A Kosambi-Karhunen–Loève Learning Approach to Cooperative Spectrum Sensing in Cognitive Radio Networks

This paper focuses on the issues of cooperative spectrum sensing (CSS) in a large cognitive radio network (CRN) where cognitive radio (CR) nodes can cooperative with neighboring nodes using spatial cooperation. A novel optimal global primary user (PU) detection framework with geographical cooperation using a deflection coefficient metric measure to characterize detection performance is proposed. It is assumed that only a small fraction of CR nodes communicate with the fusion center (FC). Optimal cooperative techniques which are global for class deterministic PU signals are proposed. By establishing the relationship between the CSS technique design issues and Kosambi-Karhunen–Loève transform (KLT) the problem is solved efficiently and the impact on detection performance is evaluated using simulation.Peer reviewedFinal Accepted Versio

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

Nonlinear robust H∞ control.

A new theory is proposed for the full-information finite and infinite horizontime robust H∞ control that is equivalently effective for the regulation and/or tracking problems of the general class of time-varying nonlinear systems under the presence of exogenous disturbance inputs. The theory employs the sequence of linear-quadratic and time-varying approximations, that were recently introduced in the optimal control framework, to transform the nonlinear H∞ control problem into a sequence of linearquadratic robust H∞ control problems by using well-known results from the existing Riccati-based theory of the maturing classical linear robust control. The proposed method, as in the optimal control case, requires solving an approximating sequence of Riccati equations (ASRE), to find linear time-varying feedback controllers for such disturbed nonlinear systems while employing classical methods. Under very mild conditions of local Lipschitz continuity, these iterative sequences of solutions are known to converge to the unique viscosity solution of the Hamilton-lacobi-Bellman partial differential equation of the original nonlinear optimal control problem in the weak form (Cimen, 2003); and should hold for the robust control problems herein. The theory is analytically illustrated by directly applying it to some sophisticated nonlinear dynamical models of practical real-world applications. Under a r -iteration sense, such a theory gives the control engineer and designer more transparent control requirements to be incorporated a priori to fine-tune between robustness and optimality needs. It is believed, however, that the automatic state-regulation robust ASRE feedback control systems and techniques provided in this thesis yield very effective control actions in theory, in view of its computational simplicity and its validation by means of classical numerical techniques, and can straightforwardly be implemented in practice as the feedback controller is constrained to be linear with respect to its inputs

Nonlinear Systems

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers

Mathematical Economics

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Performance Analysis of Recoverable Flight Control Systems Subject to Neutron-Induced Upsets Using Hybrid Dynamical Models

It has been observed that atmospheric neutrons can produce single-event upsets in digital flight control hardware. Potentially, they can reduce system performance and introduce a safety hazard. One experimental system-level approach investigated to help mitigate the effects of these upsets is NASA Langley\u27s Recoverable Computer System. It employs rollback error recovery using dual-lock-step processors together with new fault tolerant architectures and communication subsystems. In this dissertation, a class of stochastic hybrid dynamical models, which consists of a jump-linear system and a stochastic finite-state automaton, is used to describe the performance of a Boeing 737 aircraft system in closed-loop with a Recoverable Computer System. The jump-linear system models the switched dynamics of the closed-loop system due to the presence of controller recoveries. Each dynamical model in the jump-linear system was obtained separately using system identification techniques and high fidelity flight simulation software. The stochastic finite-state automaton approximates the recovery logic of the Recoverable Computer System. The upsets process is modeled by either an independent, identically distributed process or a first-order Markov chain. Mean-square stability and output tracking performance of the recoverable flight control system are analyzed theoretically via a model-equivalent Markov jump-linear system of the stochastic hybrid model. The model was validated using data from a controlled experiment at NASA Langley, where simulated neutron-induced upsets were injected into the system at a desired rate. The effects on the output tracking performance of a simulated aircraft were then directly observed and quantified. The model was then used to analyze a neutron-based experiment on the Recoverable Computer System at the Los Alamos National Laboratory. This model predicts that the experimental flight control system, when functioning as designed, will provide robust control performance in the presence of neutron-induced single-event upsets at normal atmospheric levels