A Noise-Tolerant Zeroing Neural Network for Time-Dependent Complex Matrix Inversion Under Various Kinds of Noises

Complex-valued time-dependent matrix inversion (TDMI) is extensively exploited in practical industrial and engineering fields. Many current neural models are presented to find the inverse of a matrix in an ideal noise-free environment. However, the outer interferences are normally believed to be ubiquitous and avoidable in practice. If these neural models are applied to complex-valued TDMI in a noise environment, they need to take a lot of precious time to deal with outer noise disturbances in advance. Thus, a noise-suppression model is urgent to be proposed to address this problem. In this article, a complex-valued noise-tolerant zeroing neural network (CVNTZNN) on the basis of an integral-type design formula is established and investigated for finding complex-valued TDMI under a wide variety of noises. Furthermore, both convergence and robustness of the CVNTZNN model are carefully analyzed and rigorously proved. For comparison and verification purposes, the existing zeroing neural network (ZNN) and gradient neural network (GNN) have been presented to address the same problem under the same conditions. Numerical simulation consequences demonstrate the effectiveness and excellence of the proposed CVNTZNN model for complex-valued TDMI under various kinds of noises, by comparing the existing ZNN and GNN models

Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation

Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, zeroing neural networks (ZNNs) have been established to find the accurate solution of time-dependent Lyapunov equation (TDLE) in the noise-free conditions. However, noises are inevitable in the actual implementation process. In order to suppress the interference of various noises in practical applications, in this paper, a complex noise-resistant ZNN (CNRZNN) model is proposed and employed for the CTDLE solution. Additionally, the convergence and robustness of the CNRZNN model are analyzed and proved theoretically. For verification and comparison, three experiments and the existing noise-tolerant ZNN (NTZNN) model are introduced to investigate the effectiveness, convergence and robustness of the CNRZNN model. Compared with the NTZNN model, the CNRZNN model has more generality and stronger robustness. Specifically, the NTZNN model is a special form of the CNRZNN model, and the residual error of CNRZNN can converge rapidly and stably to order 10−5 when solving CTDLE under complex linear noises, which is much lower than order 10−1 of the NTZNN model. Analogously, under complex quadratic noises, the residual error of the CNRZNN model can converge to 2∥A∥F/ζ3 quickly and stably, while the residual error of the NTZNN model is divergent

New Noise-Tolerant ZNN Models With Predefined-Time Convergence for Time-Variant Sylvester Equation Solving

Sylvester equation is often applied to various fields, such as mathematics and control systems due to its importance. Zeroing neural network (ZNN), as a systematic design method for time-variant problems, has been proved to be effective on solving Sylvester equation in the ideal conditions. In this paper, in order to realize the predefined-time convergence of the ZNN model and modify its robustness, two new noise-tolerant ZNNs (NNTZNNs) are established by devising two novelly constructed nonlinear activation functions (AFs) to find the accurate solution of the time-variant Sylvester equation in the presence of various noises. Unlike the original ZNN models activated by known AFs, the proposed two NNTZNN models are activated by two novel AFs, therefore, possessing the excellent predefined-time convergence and strong robustness even in the presence of various noises. Besides, the detailed theoretical analyses of the predefined-time convergence and robustness ability for the NNTZNN models are given by considering different kinds of noises. Simulation comparative results further verify the excellent performance of the proposed NNTZNN models, when applied to online solution of the time-variant Sylvester equation

Simultaneous identification, tracking control and disturbance rejection of uncertain nonlinear dynamics systems: A unified neural approach

Previous works of traditional zeroing neural networks (or termed Zhang neural networks, ZNN) show great success for solving specific time-variant problems of known systems in an ideal environment. However, it is still a challenging issue for the ZNN to effectively solve time-variant problems for uncertain systems without the prior knowledge. Simultaneously, the involvement of external disturbances in the neural network model makes it even hard for time-variant problem solving due to the intensively computational burden and low accuracy. In this paper, a unified neural approach of simultaneous identification, tracking control and disturbance rejection in the framework of the ZNN is proposed to address the time-variant tracking control of uncertain nonlinear dynamics systems (UNDS). The neural network model derived by the proposed approach captures hidden relations between inputs and outputs of the UNDS. The proposed model shows outstanding tracking performance even under the influences of uncertainties and disturbances. Then, the continuous-time model is discretized via Euler forward formula (EFF). The corresponding discrete algorithm and block diagram are also presented for the convenience of implementation. Theoretical analyses on the convergence property and discretization accuracy are presented to verify the performance of the neural network model. Finally, numerical studies, robot applications, performance comparisons and tests demonstrate the effectiveness and advantages of the proposed neural network model for the time-variant tracking control of UNDS

The Complex Spherical 2+4 Spin Glass: a Model for Nonlinear Optics in Random Media

A disordered mean field model for multimode laser in open and irregular cavities is proposed and discussed within the replica analysis. The model includes the dynamics of the mode intensity and accounts also for the possible presence of a linear coupling between the modes, due, e.g., to the leakages from an open cavity. The complete phase diagram, in terms of disorder strength, source pumping and non-linearity, consists of four different optical regimes: incoherent fluorescence, standard mode locking, random lasing and the novel spontaneous phase locking. A replica symmetry breaking phase transition is predicted at the random lasing threshold. For a high enough strength of non-linearity, a whole region with nonvanishing complexity anticipates the transition, and the light modes in the disordered medium display typical discontinuous glassy behavior, i.e., the photonic glass has a multitude of metastable states that corresponds to different mode-locking processes in random lasers. The lasing regime is still present for very open cavities, though the transition becomes continuous at the lasing threshold.Comment: 26 pages, 13 figure

A Novel Disturbance Rejection Zeroing Neurodynamic Approach for Robust Synchronization of Chaotic Systems

Robust synchronization of chaotic systems becomes a hot topic in scientific and engineering fields because of the ubiquitous existence of time-variant external disturbances in complex application scenarios. In contrast with existing studies that the resultant synchronization error has a supremum or even diverges under the influence of time-variant external disturbances, this paper proposes a disturbance rejection zeroing neurodynamic (DRZN) approach and its related controller for the robust synchronization of chaotic systems against time-variant external disturbances. The controller designed by the proposed DRZN approach distinctively features the rejection of external disturbances with the generated synchronization error being convergence toward zero. Theoretical analyses guarantee that the DRZN approach and its related controller inherently possess robustness. Moreover, numerical studies including three examples substantiate the effectiveness of the proposed DRZN approach and its related controller for the synchronization of chaotic systems against the time-variant external disturbances. Comparisons with existing approaches, e.g., the conventional zeroing neurodynamic (CZN) approach and the linear-active control (LAC) approach, show the superiority of the proposed DRZN approach. Extensive tests further verify that the proposed DRZN approach possesses the outstanding anti-disturbance performance, and thus is suitable for the practical applications with time-variant external disturbances

Robust GNSS Carrier Phase-based Position and Attitude Estimation Theory and Applications

Mención Internacional en el título de doctorNavigation information is an essential element for the functioning of robotic platforms and intelligent transportation systems. Among the existing technologies, Global Navigation Satellite Systems (GNSS) have established as the cornerstone for outdoor navigation, allowing for all-weather, all-time positioning and timing at a worldwide scale. GNSS is the generic term for referring to a constellation of satellites which transmit radio signals used primarily for ranging information. Therefore, the successful operation and deployment of prospective autonomous systems is subject to our capabilities to support GNSS in the provision of robust and precise navigational estimates. GNSS signals enable two types of ranging observations: –code pseudorange, which is a measure of the time difference between the signal’s emission and reception at the satellite and receiver, respectively, scaled by the speed of light; –carrier phase pseudorange, which measures the beat of the carrier signal and the number of accumulated full carrier cycles. While code pseudoranges provides an unambiguous measure of the distance between satellites and receiver, with a dm-level precision when disregarding atmospheric delays and clock offsets, carrier phase measurements present a much higher precision, at the cost of being ambiguous by an unknown number of integer cycles, commonly denoted as ambiguities. Thus, the maximum potential of GNSS, in terms of navigational precision, can be reach by the use of carrier phase observations which, in turn, lead to complicated estimation problems. This thesis deals with the estimation theory behind the provision of carrier phase-based precise navigation for vehicles traversing scenarios with harsh signal propagation conditions. Contributions to such a broad topic are made in three directions. First, the ultimate positioning performance is addressed, by proposing lower bounds on the signal processing realized at the receiver level and for the mixed real- and integer-valued problem related to carrier phase-based positioning. Second, multi-antenna configurations are considered for the computation of a vehicle’s orientation, introducing a new model for the joint position and attitude estimation problems and proposing new deterministic and recursive estimators based on Lie Theory. Finally, the framework of robust statistics is explored to propose new solutions to code- and carrier phase-based navigation, able to deal with outlying impulsive noises.La información de navegación es un elemental fundamental para el funcionamiento de sistemas de transporte inteligentes y plataformas robóticas. Entre las tecnologías existentes, los Sistemas Globales de Navegación por Satélite (GNSS) se han consolidado como la piedra angular para la navegación en exteriores, dando acceso a localización y sincronización temporal a una escala global, irrespectivamente de la condición meteorológica. GNSS es el término genérico que define una constelación de satélites que transmiten señales de radio, usadas primordinalmente para proporcionar información de distancia. Por lo tanto, la operatibilidad y funcionamiento de los futuros sistemas autónomos pende de nuestra capacidad para explotar GNSS y estimar soluciones de navegación robustas y precisas. Las señales GNSS permiten dos tipos de observaciones de alcance: –pseudorangos de código, que miden el tiempo transcurrido entre la emisión de las señales en los satélites y su acquisición en la tierra por parte de un receptor; –pseudorangos de fase de portadora, que miden la fase de la onda sinusoide que portan dichas señales y el número acumulado de ciclos completos. Los pseudorangos de código proporcionan una medida inequívoca de la distancia entre los satélites y el receptor, con una precisión de decímetros cuando no se tienen en cuenta los retrasos atmosféricos y los desfases del reloj. En contraposición, las observaciones de la portadora son super precisas, alcanzando el milímetro de exactidud, a expensas de ser ambiguas por un número entero y desconocido de ciclos. Por ende, el alcanzar la máxima precisión con GNSS queda condicionado al uso de las medidas de fase de la portadora, lo cual implica unos problemas de estimación de elevada complejidad. Esta tesis versa sobre la teoría de estimación relacionada con la provisión de navegación precisa basada en la fase de la portadora, especialmente para vehículos que transitan escenarios donde las señales no se propagan fácilmente, como es el caso de las ciudades. Para ello, primero se aborda la máxima efectividad del problema de localización, proponiendo cotas inferiores para el procesamiento de la señal en el receptor y para el problema de estimación mixto (es decir, cuando las incógnitas pertenecen al espacio de números reales y enteros). En segundo lugar, se consideran las configuraciones multiantena para el cálculo de la orientación de un vehículo, presentando un nuevo modelo para la estimación conjunta de posición y rumbo, y proponiendo estimadores deterministas y recursivos basados en la teoría de Lie. Por último, se explora el marco de la estadística robusta para proporcionar nuevas soluciones de navegación precisa, capaces de hacer frente a los ruidos atípicos.Programa de Doctorado en Ciencia y Tecnología Informática por la Universidad Carlos III de MadridPresidente: José Manuel Molina López.- Secretario: Giorgi Gabriele.- Vocal: Fabio Dovi

Robust GNSS Carrier Phase-based Position and Attitude Estimation

Navigation information is an essential element for the functioning of robotic platforms and intelligent transportation systems. Among the existing technologies, Global Navigation Satellite Systems (GNSS) have established as the cornerstone for outdoor navigation, allowing for all-weather, all-time positioning and timing at a worldwide scale. GNSS is the generic term for referring to a constellation of satellites which transmit radio signals used primarily for ranging information. Therefore, the successful operation and deployment of prospective autonomous systems is subject to our capabilities to support GNSS in the provision of robust and precise navigational estimates. GNSS signals enable two types of ranging observations: --code pseudorange, which is a measure of the time difference between the signal's emission and reception at the satellite and receiver, respectively, scaled by the speed of light; --carrier phase pseudorange, which measures the beat of the carrier signal and the number of accumulated full carrier cycles. While code pseudoranges provides an unambiguous measure of the distance between satellites and receiver, with a dm-level precision when disregarding atmospheric delays and clock offsets, carrier phase measurements present a much higher precision, at the cost of being ambiguous by an unknown number of integer cycles, commonly denoted as ambiguities. Thus, the maximum potential of GNSS, in terms of navigational precision, can be reach by the use of carrier phase observations which, in turn, lead to complicated estimation problems. This thesis deals with the estimation theory behind the provision of carrier phase-based precise navigation for vehicles traversing scenarios with harsh signal propagation conditions. Contributions to such a broad topic are made in three directions. First, the ultimate positioning performance is addressed, by proposing lower bounds on the signal processing realized at the receiver level and for the mixed real- and integer-valued problem related to carrier phase-based positioning. Second, multi-antenna configurations are considered for the computation of a vehicle's orientation, introducing a new model for the joint position and attitude estimation problems and proposing new deterministic and recursive estimators based on Lie Theory. Finally, the framework of robust statistics is explored to propose new solutions to code- and carrier phase-based navigation, able to deal with outlying impulsive noises

Intelligent Transportation Related Complex Systems and Sensors

Building around innovative services related to different modes of transport and traffic management, intelligent transport systems (ITS) are being widely adopted worldwide to improve the efficiency and safety of the transportation system. They enable users to be better informed and make safer, more coordinated, and smarter decisions on the use of transport networks. Current ITSs are complex systems, made up of several components/sub-systems characterized by time-dependent interactions among themselves. Some examples of these transportation-related complex systems include: road traffic sensors, autonomous/automated cars, smart cities, smart sensors, virtual sensors, traffic control systems, smart roads, logistics systems, smart mobility systems, and many others that are emerging from niche areas. The efficient operation of these complex systems requires: i) efficient solutions to the issues of sensors/actuators used to capture and control the physical parameters of these systems, as well as the quality of data collected from these systems; ii) tackling complexities using simulations and analytical modelling techniques; and iii) applying optimization techniques to improve the performance of these systems. It includes twenty-four papers, which cover scientific concepts, frameworks, architectures and various other ideas on analytics, trends and applications of transportation-related data

Advances in Optical Amplifiers

Optical amplifiers play a central role in all categories of fibre communications systems and networks. By compensating for the losses exerted by the transmission medium and the components through which the signals pass, they reduce the need for expensive and slow optical-electrical-optical conversion. The photonic gain media, which are normally based on glass- or semiconductor-based waveguides, can amplify many high speed wavelength division multiplexed channels simultaneously. Recent research has also concentrated on wavelength conversion, switching, demultiplexing in the time domain and other enhanced functions. Advances in Optical Amplifiers presents up to date results on amplifier performance, along with explanations of their relevance, from leading researchers in the field. Its chapters cover amplifiers based on rare earth doped fibres and waveguides, stimulated Raman scattering, nonlinear parametric processes and semiconductor media. Wavelength conversion and other enhanced signal processing functions are also considered in depth. This book is targeted at research, development and design engineers from teams in manufacturing industry, academia and telecommunications service operators