Stability Analysis of Retarded Differential Inclusions

Retarded differential inclusions have drawn more and more attention, due to the development of feedback control systems with delays and dynamical systems determined by retarded differential equations with a discontinuous right-hand side. The purpose of this paper is to establish a result on the stability and asymptotical stability for retarded differential inclusions. Comparing with the previous results, the main result obtained in this paper allows Lyapunov functions to be nonsmooth. Moreover, to deal with the asymptotical stability, it is not required that Lyapunov functions should have an infinitesimal upper limit, but this condition is needed in most of the previous results. To demonstrate applicability, we use the main result in the analysis of asymptotical stability of a class of neural networks with discontinuous activations and delays

Control of chaos in nonlinear circuits and systems

Nonlinear circuits and systems, such as electronic circuits (Chapter 5), power converters (Chapter 6), human brains (Chapter 7), phase lock loops (Chapter 8), sigma delta modulators (Chapter 9), etc, are found almost everywhere. Understanding nonlinear behaviours as well as control of these circuits and systems are important for real practical engineering applications. Control theories for linear circuits and systems are well developed and almost complete. However, different nonlinear circuits and systems could exhibit very different behaviours. Hence, it is difficult to unify a general control theory for general nonlinear circuits and systems. Up to now, control theories for nonlinear circuits and systems are still very limited. The objective of this book is to review the state of the art chaos control methods for some common nonlinear circuits and systems, such as those listed in the above, and stimulate further research and development in chaos control for nonlinear circuits and systems. This book consists of three parts. The first part of the book consists of reviews on general chaos control methods. In particular, a time-delayed approach written by H. Huang and G. Feng is reviewed in Chapter 1. A master slave synchronization problem for chaotic Lur’e systems is considered. A delay independent and delay dependent synchronization criteria are derived based on the H performance. The design of the time delayed feedback controller can be accomplished by means of the feasibility of linear matrix inequalities. In Chapter 2, a fuzzy model based approach written by H.K. Lam and F.H.F. Leung is reviewed. The synchronization of chaotic systems subject to parameter uncertainties is considered. A chaotic system is first represented by the fuzzy model. A switching controller is then employed to synchronize the systems. The stability conditions in terms of linear matrix inequalities are derived based on the Lyapunov stability theory. The tracking performance and parameter design of the controller are formulated as a generalized eigenvalue minimization problem which is solved numerically via some convex programming techniques. In Chapter 3, a sliding mode control approach written by Y. Feng and X. Yu is reviewed. Three kinds of sliding mode control methods, traditional sliding mode control, terminal sliding mode control and non-singular terminal sliding mode control, are employed for the control of a chaotic system to realize two different control objectives, namely to force the system states to converge to zero or to track desired trajectories. Observer based chaos synchronizations for chaotic systems with single nonlinearity and multi-nonlinearities are also presented. In Chapter 4, an optimal control approach written by C.Z. Wu, C.M. Liu, K.L. Teo and Q.X. Shao is reviewed. Systems with nonparametric regression with jump points are considered. The rough locations of all the possible jump points are identified using existing kernel methods. A smooth spline function is used to approximate each segment of the regression function. A time scaling transformation is derived so as to map the undecided jump points to fixed points. The approximation problem is formulated as an optimization problem and solved via existing optimization tools. The second part of the book consists of reviews on general chaos controls for continuous-time systems. In particular, chaos controls for Chua’s circuits written by L.A.B. Tôrres, L.A. Aguirre, R.M. Palhares and E.M.A.M. Mendes are discussed in Chapter 5. An inductorless Chua’s circuit realization is presented, as well as some practical issues, such as data analysis, mathematical modelling and dynamical characterization, are discussed. The tradeoff among the control objective, the control energy and the model complexity is derived. In Chapter 6, chaos controls for pulse width modulation current mode single phase H-bridge inverters written by B. Robert, M. Feki and H.H.C. Iu are discussed. A time delayed feedback controller is used in conjunction with the proportional controller in its simple form as well as in its extended form to stabilize the desired periodic orbit for larger values of the proportional controller gain. This method is very robust and easy to implement. In Chapter 7, chaos controls for epileptiform bursting in the brain written by M.W. Slutzky, P. Cvitanovic and D.J. Mogul are discussed. Chaos analysis and chaos control algorithms for manipulating the seizure like behaviour in a brain slice model are discussed. The techniques provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain. The third part of the book consists of reviews on general chaos controls for discrete-time systems. In particular, chaos controls for phase lock loops written by A.M. Harb and B.A. Harb are discussed in Chapter 8. A nonlinear controller based on the theory of backstepping is designed so that the phase lock loops will not be out of lock. Also, the phase lock loops will not exhibit Hopf bifurcation and chaotic behaviours. In Chapter 9, chaos controls for sigma delta modulators written by B.W.K. Ling, C.Y.F. Ho and J.D. Reiss are discussed. A fuzzy impulsive control approach is employed for the control of the sigma delta modulators. The local stability criterion and the condition for the occurrence of limit cycle behaviours are derived. Based on the derived conditions, a fuzzy impulsive control law is formulated so that the occurrence of the limit cycle behaviours, the effect of the audio clicks and the distance between the state vectors and an invariant set are minimized supposing that the invariant set is nonempty. The state vectors can be bounded within any arbitrary nonempty region no matter what the input step size, the initial condition and the filter parameters are. The editors are much indebted to the editor of the World Scientific Series on Nonlinear Science, Prof. Leon Chua, and to Senior Editor Miss Lakshmi Narayan for their help and congenial processing of the edition

Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics

Techniques for Decentralized and Dynamic Resource Allocation

abstract: This thesis investigates three different resource allocation problems, aiming to achieve two common goals: i) adaptivity to a fast-changing environment, ii) distribution of the computation tasks to achieve a favorable solution. The motivation for this work relies on the modern-era proliferation of sensors and devices, in the Data Acquisition Systems (DAS) layer of the Internet of Things (IoT) architecture. To avoid congestion and enable low-latency services, limits have to be imposed on the amount of decisions that can be centralized (i.e. solved in the ``cloud") and/or amount of control information that devices can exchange. This has been the motivation to develop i) a lightweight PHY Layer protocol for time synchronization and scheduling in Wireless Sensor Networks (WSNs), ii) an adaptive receiver that enables Sub-Nyquist sampling, for efficient spectrum sensing at high frequencies, and iii) an SDN-scheme for resource-sharing across different technologies and operators, to harmoniously and holistically respond to fluctuations in demands at the eNodeB' s layer. The proposed solution for time synchronization and scheduling is a new protocol, called PulseSS, which is completely event-driven and is inspired by biological networks. The results on convergence and accuracy for locally connected networks, presented in this thesis, constitute the theoretical foundation for the protocol in terms of performance guarantee. The derived limits provided guidelines for ad-hoc solutions in the actual implementation of the protocol. The proposed receiver for Compressive Spectrum Sensing (CSS) aims at tackling the noise folding phenomenon, e.g., the accumulation of noise from different sub-bands that are folded, prior to sampling and baseband processing, when an analog front-end aliasing mixer is utilized. The sensing phase design has been conducted via a utility maximization approach, thus the scheme derived has been called Cognitive Utility Maximization Multiple Access (CUMMA). The framework described in the last part of the thesis is inspired by stochastic network optimization tools and dynamics. While convergence of the proposed approach remains an open problem, the numerical results here presented suggest the capability of the algorithm to handle traffic fluctuations across operators, while respecting different time and economic constraints. The scheme has been named Decomposition of Infrastructure-based Dynamic Resource Allocation (DIDRA).Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Novel linear and nonlinear optical signal processing for ultra-high bandwidth communications

The thesis is articulated around the theme of ultra-wide bandwidth single channel signals. It focuses on the two main topics of transmission and processing of information by techniques compatible with high baudrates. The processing schemes introduced combine new linear and nonlinear optical platforms such as Fourier-domain programmable optical processors and chalcogenide chip waveguides, as well as the concept of neural network. Transmission of data is considered in the context of medium distance links of Optical Time Division Multiplexed (OTDM) data subject to environmental fluctuations. We experimentally demonstrate simultaneous compensation of differential group delay and multiple orders of dispersion at symbol rates of 640 Gbaud and 1.28 Tbaud. Signal processing at high bandwidth is envisaged both in the case of elementary post-transmission analog error mitigation and in the broader field of optical computing for high level operations (“optical processor”). A key innovation is the introduction of a novel four-wave mixing scheme implementing a dot-product operation between wavelength multiplexed channels. In particular, it is demonstrated for low-latency hash-key based all-optical error detection in links encoded with advanced modulation formats. Finally, the work presents groundbreaking concepts for compact implementation of an optical neural network as a programmable multi-purpose processor. The experimental architecture can implement neural networks with several nodes on a single optical nonlinear transfer function implementing functions such as analog-to-digital conversion. The particularity of the thesis is the new approaches to optical signal processing that potentially enable high level operations using simple optical hardware and limited cascading of components

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

On the outer synchronization of complex dynamical networks

Complex network models have become a major tool in the modeling and analysis of many physical, biological and social phenomena. A complex network exhibits behaviors which emerge as a consequence of interactions between its constituent elements, that is, remarkably, not the same as individual components. One particular topic that has attracted the researchers' attention is the analysis of how synchronization occurs in this class of models, with the expectation of gaining new insights of the interactions taking place in real-world complex systems. Most of the work in the literature so far has been focused on the synchronization of a collection of interconnected nodes (forming one single network), where each node is a dynamical system governed by a set of nonlinear differential equations, possibly displaying chaotic dynamics. In this thesis, we study an extended version of this problem. In particular, we consider a setup consisting of two complex networks which are coupled unidirectionally, in such a way that a set of signals from the master network are injected into the response network, and then investigate how synchronization is attained. Our analysis is fairly general. We impose few conditions on the network structure and do not assume that the nodes in a single network are synchronized. This work can be divided into two main parts; outer synchronization in fractional-order networks, and outer synchronization in ordinary networks. In both cases the system parameters are perturbed by bounded, time varying and unknown perturbations. The synchronizer feedback matrix is possibly perturbed with the same type of perturbations as well. In both cases, of fractional-order and ordinary networks, we build up several theorems that ensure the attainment of synchronization in various scenarios, including, e.g., cases in which the coupling matrix of the networks is non-diffusive (hence we can avoid this assumption, which is almost invariably made in the literature). In all the cases of interest, we show that the scheme for coupling the networks is very simple, as it reduces to the computation of a single gain matrix whose dimension is independent of the number of network nodes. The structure of the designed synchronizer is also very simple, making it convenient for real-world applications. Although all of the proposed schemes are assessed analytically, numerical results (obtained by computer simulations) are also provided to illustrate the proposed methods. ---------------------------------------Las redes complejas se han convertido en una herramienta fundamental en el análisis de muchos sistemas físicos, biológicos y sociales. Una red compleja presenta comportamientos que "emergen" como consecuencia de las interacciones entre sus elementos constituyentes pero que no se observan de forma individual en estos elementos. Un aspecto en concreto que ha atrapado la atención de muchos investigadores es el análisis de cómo se producen fenómenos de sincronización en esta clase de modelos, con la esperanza de alcanzar una mayor comprensión de las interacciones que tienen lugar en sistemas complejos del mundo real. La mayor parte del trabajo publicado hasta ahora ha estado centrado en la sincronización de una colección de nodos interconectados (que forman una única red con entidad propia), donde cada nodo es un sistema dinámico gobernado por un conjunto de ecuaciones diferenciales no lineales, posiblemente caóticas. En esta tesis estudiamos una versión extendida de este problema. En concreto, consideramos un sistema formado por dos redes complejas acopladas unidireccionalmente, de manera que un conjunto de señales de la red principal se inyectan en la red secundaria, e investigamos cómo se alcanza un estado de sincronización. Este fenómeno se conoce como "sincronización externa". Nuestro análisis es muy general. Se imponen pocas condiciones a las estructura de las redes y no es necesario suponer que los nodos de cada red estén sincronizados entre sí previamente. Esta memoria se puede dividir en dos bloques: la sincronización externa de redes descritas por ecuaciones diferenciales de orden fraccionario y la sincronización externa de redes ordinarias (descritas por ecuaciones diferenciales de orden entero). En ambos casos, se admite que los parámetros del sistema puedan estar sujetos a perturbaciones desconocidas, posiblemente variables con el tiempo, pero acotadas. La matriz de realimentación del esquema de sincronización puede sufrir el mismo tipo de perturbación. En ambos casos, con ecuaciones de orden fraccionario o entero, construimos varios teoremas que aseguran que se alcance la sincronización en escenarios diversos, incluyendo, por ejemplo, casos en los que la matriz de acoplamiento de las redes es no difusiva (por lo tanto, podemos evitar esta hipótesis, que es ubicua en la literatura). En todos los casos de interés, mostramos que el esquema necesario para interconectar las redes es muy simple, puesto que se reduce al cálculo de una única matriz de ganancia cuya dimensión es independiente de la dimensión total (número de nodos) de las redes. La estructura del sincronizados es también muy sencilla, lo que la hace potencialmente adecuada para aplicaciones del mundo real. Aunque todos los esquemas que se proponen se analizan de manera rigurosa, también se muestran resultados numéricos (obtenidos mediante simulación) para ilustrar los métodos propuestos.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Ángel María Bravo Santos.- Secretario: David Luengo García.- Vocal: Irene Sendiña Nada

A fixed point approach towards stability of delay differential equations with applications to neural networks

This thesis studies asymptotic behavior and stability of determinsitic and stochastic delay differential equations. The approach used in this thesis is based on fixed point theory, which does not resort to any Liapunov function or Liapunov functional. The main contribution of this thesis is to study the approach using fixed point theory in a systematic way and to unify recent results in the literature by considering some general classes of equations. The equation we considered is a combination of time dependent delays, distributed delays, impulses and stochastic perturbations. In addition, an application to stochastic delayed neural networks is investigated. The results in this thesis extend and improve some exist results in the literature in some ways. Examples are discussed in each chapter to illustrate our main results.UBL - phd migration 201

Stability Analysis and Controller Synthesis of Switched Systems

Ph.DDOCTOR OF PHILOSOPH