Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

A Multivariate Non-Gaussian Bayesian Filter Using Power Moments

In this paper, which is a very preliminary version, we extend our results on the univariate non-Gaussian Bayesian filter using power moments to the multivariate systems, which can be either linear or nonlinear. Doing this introduces several challenging problems, for example a positive parametrization of the density surrogate, which is not only a problem of filter design, but also one of the multiple dimensional Hamburger moment problem. We propose a parametrization of the density surrogate with the proofs to its existence, Positivstellensatze and uniqueness. Based on it, we analyze the error of moments of the density estimates through the filtering process with the proposed density surrogate. An error upper bound in the sense of total variation distance is also given. A discussion on continuous and discrete treatments to the non-Gaussian Bayesian filtering problem is proposed to explain why our proposed filter shall also be a mainstream of the non-Gaussian Bayesian filtering research and motivate the research on continuous parametrization of the system state. Last but not the least, simulation results on estimating different types of multivariate density functions are given to validate our proposed filter. To the best of our knowledge, the proposed filter is the first one implementing the multivariate Bayesian filter with the system state parameterized as a continuous function, which only requires the true states being Lebesgue integrable.Comment: 16 pages, 2 figures. arXiv admin note: text overlap with arXiv:2207.0851

Control and filtering of time-varying linear systems via parameter dependent Lyapunov functions

The main contribution of this dissertation is to propose conditions for linear filter and controller design, considering both robust and parameter dependent structures, for discrete time-varying systems. The controllers, or filters, are obtained through the solution of optimization problems, formulated in terms of bilinear matrix inequalities, using a method that alternates convex optimization problems described in terms of linear matrix inequalities. Both affine and multi-affine in different instants of time (path dependent) Lyapunov functions were used to obtain the design conditions, as well as extra variables introduced by the Finsler\u27s lemma. Design problems that take into account an H-infinity guaranteed cost were investigated, providing robustness with respect to unstructured uncertainties. Numerical simulations show the efficiency of the proposed methods in terms of H-infinity performance when compared with other strategies from the literature

Networked Data Analytics: Network Comparison And Applied Graph Signal Processing

Networked data structures has been getting big, ubiquitous, and pervasive. As our day-to-day activities become more incorporated with and influenced by the digital world, we rely more on our intuition to provide us a high-level idea and subconscious understanding of the encountered data. This thesis aims at translating the qualitative intuitions we have about networked data into quantitative and formal tools by designing rigorous yet reasonable algorithms. In a nutshell, this thesis constructs models to compare and cluster networked data, to simplify a complicated networked structure, and to formalize the notion of smoothness and variation for domain-specific signals on a network. This thesis consists of two interrelated thrusts which explore both the scenarios where networks have intrinsic value and are themselves the object of study, and where the interest is for signals defined on top of the networks, so we leverage the information in the network to analyze the signals. Our results suggest that the intuition we have in analyzing huge data can be transformed into rigorous algorithms, and often the intuition results in superior performance, new observations, better complexity, and/or bridging two commonly implemented methods. Even though different in the principles they investigate, both thrusts are constructed on what we think as a contemporary alternation in data analytics: from building an algorithm then understanding it to having an intuition then building an algorithm around it. We show that in order to formalize the intuitive idea to measure the difference between a pair of networks of arbitrary sizes, we could design two algorithms based on the intuition to find mappings between the node sets or to map one network into the subset of another network. Such methods also lead to a clustering algorithm to categorize networked data structures. Besides, we could define the notion of frequencies of a given network by ordering features in the network according to how important they are to the overall information conveyed by the network. These proposed algorithms succeed in comparing collaboration histories of researchers, clustering research communities via their publication patterns, categorizing moving objects from uncertain measurmenets, and separating networks constructed from different processes. In the context of data analytics on top of networks, we design domain-specific tools by leveraging the recent advances in graph signal processing, which formalizes the intuitive notion of smoothness and variation of signals defined on top of networked structures, and generalizes conventional Fourier analysis to the graph domain. In specific, we show how these tools can be used to better classify the cancer subtypes by considering genetic profiles as signals on top of gene-to-gene interaction networks, to gain new insights to explain the difference between human beings in learning new tasks and switching attentions by considering brain activities as signals on top of brain connectivity networks, as well as to demonstrate how common methods in rating prediction are special graph filters and to base on this observation to design novel recommendation system algorithms

Filtering of image sequences: on line edge detection and motion reconstruction

L'argomento della Tesi riguarda líelaborazione di sequenze di immagini, relative ad una scena in cui uno o pi˘ oggetti (possibilmente deformabili) si muovono e acquisite da un opportuno strumento di misura. A causa del processo di misura, le immagini sono corrotte da un livello di degradazione. Si riporta la formalizzazione matematica dellíinsieme delle immagini considerate, dellíinsieme dei moti ammissibili e della degradazione introdotta dallo strumento di misura. Ogni immagine della sequenza acquisita ha una relazione con tutte le altre, stabilita dalla legge del moto della scena. Líidea proposta in questa Tesi Ë quella di sfruttare questa relazione tra le diverse immagini della sequenza per ricostruire grandezze di interesse che caratterizzano la scena. Nel caso in cui si conosce il moto, líinteresse Ë quello di ricostruire i contorni dellíimmagine iniziale (che poi possono essere propagati attraverso la stessa legge del moto, in modo da ricostruire i contorni della generica immagine appartenente alla sequenza in esame), stimando líampiezza e del salto del livello di grigio e la relativa localizzazione. Nel caso duale si suppone invece di conoscere la disposizione dei contorni nellíimmagine iniziale e di avere un modello stocastico che descriva il moto; líobiettivo Ë quindi stimare i parametri che caratterizzano tale modello. Infine, si presentano i risultati dellíapplicazione delle due metodologie succitate a dati reali ottenuti in ambito biomedicale da uno strumento denominato pupillometro. Tali risultati sono di elevato interesse nellíottica di utilizzare il suddetto strumento a fini diagnostici

Inverse Optimal Control with Speed Gradient for a Power Electric System Using a Neural Reduced Model

This paper presented an inverse optimal neural controller with speed gradient (SG) for discrete-time unknown nonlinear systems in the presence of external disturbances and parameter uncertainties, for a power electric system with different types of faults in the transmission lines including load variations. It is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter (EKF) based algorithm. It is well known that electric power grids are considered as complex systems due to their interconections and number of state variables; then, in this paper, a reduced neural model for synchronous machine is proposed for the stabilization of nine bus system in the presence of a fault in three different cases in the lines of transmission

Connecting GOMMA with STROMA: an approach for semantic ontology mapping in the biomedical domain

This thesis establishes a connection between GOMMA and STROMA – both are tools of ontology processing. Consequently, a new workflow of denoting a set of correspondences with five semantic relation types has been implemented. Such a rich denotation is scarcely discussed within the literature. The evaluation of the denotation shows that trivial correspondences are easy to recognize (tF > 90). The challenge is the denotation of non-trivial types ( 30 < ntF < 70). A prerequisite of the implemented workflow is the extraction of semantic relations between concepts. These relations represent additional background knowledge for the enrichment tool STROMA and are integrated to the repository SemRep which is accessed by this tool. Thus, STROMA is able to calculate a semantic type more precisely. UMLS was chosen as a biomedical knowledge source because it subsumes many different ontologies of this domain and thus, it represents a rich resource. Nevertheless, only a small set of relations met the requirements which are imposed to SemRep relations. Further studies may analyze whether there is an appropriate way to integrate the missing relations as well. The connection of GOMMA with STROMA allows the semantic enrichment of a biomedical mapping. As a consequence, this thesis enlightens two subjects of research. First, STROMA had been tested with general ontologies, which models common sense knowledge. Within this thesis, STROMA was applied to domain ontologies. Studies have shown that overall, STROMA was able to treat such ontologies as well. However, some strategies for the enrichment process are based on assumption which are misleading in the biomedical domain. Consequently, further strategies are suggested in this thesis which might improve the type denotation. These strategies may lead to an optimization of STROMA for biomedical data sets. A more thorough analysis will review their scope, also beyond the biomedical domain. Second, the established connection may lead to deeper investigations about advantages of semantic enrichment in the biomedical domain as an enriched mapping is returned. Despite heterogeneity of source and target ontology, such a mapping results in an improved interoperability at a finer level of granularity. The utilization of semantically rich correspondences in the biomedical domain is a worthwhile focus for future research

Sub-band detection of small-sized objects during airspace sensing with ultra-short radio pulses

The possibility of solving the problem of detecting such objects on the basis of radar soundings in the resonant frequency range of the UHF radio wave range is considered. Sub-band processing of the received signals is proposed, based on the division of the spectral definition area into sub-bands, for adaptation to the frequency response band and noise filterin

Payload/orbiter signal-processing and data-handling system evaluation

Incompatibilities between orbiter subsystems and payload communication systems to assure that acceptable and to end system performamce will be achieved are identified. The potential incompatabilities are associated with either payloads in the cargo bay or detached payloads communicating with the orbiter via an RF link. The payload signal processing and data handling systems are assessed by investigating interface problems experienced between the inertial upper stage and the orbiter since similar problems are expected for other payloads

Half-wave Plates for the Spider Cosmic Microwave Background Polarimeter

Spider is a balloon-borne array of six telescopes that will observe the Cosmic Microwave Background. The 2400 antenna-coupled bolometers in the instrument will make a polarization map of the CMB with ~degree resolution at 150 GHz and 95 GHz. Polarization modulation is achieved via a cryogenic sapphire half-wave plate (HWP) skyward of the primary optic. In this thesis, the design, construction, and lab testing of the HWP system are discussed. The polarization modulation of these optical stacks is modeled using a physical optics calculation and Mueller matrices. Performance tests in both the lab and integrated in the flight cryostat show consistency with the model.Comment: 165 pages, PhD Thesi