Analysis of Large-Scale Asynchronous Switched Dynamical Systems

This dissertation addresses research problems related to the switched system as well as its application to large-scale asynchronous dynamical systems. For decades, this switched system has been widely studied in depth, owing to the broad applicability of the switched system framework. For example, the switched system can be adopted for modeling the dynamics of numerous systems including power systems, manufacturing systems, aerospace systems, networked control systems, etc. Despite considerable research works that have been developed during last several decades, there are still remaining yet important and unsolved problems for the switched systems. In the first part of this dissertation, new methods are developed for uncertainty propagation of stochastic switched systems in the presence of the state uncertainty, represented by probability density functions(PDFs). The main difficulty of this problem is that the number of PDF components in the state increases exponentially under the stochastic switching, incurring the curse of dimensionality. This dissertation provides a novel method that circumvents the issue regarding the curse of dimensionality. As an extension of this research, the new method for the switching synthesis is presented in the second part, to achieve the optimal performance of the switched system. This research is relevant to developing the switching synthesis on how to switch between different switching modes. In the following chapters, some interesting applications that emerges as today's leading-edge technology in high-performance computing (HPC) will be introduced. Generally, the massive parallel computing entails idle process time in multi-core processors or distributed computing devices as up to 80% of total computation time, owing to the synchronization of the data. Thus, there is a trend toward relaxing such a restriction on synchronization penalty to overcome this bottleneck problem. This dissertation presents a synchronous computing algorithms as a key solution to Leverage the computing performance to the maximum capabilities. The price to Pay for adopting the asynchronous computing algorithms is, however, unpredictability of the solution due to the randomness in the behavior of asynchrony. In this dissertation, the switched system is employed to model the characteristics of the asynchrony in parallel computing, enabling analysis of the asynchronous algorithm. Particularly, the analysis will be performed for massively parallel asynchronous numerical algorithms implemented on 1D heat equation and large-scale asynchronous distributed quadratic programming problems. As another case study, this switched system is also implemented on the stability analysis of large-scaled is tribute networked control systems (DNCS) having random communication delays. For these problems, the convergence or stability analysis is carried out by the switched system framework. One of major concerns when adopting the switched system framework for analysis of these systems is the scalability issues associated with extremely large switching mode numbers. Due to the massive parallelism or large-scale distributed nodes, the switching mode numbers are beyond counting, leading to the computational intractability. The proposed methods are developed targeting the settlement of this scalability issue, which inevitably takes place in adopting the switched system framework. Thus, the primary emphasis of this dissertation is placed on the mathematical development of computationally efficient tools, particularly for analysis of the large-scale asynchronous switched dynamical system, which has broad applications including massively parallel asynchronous numerical algorithms to solve ODE/PDE problems, distributed optimization problems, and large-scale DNCS with random communication delays

The structure and dynamics of multilayer networks

In the past years, network theory has successfully characterized the interaction among the constituents of a variety of complex systems, ranging from biological to technological, and social systems. However, up until recently, attention was almost exclusively given to networks in which all components were treated on equivalent footing, while neglecting all the extra information about the temporal- or context-related properties of the interactions under study. Only in the last years, taking advantage of the enhanced resolution in real data sets, network scientists have directed their interest to the multiplex character of real-world systems, and explicitly considered the time-varying and multilayer nature of networks. We offer here a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201

Hereditary Stochastic Hybrid Systems Application to E. coli Movement

A stochastic hybrid system (SHS) is a dynamic system that exhibits both a continuous and a discrete dynamical behavior. In the scientific literature on SHS the principle of causality is commonly assumed, but more realistic models should account on history dependence. In this thesis we developed and analyze a new mathematical model called Hereditary Stochastic Hybrid System which, with the help of a generalization of stochastic time change, allows for general history dependence. We apply the above model to the study of the movement of the bacterium E. coli: when these bacteria swim in a field of chemoattractant molecules, they perform a random walk characterized by a run-and-tumble motion. This random walk is biased towards regions of higher concentration of the chemoattractant. These bacteria are, however too small to sense spatial gradients along their body axis. Instead they developed a history-dependent strategy to search of food, namely the use of memory of previous mea- surements of chemical concentrations. In this way the bacteria are able to infer whether they swim up or down a chemical gradient. By using our framework we are able to generalize the existing models for E. coli movement and have a better fitting of the experimental data. We developed also a software that simulates and compares the different models existing in the literature, with special care for high performance and usability

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Efficiency and Sustainability of the Distributed Renewable Hybrid Power Systems Based on the Energy Internet, Blockchain Technology and Smart Contracts

The climate changes that are visible today are a challenge for the global research community. In this context, renewable energy sources, fuel cell systems, and other energy generating sources must be optimally combined and connected to the grid system using advanced energy transaction methods. As this book presents the latest solutions in the implementation of fuel cell and renewable energy in mobile and stationary applications such as hybrid and microgrid power systems based on energy internet, blockchain technology, and smart contracts, we hope that they are of interest to readers working in the related fields mentioned above

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described