique is then used to develop a provably convergent distributed algorithm for obtaining the root of the equation, even when the link flows and the available capacities are obtained from on-line measurements. The switch algorithm does not require per connection monitoring, nor does it require per connection marking of control packets. A virtual buffer based approach for on-line estimation of the ESC is utilized. We also propose techniques for handling large variations in the available capacity owing to the arrivals or departures of CBR/VBR sessions. Finally, simulation results are provided to demonstrate the performance of this class of algorithms in the local and wide area network context

Energy Management

Forecasts point to a huge increase in energy demand over the next 25 years, with a direct and immediate impact on the exhaustion of fossil fuels, the increase in pollution levels and the global warming that will have significant consequences for all sectors of society. Irrespective of the likelihood of these predictions or what researchers in different scientific disciplines may believe or publicly say about how critical the energy situation may be on a world level, it is without doubt one of the great debates that has stirred up public interest in modern times. We should probably already be thinking about the design of a worldwide strategic plan for energy management across the planet. It would include measures to raise awareness, educate the different actors involved, develop policies, provide resources, prioritise actions and establish contingency plans. This process is complex and depends on political, social, economic and technological factors that are hard to take into account simultaneously. Then, before such a plan is formulated, studies such as those described in this book can serve to illustrate what Information and Communication Technologies have to offer in this sphere and, with luck, to create a reference to encourage investigators in the pursuit of new and better solutions

The decisive reset: attainable governance for revitalising democracy

To improve democratic legitimacy, successful resolution of public policy challenges has to emerge from highly pressurised political predicaments. Increasing civic functionality requires integrative Civil Service practice, building trust in adaptive oversight. With the task of effective governance stretching out-of-reach in straining institutional arrangements, a proposition is developed for an “Attainable Governance” reset to revitalise democracy. Motivated by the need for progress that is sensitive to the reality and risks of the present and embodying requirements to hold open unforeseen possibilities for future action, the groundwork is laid for a new “decision architecture” that improves policy-framing and decision-making. With a mission to compose a conceptual framework for “facing the future” in the United Kingdom, I make the case for refreshing democratic arrangements, including a proposed structural intervention to the policy-making system with a correlative cultural step-change in leadership. Laying out a novel framework, the analysis draws widely on strands of thinking in social theory and political philosophy, public administration and policy-making, systems thinking and design, planning and strategic management, anticipation and futures, economics, and sociology. Taking an “integral” methodological orientation, in three parts I: (1) diagnose the converging Predicament, (2) develop a conceptual Proposition, and 3) sketch-out an approach to leadership that facilitates operational adaption in Procedures for applied practice. Positing that we have to deal with systems-of-problems (“messes”) and system-of-systems (“systemic messes”) with an analytic primacy on expanding temporal considerations to factor in more anticipative insights, I take a Complex Adaptive Systems-informed stance. The need for a “Decisive Reset” to refresh democracy, featuring phased systemic reordering and tactical modularity to produce better public decision-making that is responsive and agile in the short-run, while actively gauging medium-term realities and future-proofing for long-run uncertainties, results in a new decision architecture and methodology