Development and Evaluation of Blind Identification Techniques for Nonlinear Systems

Identification and Control of Non‐linear dynamical systems are challenging problems to the control engineers.The topic is equally relevant in communication,weather prediction ,bio medical systems and even in social systems,where nonlinearity is an integral part of the system behavior.Most of the real world systems are nonlinear in nature and wide applications are there for nonlinear system identification/modeling.The basic approach in analyzing the nonlinear systems is to build a model from known behavior manifest in the form of system output.The problem of modeling boils down to computing a suitably parameterized model,representing the process.The parameters of the model are adjusted to optimize a performanace function,based on error between the given process output and identified process/model output.While the linear system identification is well established with many classical approaches,most of those methods cannot be directly applied for nonlinear system identification.The problem becomes more complex if the system is completely unknown but only the output time series is available.Blind recognition problem is the direct consequence of such a situation.The thesis concentrates on such problems.Capability of Artificial Neural Networks to approximate many nonlinear input-output maps makes it predominantly suitable for building a function for the identification of nonlinear systems,where only the time series is available.The literature is rich with a variety of algorithms to train the Neural Network model.A comprehensive study of the computation of the model parameters,using the different algorithms and the comparison among them to choose the best technique is still a demanding requirement from practical system designers,which is not available in a concise form in the literature.The thesis is thus an attempt to develop and evaluate some of the well known algorithms and propose some new techniques,in the context of Blind recognition of nonlinear systems.It also attempts to establish the relative merits and demerits of the different approaches.comprehensiveness is achieved in utilizing the benefits of well known evaluation techniques from statistics. The study concludes by providing the results of implementation of the currently available and modified versions and newly introduced techniques for nonlinear blind system modeling followed by a comparison of their performance.It is expected that,such comprehensive study and the comparison process can be of great relevance in many fields including chemical,electrical,biological,financial and weather data analysis.Further the results reported would be of immense help for practical system designers and analysts in selecting the most appropriate method based on the goodness of the model for the particular context.

Nonlinear Optical Properties of Organic and Polymer Systems

Present thesis has discussed the design and synthesis of polymers suitable for nonlinear optics. Most of the molecules that were studied have shown good nonlinear optical activity. The second order nonlinear optical activity of the polymers was measured experimentally by Kurtz and Perry powder technique. The thesis comprises of eight chapters.The theory of NLO phenomenon and a review about the various nonlinear optical polymers has been discussed in chapter 1. The review has provided a survey of NLO active polymeric materials with a general introduction, which included the principles and the origin of nonlinear optics, and has given emphasis to polymeric materials for nonlinear optics, including guest-host systems, side chain polymers, main chain polymers, crosslinked polymers, chiral polymers etc.Chapter 2 has discussed the stability of the metal incorporated tetrapyrrole molecules, porphyrin, chlorin and bacteriochlorin.Chapter 3 has provided the NLO properties of certain organic molecules by computational tools. The chapter is divided into four parts. The first part has described the nonlinear optical properties of chromophore (D-n-A) and bichromophore (D-n-A-A-n-D) systems, which were separated by methylene spacer, by making use of DPT and semiempirical calculations.Chapter 4: A series of polyurethanes was prepared from cardanol, a renewable resource and a waste of the cashew industry by previously designed bifunctional and multifunctional polymers using quantum theoretical approach.Chapter 5: A series of chiral polyurethanes with main chain bis azo diol groups in the polymer backbone was designed and NLO activity was predicted by ZlNDO/ CV methods.In Chapter 7, polyurethanes were first designed by computational methods and the NLO properties were predicted by correction vector method. The designed bifunctional and multifunctional polyurethanes were synthesized by varying the chiral-achiral diol compositions

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.

Laser induced thermal lens and near infrared absorption studies of ch overtones in some organic compounds

Vibrational overtone spectroscopy of X-H (X=C,N,O) containing molecules is an area of recent interest. The spectroscopic studies of higher vibrational levels yield valuable informations, regarding,the molecular structure, intra- and inter-molecular interactions, radiationless transitions, intra-molecular vibrational relaxations, multiphoton excitations and chemical reactivities, which cannot be z obtained by other spectroscopic methods. This thesis presents the results of experimental investigations on the overtone spectra of some organic compounds in the liquid phase for the characterization of CH bonds. The spectra in the fifth overtone region (1fiV=6) are recorded using a dual beam thermal lens setup and the lower overtones (.AV=2-5) are recorded spectrophotometrically.The thesis is presented in six chapters.

Studies on some nonlinear schrodinger type equations describing pulse propagation through optical fibers

The discovery of the soliton is considered to be one of the most significant events of the twentieth century. The term soliton refers to special kinds of waves that can propagate undistorted over long distances and remain unaffected even after collision with each other. Solitons have been studied extensively in many fields of physics. In the context of optical fibers, solitons are not only of fundamental interest but also have potential applications in the field of optical fiber communications. This thesis is devoted to the theoretical study of soliton pulse propagation through single mode optical fibers.

Studies on some aspects of wave propagation through nonlinear media

Nonlinearity is a charming element of nature and Nonlinear Science has now become one of the most important tools for the fundamental understanding of the nature. Solitons— solutions of a class of nonlinear partial differential equations — which propagate without spreading and having particle— like properties represent one of the most striking aspects of nonlinear phenomena. The study of wave propagation through nonlinear media has wide applications in different branches of physics.Different mathematical techniques have been introduced to study nonlinear systems. The thesis deals with the study of some of the aspects of electromagnetic wave propagation through nonlinear media, viz, plasma and ferromagnets, using reductive perturbation method. The thesis contains 6 chapters

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Microwave absorption and magnetization tunneling in Mn12-acetate molecular clusters

In this paper we study the effect of microwave absorption on the quantum relaxation rate of Mn12 molecular clusters. We have determined first the resonant frequencies of a microwave resonator containing a single crystal of Mn12-Acetate and measured initial isothermal magnetization curves while microwave power was put into the resonator. We have found that the tunneling rate changes one order of magnitude for certain frequencies. This suggests that the microwave shaking of the nuclear spin and molecular vibrational degrees of freedom is responsible for the huge increasing of the tunneling rate.

Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer

Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a beam, splitting in two "beams," single or double traces with suppressed reflection or transmission, etc.

Investigations on some amino acid based single crystals for nonlinear optical applications and amino acid capped nanocrystals

Organic crystals possess extremely large optical nonlinearity compared to inorganic crystals. Also organic compounds have the amenability for synthesis and scope for introducing desirable characteristics by inclusions. A wide variety of organic materials having electron donor and acceptor groups, generate high order of nonlinearity. In the present work, a new nonlinear optical crystal, L-citrulline oxalate (LCO) based on the aminoacid L-citrulline was grown using slow evaporation technique. Structural characterization was carried out by single crystal XRD. It crystallizes in the noncentrosymmetric, orthorhombic structure with space group P21 P21 P21. Functional groups present in the sample were identified by Fourier transform infra red (FTIR) and FT-Raman spectral analysis. On studying the FTIR and Raman spectra of the precursors L-citrulline and oxalic acid, used for growing L-citrulline oxalate crystal, it is found that the significant peaks of the precursors are present in the spectra of the L-citrulline oxalate crystal . This observation along with the presence of NH3 + group in the spectra of L-citrulline oxalate, confirms the formation of the charge transfer complex

Synthesis and characterization of Tellurium oxide glasses for photonic applications

Tellurite glasses are photonic materials of special interest to the branch of optoelectronic and communication, due to its important optical properties such as high refractive index, broad IR transmittance, low phonon energy etc. Tellurite glasses are solutions to the search of potential candidates for nonlinear optical devices. Low phonon energy makes it an efficient host for dopant ions like rare earths, allowing a better environment for radiative transitions. The dopant ions maintain majority of their individual properties in the glass matrix. Tellurites are less toxic than chalcogenides, more chemically and thermally stable which makes them a highly suitable fiber material for nonlinear applications in the midinfrared and they are of increased research interest in applications like laser, amplifier, sensor etc. Low melting point and glass transition temperature helps tellurite glass preparation easier than other glass families. In order to probe into the versatility of tellurite glasses in optoelectronic industry; we have synthesized and undertaken various optical studies on tellurite glasses. We have proved that the highly nonlinear tellurite glasses are suitable candidates in optical limiting, with comparatively lower optical limiting threshold. Tuning the optical properties of glasses is an important factor in the optoelectronic research. We have found that thermal poling is an efficient mechanism in tuning the optical properties of these materials. Another important nonlinear phenomenon found in zinc tellurite glasses is their ability to switch from reverse saturable absorption to saturable absorption in the presence of lanthanide ions. The proposed thesis to be submitted will have seven chapters

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

Paper industry in Kerala: An evaluation of labour absorption,capacity utilisation, and environmental pollution

Paper industry is one of the oldest and largest industries in Kerala. Despite the developments in the industry in terms of growth in output , value added and employment generation, many of the units face grave problems. Irrespective of the size of the plant, the problems of the industry are general in nature. The problems are galore in the supply, not the demand side. Amomg the problems, the important ones are: raw material scarcity, energy deficiency and obsolete technology. Further, the industry is subject to many controls by the Government — price control, product control and raw materials control — which result in the dwindling of profits and investments. Equally important are the reservations against the industry for polluting the environment byeffluent disposal on the one hand and affecting ecological balance by depleting the existing forest on the other. Apart from the large, medium and small pulp and paper mills, there are about 30 hand made paper units in Kerala which can be categorised as village and cottage industry. Almost all of these units began at the initiative and support of Khadi and Village Industries Commission. The primary purpose of these units is employment generation, and not profit making. Currently many of these units are in the red and many others are on the verge of closure. Therefore, a separate analysis of the growth performance, and problems and prospects of the hand made paper industry has also been attempted. It is analysed separately because of the very small size of the hand made paper units