Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area

Innovations and advances in structural engineering: Honoring the career of Yozo Fujino

This special issue of Smart Structures and Systems (SSS) is dedicated to Dr. Yozo Fujino to celebrate his outstanding and innovative contributions to structural engineering during his career. The papers in this issue present a wide range of recent results on bridge dynamics, wind and earthquake effects on structures, health monitoring, and passive/active control technology. This collection of papers also provides a glimpse into the broad nature of Dr. Fujino’s interests. Prof. Fujino is an internationally recognized leader who has been an inspiration to industrial and academic scientists and engineers for over 30 years. During his brilliant academic career, Prof. Fujino has made and continues to make fundamental contributions to dynamics, control and monitoring of bridges considering both wind actions and earthquakes loading. In addition, he has consulted on over 30 signature bridge projects including Akashi Kaikyo Bridge in Japan, Millennium Bridge (vibration control) in UK and Stonecutters Bridge in Hong Kong, demonstrating his recognition not only for his research achievements, but also for his practical knowledge and experience in bridge engineering. In addition to his numerous contributions to science and engineering, Dr. Fujino is a dedicated and passionate teacher and professor, inspiring young scientists and engineers to advance their knowledge and experiences. Dr. Fujino is currently a Distinguished Professor of Advanced Sciences at Yokohama National University (YNU) in Japan. He is also jointly appointed as a Program Director (Policy Adviser) for the Council for Science, Technology and Innovation, Cabinet Office, Japanese Government. Prior to joining YNU, he served for more than 30 years as a Professor of Civil Engineering and the head of the Bridge and Structures Laboratory at The University of Tokyo. On behalf of all the contributors to this special issue, we would like to sincerely congratulate Dr. Yozo Fujino on a truly amazing career and wish him good health, happiness, and many more contributions to structural engineering in the years to come.Ope

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

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

Aeronautical engineering: A continuing bibliography with indexes (supplement 256)

This bibliography lists 426 reports, articles, and other documents introduced into the NASA scientific and technical information system in August 1990. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Control and game-theoretic methods for secure cyber-physical-human systems

This work focuses on systems comprising tightly interconnected physical and digital components. Those, aptly named, cyber-physical systems will be the core of the Fourth Industrial Revolution. Thus, cyber-physical systems will be called upon to interact with humans, either in a cooperative fashion, or as adversaries to malicious human agents that will seek to corrupt their operation. In this work, we will present methods that enable an autonomous system to operate safely among human agents and to gain an advantage in cyber-physical security scenarios by employing tools from control, game and learning theories. Our work revolves around three main axes: unpredictability-based defense, operation among agents with bounded rationality and verification of safety properties for autonomous systems. In taking advantage of the complex nature of cyber-physical systems, our unpredictability-based defense work will focus both on attacks on actuating and sensing components, which will be addressed via a novel switching-based Moving Target Defense framework, and on Denial-of-Service attacks on the underlying network via a zero-sum game exploiting redundant communication channels. Subsequently, we will take a more abstract view of complex system security by exploring the principles of bounded rationality. We will show how attackers of bounded rationality can coordinate in inducing erroneous decisions to a system while they remain stealthy. Methods of cognitive hierarchy will be employed for decision prediction, while closed form solutions of the optimization problem and the conditions of convergence to the Nash equilibrium will be investigated. The principles of bounded rationality will be brought to control systems via the use of policy iteration algorithms, enabling data-driven attack prediction in a more realistic fashion than what can be offered by game equilibrium solutions. The issue of intelligence in security scenarios will be further considered via concepts of learning manipulation through a proposed framework where bounded rationality is understood as a hierarchy in learning, rather than optimizing, capability. This viewpoint will allow us to propose methods of exploiting the learning process of an imperfect opponent in order to affect their cognitive state via the use of tools from optimal control theory. Finally, in the context of safety, we will explore verification and compositionality properties of linear systems that are designed to be added to a cascade network of similar systems. To obfuscate the need for knowledge of the system's dynamics, we will state decentralized conditions that guarantee a specific dissipativity properties for the system, which are shown to be solved by reinforcement learning techniques. Subsequently, we will propose a framework that employs a hierarchical solution of temporal logic specifications and reinforcement learning problems for optimal tracking.Ph.D

The complexity of simulating quantum physics: dynamics and equilibrium

Quantum computing is the offspring of quantum mechanics and computer science, two great scientific fields founded in the 20th century. Quantum computing is a relatively young field and is recognized as having the potential to revolutionize science and technology in the coming century. The primary question in this field is essentially to ask which problems are feasible with potential quantum computers and which are not. In this dissertation, we study this question with a physical bent of mind. We apply tools from computer science and mathematical physics to study the complexity of simulating quantum systems. In general, our goal is to identify parameter regimes under which simulating quantum systems is easy (efficiently solvable) or hard (not efficiently solvable). This study leads to an understanding of the features that make certain problems easy or hard to solve. We also get physical insight into the behavior of the system being simulated. In the first part of this dissertation, we study the classical complexity of simulating quantum dynamics. In general, the systems we study transition from being easy to simulate at short times to being harder to simulate at later times. We argue that the transition timescale is a useful measure for various Hamiltonians and is indicative of the physics behind the change in complexity. We illustrate this idea for a specific bosonic system, obtaining a complexity phase diagram that delineates the system into easy or hard for simulation. We also prove that the phase diagram is robust, supporting our statement that the phase diagram is indicative of the underlying physics. In the next part, we study open quantum systems from the point of view of their potential to encode hard computational problems. We study a class of fermionic Hamiltonians subject to Markovian noise described by Lindblad jump operators and illustrate how, sometimes, certain Lindblad operators can induce computational complexity into the problem. Specifically, we show that these operators can implement entangling gates, which can be used for universal quantum computation. We also study a system of bosons with Gaussian initial states subject to photon loss and detected using photon-number-resolving measurements. We show that such systems can remain hard to simulate exactly and retain a relic of the "quantumness" present in the lossless system. Finally, in the last part of this dissertation, we study the complexity of simulating a class of equilibrium states, namely ground states. We give complexity-theoretic evidence to identify two structural properties that can make ground states easier to simulate. These are the existence of a spectral gap and the existence of a classical description of the ground state. Our findings complement and guide efforts in the search for efficient algorithms