Системи диференциални уравнения и невронни мрежи със закъснения и импулси

Department of Mathematics & Statistics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman и ИМИ-БАН, 16.06.2014 г., присъждане на научна степен "доктор на науките" на Валерий Ковачев по научна специалност 01.01.13. математическо моделиране и приложение на математиката. [Covachev Valery Hristov; Ковачев Валерий Христов

Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, 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 UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Asymptotic stability for population models and neural networks with delays

Tese de doutoramento em Matemática (Análise Matemática), apresentada à Universidade de Lisboa através da Faculdade de Ciências, 2008In this thesis, the global asymptotic stability of solutions of several functional differential equations is addressed, with particular emphasis on the study of global stability of equilibrium points of population dynamics and neural network models. First, for scalar retarded functional differential equations, we use weaker versions of the usual Yorke and 3/2-type conditions, to prove the global attractivity of the trivial solution. Afterwards, we establish new sufficient conditions for the global attractivity of the positive equilibrium of a general scalar delayed population model, and illustrate the situation applying these results to two food-limited population models with delays. Second, for n-dimensional Lotka-Volterra systems with distributed delays, the local and global stability of a positive equilibrium, independently of the choice of the delay functions, is addressed assuming that instantaneous negative feedbacks are present. Finally, we obtain the existence and global asymptotic stability of an equilibrium point of a general neural network model by imposing a condition of dominance of the nondelayed terms. The generality of the model allows us to study, as particular situations, the neural network models of Hop_eld, Cohn-Grossberg, bidirectional associative memory, and static with S-type distributed delays. In our proofs, we do not use Lyapunov functionals and our method applies to general delayed di_erential equations.Nesta tese estuda-se a estabilidade global assimptótica de soluções de equações diferenciais funcionais que, pela generalidade com que são apresentadas, possuem uma vasta aplicabilidade em modelos de dinâmica de populações e em modelos de redes neuronais. Numa primeira fase, para equações diferenciais funcionais escalares retardadas, assumem-se novas versões das condições de Yorke e tipo 3/2 para provar a atractividade global da solução nula. Seguidamente, aplicam-se os resultados obtidos a um modelo geral de dinâmica de populações escalar com atrasos, obtendo-se condições suficientes para a atractividade global de um ponto de equilíbrio positivo, e ilustra-se a situação com o estudo de dois modelos conhecidos. Numa segunda fase, para sistemas n-dimensionais de tipo Lotka-Volterra com atrasos distribuídos, estuda-se a estabilidade local e global de um ponto de equilíbrio positivo (caso exista) assumindo condições de dominância dos termos com atrasos pelos termos sem atrasos. Por último, novamente assumindo condições de donimância, obtém-se a existência e estabilidade global assimptótica de um ponto de equilíbrio para um modelo geral de redes neuronais com atrasos. A generalidade do modelo estudado permite obter, como situações particulares, critérios de estabilidade global para modelos de redes neuronais de Hopfield, de Cohn-Grossberg, modelos de memória associativa bidireccional e modelos estáticos com atrasos distribuídos tipo-S. De referir que as demonstrações apresentadas não envolvem o uso de funcionais de Lyapunov, o que permite obter critérios de estabilidade para equações diferenciais funcionais bastante gerais.Universidade do Minho (UM), Departamento de Matemática (DMAT), Centro de Matemática (CMAT); Fundação para a Ciência e Tecnologia (FCT)

Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays

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Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included

Nonlinear Observers for Human-in-the-loop Control Systems

The development of models for a human-in-the-loop with hardware is an area of ongoing research. The ability to simulate a human-in-the-loop with hardware provides a platform for better understanding the dynamics of human and machine cognition. A human-in-the-loop model provides information that can be used to design more efficient human interfaces and smarter autonomous assistant controllers. This can make a complex task such as flying an aircraft safer and more accessible. This thesis explores different possibilities for human operator models to be modeled in the loop with a vehicle. A human is modeled as a linear state feedback controller in the loop with the task of controlling a simple solid ball. The human arm is modeled controlling a joystick as the human is considered to control the ball with a joystick. Nonlinear sliding mode observers are developed to estimate the gains of a feedback control law and nonlinear sliding mode observers are developed to estimate the torques on the shoulder, elbow, and joystick joints. The nonlinear observers are simulated on a human-in-the-loop system to show the accuracy of the observers