Control of a Nonlinear Teleoperation System by State Convergence

In this work, we proposes a control strategy that allows the remote manipulator follow the local manipulator through the state convergence even if it has a delay in the communication channel. The bilateral control of the teleoperator system considers the case were the human operator applies a constant force on the local manipulator and when the interaction of the remote manipulator with the environment is considered passive. The stability analysis was performed using Lyapunov- Krasovskii functional, it showed for the case with constant delay, that using a proposed control algorithm by state convergence resulted in asymptotically stable, local and remote the nonlinear teleoperation system.

Tracking the states of a nonlinear and nonstationary system in the weight-space of artificial neural networks

We propose a novel interpretation and usage of Neural Network (NN) in modeling physiological signals, which are allowed to be nonlinear and/or nonstationary. The method consists of training a NN for the k-step prediction of a physiological signal, and then examining the connection-weight-space (CWS) of the NN to extract information about the signal generator mechanism. We de. ne a novel feature, Normalized Vector Separation (gamma(ij)), to measure the separation of two arbitrary states i and j in the CWS and use it to track the state changes of the generating system. The performance of the method is examined via synthetic signals and clinical EEG. Synthetic data indicates that gamma(ij) can track the system down to a SNR of 3.5 dB. Clinical data obtained from three patients undergoing carotid endarterectomy of the brain showed that EEG could be modeled (within a root-means-squared-error of 0.01) by the proposed method, and the blood perfusion state of the brain could be monitored via gamma(ij), with small NNs having no more than 21 connection weight altogether.

Experimental observation of autosoliton propagation in a dispersion-managed system guided by nonlinear optical loop mirrors

Observation of autosoliton propagation in a dispersion-managed optical transmission system controlled by in-line nonlinear fiber loop switches is reported for what is believed to be the first time. The system is based on a strong dispersion map with large amplifier spacing. Operation at transmission rates of 10 and 40 Gbits/s is demonstrated. ©2004 Optical Society of America.

Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.

Fabrication and characterisation of 45º and Ex 45º:tilted fibre gratings and their applications in fibre lasers and sensors

In this thesis, I present the studies on fabrication, spectral and polarisation characterisation of fibre gratings with tilted structures at 45º and > 45º (namely 45º- TFGs and ex 45º-TFGs throughout this thesis) and a range of novel applications with these two types of grating. One of the major contributions made in this thesis is the systematic investigation of the grating structures, inscription analysis and spectral and polarisation properties of both types of TFGs. I have inscribed 45º-TFGs in standard telecom and polarisation maintaining (PM) fibres. Two wavelength regions of interest have been explored including 1.55 µm and 1.06 µm. Detailed analysis on fabrication and characterisation of 45º-TFGs on PM fibres have also been carried out for the first time. For ex 45º- TFGs, fabrication has been investigated only on low-cost standard telecom fibre. Furthermore, thermal responses have been measured and analysed showing that both types of TFG have low responsivity to temperature change. More importantly, their refractive index (RI) responses have been characterised to verify the high responsivity to surrounding medium. Based on the unique polarisation properties, both types of TFG have been applied in fibre laser systems to improve the laser performance, which forms another major contribution of the research presented in this thesis. The integration of a 45º-TFG to the Erbium doped fibre laser (EDFL) enables single polarisation laser output at a single wavelength. When combing with ex 45º-TFGs, the EDFL can be transformed to a multi-wavelength switchable laser with single polarisation output. Furthermore, by utilising the polarisation property of the TFGs, a 45º-TFG based mode locked fibre laser is implemented. This laser can produce laser pulses at femtosecond scale and is the first application of TFG in the field of nonlinear optics. Another important contribution from the studies is the development of TFG based passive and active optical sensor systems. An ex 45º-TFG has been successfully developed into a liquid level sensor showing high sensitivity to water based solvents. Strain and twist sensors have been demonstrated via a fibre laser system using both 45°- and ex 45º-TFG with capability identifying not just the twist rate but also the direction. The sensor systems have shown the added advantage of low cost signal demodulation. In addition, load sensor applications have been demonstrated using the 45º-TFG based single polarisation EDFL and the experimental results show good agreement with the theoretical simulation.

Span design for reduced noise and nonlinear impairments in a dispersion-managed Raman amplified system

We study a periodic Raman amplified dispersion-managed system with backward-pumping configuration, considering noise and nonlinear impairments. A general optimization method based on nonlinearity management is applied in order to find the configuration that maximizes the system performance. The system is later tested using a full numerical implementation of the nonlinear Schrödinger equation and shown to effectively deliver its longest propagation distance in the same optimal region.

Impact of the fiber type and nonlinear management over the performance of a 16x40 Gb/s DWDM transmission system

We examine impact of the fiber type and nonlinear management over the performance of a 16x40Gb/s DWDM NRZ transmission system. The line is constituted of 3x100km of G.652 or G.655 fiber with hybrid Raman-EDFA amplification.

Self-Learning Fuzzy Spiking Neural Network as a Nonlinear Pulse-Position Threshold Detection Dynamic System Based on Second-Order Critically Damped Response Units

Architecture and learning algorithm of self-learning spiking neural network in fuzzy clustering task are outlined. Fuzzy receptive neurons for pulse-position transformation of input data are considered. It is proposed to treat a spiking neural network in terms of classical automatic control theory apparatus based on the Laplace transform. It is shown that synapse functioning can be easily modeled by a second order damped response unit. Spiking neuron soma is presented as a threshold detection unit. Thus, the proposed fuzzy spiking neural network is an analog-digital nonlinear pulse-position dynamic system. It is demonstrated how fuzzy probabilistic and possibilistic clustering approaches can be implemented on the base of the presented spiking neural network.

Stability and Instability of Solitary Wave Solutions of a Nonlinear Dispersive System of Benjamin-Bona-Mahony Type

2000 Mathematics Subject Classification: 35B35, 35B40, 35Q35, 76B25, 76E30.

Complete Integrability of a Nonlinear Elliptic System, Generating Bi-umbilical Foliated Semi-symmetric Hypersurfaces in R^4

Николай Кутев, Величка Милушева - Намираме експлицитно всичките би-омбилични фолирани полусиметрични повърхнини в четиримерното евклидово пространство R^4

Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

2000 Mathematics Subject Classification: 35K55, 35K60.

Nonlinear limit of alternative method to 2 × 2 MIMO for LTE RoF system

Owing to the limited cell size of eNodeB (eNB), the relay node has emerged as an attractive solution for the long-term evolution (LTE) system. The nonlinear limit of the alternative method to multipleinput and multiple-output (MIMO) based on frequency division multiplexing (FDM) for orthogonal FDM (OFDM) is analysed over varying transmission spans. In this reported work, it is shown that the degradation pattern over the linear, intermixing and nonlinear propagation regions is consistent for the 2 and the 2.6 GHz bands. The proposed bands experienced a linear increase in the error vector magnitude (EVM) for both the linear and the nonlinear regions proportional to the increasing transmission spans. In addition, an optical launch power between -2 and 2 dBm achieved a significantly lower EVM than the LTE limit of 8% for the 10-60 km spans. © The Institution of Engineering and Technology 2014.

Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^