Tesi sul tema "Nonlinear systems"
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1
Kozinsky, Inna Roukes Michael Lee Roukes Michael Lee. "Nonlinear nanoelectromechanical systems /". Diss., Pasadena, Calif. : California Institute of Technology, 2007. http://resolver.caltech.edu/CaltechETD:etd-03022007-142824.
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2
Sun, Hongyan. "Coupled nonlinear dynamical systems". Morgantown, W. Va. : [West Virginia University Libraries], 2000. http://etd.wvu.edu/templates/showETD.cfm?recnum=1636.
Testo completoAbstract (sommario):
Thesis (Ph. D.)--West Virginia University, 2000.Title from document title page. Document formatted into pages; contains xi, 113 p. : ill. (some col.). Includes abstract. Includes bibliographical references.
3
Wei, Jianfeng. "Observation and Estimation of Nonlinear Systems". Case Western Reserve University School of Graduate Studies / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=case1143611470.
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4
Nersesov, Sergey G. "Nonlinear Impulsive and Hybrid Dynamical Systems". Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7147.
Testo completoAbstract (sommario):
Modern complex dynamical systems typically possess a
multiechelon hierarchical hybrid structure characterized by
continuous-time dynamics at the lower-level units and logical
decision-making units at the higher-level of hierarchy. Hybrid
dynamical systems involve an interacting countable collection of
dynamical systems defined on subregions of the partitioned state
space. Thus, in addition to traditional control systems, hybrid
control systems involve supervising controllers which serve to
coordinate the (sometimes competing) actions of the lower-level
controllers. A subclass of hybrid dynamical systems are impulsive
dynamical systems which consist of three elements, namely, a
continuous-time differential equation, a difference equation, and
a criterion for determining when the states of the system are to
be reset. One of the main topics of this dissertation is the
development of stability analysis and control design for impulsive
dynamical systems. Specifically, we generalize Poincare's
theorem to dynamical systems possessing left-continuous flows to
address the stability of limit cycles and periodic orbits of
left-continuous, hybrid, and impulsive dynamical systems. For
nonlinear impulsive dynamical systems, we present partial
stability results, that is, stability with respect to part of the
system's state. Furthermore, we develop adaptive control framework
for general class of impulsive systems as well as energy-based
control framework for hybrid port-controlled Hamiltonian systems.
Extensions of stability theory for impulsive dynamical systems
with respect to the nonnegative orthant of the state space are
also addressed in this dissertation. Furthermore, we design
optimal output feedback controllers for set-point regulation of
linear nonnegative dynamical systems. Another main topic that has
been addressed in this research is the stability analysis of
large-scale dynamical systems. Specifically, we extend the theory
of vector Lyapunov functions by constructing a generalized
comparison system whose vector field can be a function of the
comparison system states as well as the nonlinear dynamical system
states. Furthermore, we present a generalized convergence result
which, in the case of a scalar comparison system, specializes to
the classical Krasovskii-LaSalle invariant set theorem. Moreover,
we develop vector dissipativity theory for large-scale dynamical
systems based on vector storage functions and vector supply rates.
Finally, using a large-scale dynamical systems perspective, we
develop a system-theoretic foundation for thermodynamics.
Specifically, using compartmental dynamical system energy flow
models, we place the universal energy conservation, energy
equipartition, temperature equipartition, and entropy
nonconservation laws of thermodynamics on a system-theoretic
basis.
5
Enqvist, Martin. "Linear Models of Nonlinear Systems". Doctoral thesis, Linköping : Linköpings universitet, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5330.
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6
Mathew, Manu K. "Nonlinear system identification and prediction /". Online version of thesis, 1993. http://hdl.handle.net/1850/11594.
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7
Chow, Po-Chuan. "Recursive nonlinear identification of Hammerstein-type systems". Case Western Reserve University School of Graduate Studies / OhioLINK, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=case1054758543.
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8
Nevistić, Vesna. "Constrained control of nonlinear systems". Online version, 1997. http://bibpurl.oclc.org/web/26200.
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9
Senalp, Erdem Turker. "Cascade Modeling Of Nonlinear Systems". Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/3/12608578/index.pdf.
Testo completoAbstract (sommario):
Modeling of nonlinear systems based on special Hammerstein forms has been considered. In Hammerstein system modeling a static nonlinearity is connected to a dynamic linearity in cascade form.
Fundamental contributions of this work are: 1) Introduction of Bezier curve nonlinearity representations2) Introduction of B-Spline curve nonlinearity representations instead of polynomials in cascade modeling. As a result, local control in nonlinear system modeling is achieved. Thus, unexpected variations of the output can be modeled more closely. As an important demonstration case, a model is developed and named as Middle East Technical University Neural Networks and Cascade Model (METU-NN-C). Application examples are chosen by considering the Near-Earth space processes, which are important for navigation, telecommunication and many other technical applications. It is demonstrated that the models developed based on the contributions of this work are especially more accurate under disturbed conditions, which are quantified by considering Space Weather parameters. Examples include forecasting of Total Electron Content (TEC), and mapping
estimation of joint angle of simple forced pendulum
estimation of joint angles of spring loaded inverted double pendulum with forced table
identification of Van der Pol oscillator
and identification of speakers. The operation performance results of the International Reference Ionosphere (IRI-2001), METU Neural Networks (METU-NN) and METU-NN-C models are compared qualitatively and quantitatively. As a numerical example, in forecasting the TEC by using the METU-NN-C having Bezier curves in nonlinearity representation, the average absolute error is 1.11 TECu. The new cascade models are shown to be promising for system designers and operators.
10
Tsukamoto, Naofumi. "Phase dynamics in nonlinear systems". 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/136010.
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11
Tse, Wilfred See Foon. "Linear equivalents of nonlinear systems". Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26652.
Testo completoAbstract (sommario):
Consider the following nonlinear system
[Formula Omitted]
where ϰ ∈ Rⁿ, f, ℊ₁,…,ℊｍ are C∞ function in Rⁿ and ℎ is a C∞ function in R⍴, all defined on a neighborhood of 0. The problem of finding a necessary and sufficient condition such that system (1) can be transformed to a linear controllable system by a state coordinate change and feedback has been studied
quite well. In this thesis, we first discuss a few different approaches to this problem and eventually we will show that the slightly different versions of the necessary and sufficient condition discovered are equivalent. Next we consider
system (1) with all սi,= 0 together with system (2), and study the dual problem of transforming it to a linear observable system by a state and output coordinate change. Finally, we consider briefly system (l) and (2) with nonzero սi and study the problem of transforming it to a linear system that is both completely controllable and observable. Examples are given and applications to local stabilization and estimation are discussed.Science, Faculty of
Mathematics, Department of
Graduate
12
Tatlicioglu, Enver. "Control of nonlinear mechatronic systems". Connect to this title online, 2007. http://etd.lib.clemson.edu/documents/1193079994/.
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13
Dall, Ian W. "Signals in nonlinear bandpass systems /". Title page, abstract and contents only, 1991. http://web4.library.adelaide.edu.au/theses/09PH/09phd1444.pdf.
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14
Grönberg, Fredrik. "Crowd Control of Nonlinear Systems". Thesis, KTH, Reglerteknik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-138438.
Testo completoAbstract (sommario):
We study a multi-agent system in R2 where agents have unicycle dynamics with time varying speed and control inputs corresponding to acceleration and angular velocity. The system has a dynamic communication topology based on proximity. We propose a novel decentralized control algorithm derived from a double integrator model using a pairwise potential function. By using an energy function we show that a leaderless system converges to a set where connected agents have equal direction and velocity and potential contributions to the control action cancel each other out. The concept of formation density is defined and studied by numerical simulation. We find a relation between parameters of the controller and the system that makes the system converge to a formation with low density, corresponding to agents being at appropriate distances from each other, also when agents are not restricted to communicating only with their closest neighbors. The algorithm is tested for a system with leaders and properties of this system are investigated numerically. The results confirm that the proportion of leaders needed to guide a certain proportion of the agent in average is nonlinear and decreasing with respect to the number of agents.
15
Pointon, Craig T. "Nonlinear dynamics in telecommunication systems". Thesis, Staffordshire University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282553.
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Xu, Xu. "Nonlinear systems and cellular maps". Thesis, University of Sheffield, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.538077.
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Skrobic, Stevan. "Harmonic Suppression in Nonlinear Systems". Thesis, KTH, Tillämpad fysik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-170394.
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Batchelor, Andrew. "Modelling of interconnected nonlinear systems". Thesis, University of Newcastle Upon Tyne, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.413386.
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Samavat, Mohmoud. "Robust control of nonlinear systems". Thesis, University of Sheffield, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327647.
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May, Andrew. "Nonlinear systems in applied mathematics". Thesis, University of Exeter, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312068.
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Jang, Stella 1976. "Nonlinear stability of multibody systems". Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/82778.
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Lu, Weiping. "Nonlinear dynamics of optical systems". Thesis, Heriot-Watt University, 1991. http://hdl.handle.net/10399/836.
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23
Sayyaddelshad, Saleh. "State estimation of nonlinear systems". Licentiate thesis, Luleå tekniska universitet, Signaler och system, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25774.
Testo completoAbstract (sommario):
Observer design for nonlinear systems is a popular problem in control theory that has beenstudied from many angles. Since the system state variables, in general, are not available, stateestimation is essential in many control applications, which is why the problem is so attractivefor researchers. One example of a process that has nonlinear dynamics is wood drying.In the wood drying process, there are some unmeasurable variables such as the moisturecontent at the surface and inside the wood, which are important for controlling the drying processfor the purpose of minimizing the energy consumption of the wood drying kiln. However,to the best of our knowledge, there is no straightforward observer design for the wood-dryingprocess in the current literature. In the first two research papers that compose this thesis, afterintroducing a state space realization of the wood drying process, a novel method for estimatingthe moisture content of the wood during drying is proposed.Compared to typical systems, observer design for nonlinear uncertain systems with timedelays, is significantly more complicated and thus attractive for research. In this thesis, theproblem of the observer design for a class of uncertain discrete-time nonlinear systems withunknown time delay has also been investigated. The study shows that by using upper and lowerbounds of the time delay, the time delay can be excluded in the observer structure. The thirdand fourth papers mostly focus on this topic based on an optimization approach.Godkänd; 2013; 20131026 (salsay); Tillkännagivande licentiatseminarium 2013-11-25 Nedanstående person kommer att hålla licentiatseminarium för avläggande av teknologie licentiatexamen. Namn: Saleh Sayyaddelshad Ämne: Reglerteknik/Automatic Control Uppsats: State Estimation of Nonlinear Systems Examinator: Professor Thomas Gustafsson, Institutionen för system- och rymdteknik, Luleå tekniska universitet Diskutant: Professor Alexander Medvedev, Avdelningen för systemteknik, Uppsala universitet Tid: Onsdag den 18 december 2013 kl 13.00 Plats: A1545, Luleå tekniska universitet
24
Nayfeh, Mahir Ali. "Nonlinear dynamics in power systems". Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41582.
Testo completoAbstract (sommario):
We use a perturbation analysis to predict some of the instabilities in a single-machine quasi-infinite busbar system. The system’s behavior is described by the so-called swing equation, which is a nonlinear second-order ordinary-differential equation with additive and multiplicative harmonic terms having the frequency Ω. When Ω≈ω₀, and Ω≈2ω₀, where ω₀ is the linear natural frequency of the machine, we use digital-computer simulations to exhibit some of the complicated responses of the machine, including period-doubling bifurcations, chaotic motions, and unbounded motions (loss of synchronism). To predict the onset of these complicated behaviors, we use the method of multiple scales to develop approximate closed-form expressions for the periodic responses of the machine. Then, we use various techniques to determine the stability of the analytical solutions. The analytically predicted periodic solutions and conditions for their instability are in good agreement with the digital-computer results.Master of Science
25
Krauss, Ryan. "Experimental Identification of Nonlinear Systems". Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36912.
Testo completoAbstract (sommario):
A procedure is presented for using a primary resonance excitation in
experimentally identifying the nonlinear parameters of a model approximating the
response of a cantilevered beam by a single mode. The model accounts for cubic
inertia and stiffness nonlinearities and quadratic damping. The method of
multiple scales is used to determine the frequency-response function for the
system. Experimental frequency- and amplitude-sweep data are compared with the
prediction of the frequency-response function in a least-squares curve-fitting
algorithm. The algorithm is improved by making use of experimentally known
information about the location of the bifurcation points. The method is
validated by using the parameters extracted to predict the force-response curves
at other nearby frequencies.
We then compare this technique with two other techniques that have been presented in the literature. In addition to the amplitude- and frequency-sweep technique presented, we apply a second frequency-domain technique and a time-domain technique to the second mode of a cantilevered beam. We apply the restoring-force surface method assuming no a priori knowledge of the system and use the shape of the surface to guide us in assuming a form for the equation of motion. This equation is used in applying the frequency-domain techniques: a backbone curve-fitting technique based on the describing-function method and the amplitude- and frequency-sweep technique based on the method of multiple scales. We derive the equation of motion from a Lagrangian and discover that the form assumed based on the restoring-force surface is incorrect. All of the methods are reapplied with the new form for the equation of motion. Differences in the parameter estimates are discussed. We conclude by discussing the limitations encountered for each technique. These include the inability to separate the nonlinear curvature and inertia effects and problems in estimating the coefficients of small terms with the time-domain technique.
Master of Science
26
Hill, Thomas Lewis. "Modal interactions in nonlinear systems". Thesis, University of Bristol, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.702150.
Testo completoAbstract (sommario):
As engineering structures become increasingly lightweight and flexible, their nonlinear dynamic behaviour becomes increasingly significant; however, such behaviour presents a number of challenges. For example, nonlinear system identification is often restricted to relatively simple structures, or to methods that provide limited physical insight, whilst features such as bifurcations and multiple solutions present numerous challenges for modelling and experimental testing. The aim of this thesis is to further the theoretical understanding of the behaviour of systems with smooth nonlinear characteristics, and provide practical insight into the significance of such behaviour. An analytical approach is employed throughout, providing an understanding of the relationship between the physical characteristics of a system, and the behaviour it exhibits. Backbone curve analysis is also utilised, which considers the equivalent unforced and undamped system to provide an interpretation of the underlying nonlinear dynamic behaviour. A number of novel behaviours are identified in a conceptually simple, two-mass oscillator, including out-of-unison and phase-varying backbone curves, the former of which is shown to be equivalent whirling motion in a cable. An analytical, energy-based technique is then introduced as a method for formulating a link between backbone curves and resonant forced responses. This is first demonstrated using a two-mass oscillator, before being applied to a nonlinear beam where it is used to predict the existence of an isola in the forced response. The concept of a general periodic motion in an undamped nonlinear system is then considered, and it is shown that two classes of backbone curve may exist: one where locking exists between the fundamental components of the motion, and one where only the harmonics exhibit locking. The mechanism behind locking is described via an extension of the aforementioned energy approach, and this is used to explain why motions that are locked in the harmonics are seldom observed. The theoretical understanding gained in this thesis is then used to develop a practical framework for nonlinear system identification, which draws upon the advantages of both the analytical method and the backbone curve analysis. Furthermore, the energy based approaches developed throughout are used to understand the limitations of the proposed identification framework, and provide insight into how these limitations may be overcome.
27
Pepona, Eleni. "Identification of nonlinear interconnected systems". Thesis, Brunel University, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.540757.
Testo completoAbstract (sommario):
In this work we address the problem of identifying a discrete-time nonlinear system composed of a linear dynamical system connected to a static nonlinear component. We use linear fractional representation to provide a united framework for the identification of two classes of such systems. The first class consists of discrete-time systems consists of a linear time invariant system connected to a continuous nonlinear static component. The identification problem of estimating the unknown parameters of the linear system and simultaneously fitting a math order spline to the nonlinear data is addressed. A simple and tractable algorithm based on the separable least squares method is proposed for estimating the parameters of the linear and the nonlinear components. We also provide a sufficient condition on data for consistency of the identification algorithm. Numerical examples illustrate the performance of the algorithm. Further, we examine a second class of systems that may involve a nonlinear static element of a more complex structure. The nonlinearity may not be continuous and is approximated by piecewise a±ne maps defined on different convex polyhedra, which are defined by linear combinations of lagged inputs and outputs. An iterative identification procedure is proposed, which alternates the estimation of the linear and the nonlinear subsystems. Standard identification techniques are applied to the linear subsystem, whereas recently developed piecewise affine system identification techniques are employed for the estimation of the nonlinear component. Numerical examples show that the proposed procedure is able to successfully profit from the knowledge of the interconnection structure, in comparison with a direct black box identification of the piecewise a±ne system.
28
Lohmiller, Winfried Stefan 1971. "Contraction analysis of nonlinear systems". Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/9793.
Testo completoAbstract (sommario):
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.Includes bibliographical references (leaves 87-90).
This thesis derives new results in nonlinear system analysis using methods inspired from fluid mechanics and differential geometry. Based on a differential analysis of convergence, these results may be viewed as generalizing the classical Krasovskii theorem, as well as linear eigenvalue analysis. A central feature is that convergence and limit behavior are in a sense treated separately, leading to significant conceptual simplifications. We establish new combination properties of nonlinear dynamic systems and use them to derive simple controller and observer designs for mechanical systems such as aircraft, underwater vehicles, and robots. The method is also applied to chemical chain reactions and mixture processes. The relative simplicity of these designs stems from their effective exploitation of the systems' structural specificities. Next, we analyze and quantify the global stability properties of physical partial differential equations such as the heat equation, or the Schroedinger equation. Lyapunov exponents are not coordinate-invariant, and thus their exact physical meaning is somewhat questionable. As an alternative, we suggest an extension of linear eigenvalue analysis to nonlinear dynamic systems. Finally, the thesis derives new controller and observer designs for general nonlinear dynamic systems. In particular, an extension of feedback linearization is proposed when the corresponding integrability conditions are violated.
by Winfried Stefan Lohmiller.
Ph.D.
29
Chetwynd, Daley. "Uncertainty propagation in nonlinear systems". Thesis, University of Sheffield, 2005. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.425587.
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Ruzziconi, Laura. "Nonlinear dynamics in microelectromechanical systems". Doctoral thesis, Università Politecnica delle Marche, 2011. http://hdl.handle.net/11566/242133.
Testo completoAbstract (sommario):
La tesi affronta lo studio delle dinamiche nonlineari in alcuni dispositivi MEMS. Le tematiche di dinamica nonlineare attualmente affrontate in letteratura sono indispensabili per studiare la
loro risposta. L’accuratezza della modellazione dinamica nonlineare è importante per garantire l’affidabilità dei risultati e gli strumenti attuali di dinamica nonlineare riescono ad
interpretare scrupolosamente i dati sperimentali della risposta di questi dispositivi. La tesi considera due diversi casi-studio. Il primo caso-studio è un dispositivo MEMS con carico assiale, forma iniziale ad arco molto ribassato e attuazione elettrostatica ed elettrodinamica. È analizzato in un intorno della biforcazione da una singola ad una doppia buca di potenziale. Sia le configurazioni statiche nonlineari sia l’analisi dinamica lineare non possono essere risolte in forma chiusa e sono
approssimate con il metodo di Galerkin. Vengono usate per costruire un accurato modello ridotto delle dinamiche nonlineari ad un solo grado di libertà. In questo modello il termine del quinto ordine (che dipende dall’espansione in serie di Taylor nell’equazione del moto) è eliminato per avere una buona approssimazione delle buche di potenziale e del comportamento globale. Altri modelli ridotti sono considerati e paragonati. Si esegue l’analisi
dinamica nonlineare, con l’uso combinato di curve di risposta in frequenza, ritratti di fase attrattori-bacini e mappe di comportamento. In un intorno di ciascuna frequenza naturale, la risposta del dispositivo presenta le tipiche caratteristiche di un oscillatore softening. I casi di singola e doppia buca di potenziale vengono paragonati.
Il secondo caso-studio analizza i dati sperimentali di pull-in dinamico in risonanza primaria di
un dispositivo MEMS (un accelerometro capacitivo). Iniziando da questo caso particolare, si affronta la tematica dell’integrità dinamica in un sistema meccanico. Viene eseguito il suo
calcolo qualitativo, scegliendo gli strumenti più appropriati in base alle condizioni sperimentali considerate. Si evidenzia l’efficacia di questa analisi, mostrando l’accuratezza delle curve di percentuale costante di fattore di integrità nell’interpretare l’esistenza di
disturbi negli esperimenti e nella pratica. Inoltre, si mostra il loro utilizzo nella progettazione.This dissertation deals with the nonlinear dynamics in MEMS devices. The nonlinear dynamic topics currently addressed in the literature are essential to investigate their response. The accuracy of the nonlinear dynamic modeling is important to guarantee the reliability of the results and current nonlinear dynamic tools succeed in carefully interpreting the experimental data of the response of these devices. The dissertation considers two different case-studies. The first case-study is a MEMS device with axial load, very shallow arched initial shape and electrostatic and electrodynamic actuation. It is analyzed in the neighborhood of the bifurcation from a single potential well to a twin well. Both the nonlinear static configurations and the linear dynamic analysis cannot be solved in closed form and they are approximated by the Galerkin technique. They are used to derive an accurate single degree of freedom reduced order model of the nonlinear dynamics. In this model the fifth order term (connected to the Taylor expansion in the equation of motion) is removed to obtain a good approximation of the potential wells and of the global behavior. Other reduced order models are considered and compared. The nonlinear dynamic analysis is performed, with the combined use of frequency response curves, attractor-basins phase portraits and behavior charts. In a neighborhood of each natural frequency, the response of the device has the typical characteristics of a softening oscillator. The cases of the single and the double potential well are compared. The second case-study analyzes the experimental dynamic pull-in data at primary resonance for a MEMS device (a capacitive accelerometer). Starting from this particular case, the issue of the dynamical integrity in a mechanical system is addressed. Its qualitative evaluation is performed, choosing the most suitable tools according to the considered experimental conditions. The effectiveness of this analysis is highlighted, showing the accuracy of the curves of constant percentage of integrity factor in interpreting the existence of disturbances in experiments and practice. Also, their use in a design is proposed.
31
Lei, Hao. "Universal Output Feedback Control of Nonlinear Systems". Case Western Reserve University School of Graduate Studies / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=case1193422144.
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Brunke, Shelby Scott. "Nonlinear filtering and system identification algorithms for autonomous systems /". Thesis, Connect to this title online; UW restricted, 2001. http://hdl.handle.net/1773/7095.
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Mattsson, Per. "Modeling and identification of nonlinear and impulsive systems". Doctoral thesis, Uppsala universitet, Avdelningen för systemteknik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-304837.
Testo completoAbstract (sommario):
Mathematical modeling of dynamical systems plays a central roll in science and engineering. This thesis is concerned with the process of finding a mathematical model, and it is divided into two parts - one that concentrates on nonlinear system identification and another one where an impulsive model of testosterone regulation is constructed and analyzed. In the first part of the thesis, a new latent variable framework for identification of a large class of nonlinear models is developed. In this framework, we begin by modeling the errors of a nominal predictor using a flexible stochastic model. The error statistics and the nominal predictor are then identified using the maximum likelihood principle. The resulting optimization problem is tackled using a majorization-minimization approach, resulting in a tuning parameter-free recursive identification method. The proposed method learns parsimonious predictive models. Many popular model structures can be expressed within the framework, and in the thesis it is applied to piecewise ARX models. In the first part, we also derive a recursive prediction error method based on the Hammerstein model structure. The convergence properties of the method are analyzed by application of the associated differential equation method, and conditions ensuring convergence are given. In the second part of the thesis, a previously proposed pulse-modulated feedback model of testosterone regulation is extended with infinite-dimensional dynamics, in order to better explain testosterone profiles observed in clinical data. It is then shown how the analysis of oscillating solutions for the finite-dimensional case can be extended to the infinte-dimensional case. A method for blind state estimation in impulsive systems is introduced, with the purpose estimating hormone concentrations that cannot be measured in a non-invasive way. The unknown parameters in the model are identified from clinical data and, finally, a method of incorporating exogenous signals portraying e.g. medical interventions is studied.
34
Kozak, Kristopher C. "Robust command generations for nonlinear systems". Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/15849.
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Sotero, De Menezes Thiago Diniz. "Nonlinear Compensation in Optical Communications Systems using the Nonlinear Fourier Transform". Diss., North Dakota State University, 2017. https://hdl.handle.net/10365/27607.
Testo completoAbstract (sommario):
Nonlinear effects in optical fibers impose a capacity limit for optical communication systems. In this dissertation, the nonlinear Fourier transform (NFT) is investigated as a method to mitigate and compensate for those effects. This study consists of two parts: first a computational complexity analysis for the use of the NFT for nonlinear compensation in the normal dispersion regime, and second, an analysis of the robustness of the performance of the discrete spectrum modulation in the anomalous dispersion regime using the NFT. The first part investigates the computational complexity of the NFT based on the Zakharov-Shabat scattering problem as a nonlinear compensation technique for quadrature-phase-shift keyed (QPSK) signals with raised cosine frequency characteristic in optical fiber transmission systems with normal dispersion fibers. Results show that there are two primary sources of computational errors that arise from the use of the NFT: The computational error due to the finite eigenvalue resolution of the reflection spectra and the computational error due to the Born approximation used in the inverse NFT. In this scenario, computational costs become unacceptably large at data frame lengths and powers that are too small for this approach to be competitive with standard transmission methods. The second part investigates the robustness of a recently proposed nonlinear frequency-division multiplexing (NFDM) system comprised of two independent QPSK channels modulated in the discrete spectrum associated with two distinct eigenvalues. Among the many fiber impairments that may limit this system, we focus on determining the limits given by third-order dispersion, the Raman effect, amplified spontaneous emission (ASE) noise from erbium-doped fiber amplifiers (EDFAs), and lumped gain from EDFAs. Each of these impairments impact this system with discrete spectrum modulation and 1600 km of propagation distance in different ways: Third-order dispersion limits the maximum launch power to 13 dBm, the Raman effect limits the maximum launch power to 10.25 dBm, the ASE noise limits the maximum launch power to 9 dBm, while lumped gain limits the maximum launch power at 3.75 dBm. Additional studies are needed to investigate the effectiveness of the NFT for discrete spectrum modulation formats with three or more eigenvalues.
36
Arain, Muhammad Asif, Ayala Helon Vicente Hultmann e Muhammad Adil Ansari. "Nonlinear System Identification Using Neural Network". University of Genova (Italy) and Warsaw University of Technology (Poland), 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:oru:diva-28937.
Testo completoAbstract (sommario):
Magneto-rheological damper is a nonlinear system. In this case study, system has been identified using Neural Network tool. Optimization between number of neurons in the hidden layer and number of epochs has been achieved and discussed by using multilayer perceptron Neural Network.
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Strandberg, Mattias. "Portfolio Optimization with NonLinear Instruments". Thesis, Umeå universitet, Institutionen för fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-137233.
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Tang, Xiafei. "Periodic disturbance rejection of nonlinear systems". Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/periodic-disturbance-rejection-of-nonlinear-systems(0bddefd9-2750-47fd-8c92-c90a01b8e1ef).html.
Testo completoAbstract (sommario):
Disturbance rejection is an important topic in control design since disturbances are inevitable in practical systems. To realise this target for nonlinear systems, this thesis brings in an assumption about the existence of a controlled invariant mani- fold and a Desired Feedforward Control (DFC) which is contained in the input to compensate the influence of disturbances. According to the approximation property of Neural Networks (NN) that any periodic signals defined in a compact set can be approximated by NN, the NN-based disturbance approximator is applied to approximate the DFC. Algorithmically, two important types of NN approximators that are Multi-layer Neural Networks (MNN) and Radial Basis Function Neural Networks (RBFNN) are presented in detail.In this thesis, a variety of nonlinear systems in standard canonical form are looked into. These forms are the output feedback form, the extended output feedback form, the decentralised output feedback form and the partial state feedback form. For these systems, four types of uncertainties are mainly considered. The first one is the disturbance that can be eliminated by the DFC. Secondly, the parameter uncertainty is taken into account. To get rid of this uncertainty, the adaptive control technique is employed for the estimation of unknown parameters, e.g. the NN gain matrix. The third one is the nonlinear uncertainty. For the case that nonlinear uncertainties are polynomials, it has a bound consisting of an unknown constant and a function of the regulated error such that this uncertainty can be also treated as the parameter uncertainty. Delay is the last type of uncertainty. Particularly, the delay is supposed to appear in output only. This uncertainty can be eliminated together with the nonlinear uncertainty. To establish the closed- loop stability, a Lyapunov-Krasovskii function is invoked. In addition, due to the requirement of the system structure or the stability analysis, some general control techniques are also involved such like the backstepping control and the high gain control.Throughout the results are illustrated by simulations.
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Ghassem-Sani, Gholam-Reza. "Recursive nonlinear plans". Thesis, University of Essex, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315683.
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Du, Suguo. "Fault detection for polynomial nonlinear systems". Thesis, Coventry University, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.247208.
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Spelman, Graham Michael. "Energy scattering in weakly nonlinear systems". Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648253.
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Manzoni, Marco Tommaso. "New systems for quantum nonlinear optics". Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/461495.
Testo completoAbstract (sommario):
Photons travelling through free space do not interact with each other. This characteristic makes them perfect candidates to carry quantum information over long distances. On the other hand, processing the information they encode requires interaction mechanisms. In recent years, there have been growing efforts to realize strong, controlled interactions between photons by making them interact with individual atoms, which are intrinsically nonlinear objects. This, and the efforts to understand the phenomena that can emerge, have spawned the new field of`"quantum nonlinear optics."
A number of approaches have been pursued to attain near-deterministic atom-photon interactions, including the use of cavities (CQED), of atomic ensembles, and more recently of dielectric nanostructures able to confine light without defocusing, thus enabling the interaction with atoms trapped in the proximity of the structures. While for the CQED case powerful theoretical tools have been developed to treat the interactions of photons, in the case of atomic ensembles, either in free space or coupled to nanophotonic structures, there is a general lack of theoretical methods beyond the linear regime. This relative lack of understanding also implies that there could be rich new physical phenomena that have thus far not been identified. The overall goal of this thesis is to explore these themes in greater detail.
In Chapter 2 of this thesis we develop a new formalism to calculate the properties of quantum light when interfaced with atomic ensembles. The method consists of using a "spin model" that maps a quasi one-dimensional (1D) light propagation problem to the dynamics of an open 1D interacting spin system, where all of the photon correlations are obtained from those of the spins. The spin dynamics can be numerically solved using the toolbox of matrix product states (MPS), thus providing a technique to study strongly interacting photons in the true many-body limit.
In Chapter 3 we investigate the possibility of creating exotic phases of matter using the recently realized photonic crystal waveguide (PCW)-atoms interface. In particular, we examine the consequences that arise from the strong interatomic forces mediated by the exchange of band gap photons, whose strengths also depend strongly on the internal atomic states (¿spins¿). Taking one realistic model, we show that "quantum crystallization" can occur, in which the emergent spatial orders of atoms depend intricately on the spin correlations.
In Chapter 4 we investigate the possibility of implementing second-order nonlinear quantum optical processes with graphene nanostructures, as a more robust alternative to the use of atomic systems. We quantify the second-order nonlinear properties, showing that the tight confinement of surface plasmons (SP) in graphene gives rise to extraordinary interaction strengths at the single-photon level. Finally, we predict that opportunely engineered arrays of graphene nanostructures can provide a second harmonic generation efficiency comparable with that of state-of-the-art nonlinear crystals, with the high Ohmic losses of graphene serving as the fundamental limitation for deterministic processes.
In Chapter 5 we investigate a new paradigm for quantum memories of light based upon ordered atomic arrays. In particular, we show that the strong constructive interference in optical emission can give rise to a significantly enhanced atom-light interface, as compared to a standard, disordered atomic ensemble. In the case of a single, 2D atomic layer, we find the impressive result that a memory realized with 16 atoms can have the same storage efficiency as an atomic ensemble with optical depth larger than 100.Los fotones que viajan por el espacio libre no interactúan entre sí. Esta característica los hace perfectos candidatos para transportar la información cuántica a largas distancias. Por otro lado, el procesamiento de la información que codifican requiere mecanismos de interacción. En los últimos años se han realizado esfuerzos crecientes para realizar interacciones fuertes y controladas entre los fotones y para comprender las leyes subyacentes que describen los fenómenos que pueden surgir, generando así el nuevo campo de la "óptica cuántica no lineal". Mientras que los materiales tridimensionales tienen coeficientes no lineales extremadamente débiles, se pueden obtener interacciones entre los fotones haciéndolos interactuar con átomos individuales, que son objetos intrínsecamente no lineales, teniendo la capacidad de absorber únicamente un solo fotón a la vez. La realización de interacciones determinísticas entre fotones y átomos es uno de los principales retos de la óptica cuántica no lineal. Para eludir las limitaciones debidas a la pequeña sección eficaz óptica de los átomos y el límite de difracción en el espacio libre, se han aplicado diferentes estrategias, entre ellas el uso de cavidades (CQED), de colectividades atómicas y, más recientemente, de nanoestructuras dieléctricas capaces de confinar la luz sin desenfocarse, permitiendo así la interacción con átomos atrapados en la proximidad de esas estructuras. Mientras que para el caso de la CQED se han desarrollado potentes herramientas teóricas para tratar las interacciones de los fotones, en el caso de colectividades atómicas hay una falta general de métodos teóricos más allá del régimen lineal. Esta relativa falta de comprensión también implica que podría haber nuevos fenómenos físicos interesantes que hasta ahora no se han identificado. El objetivo general de esta tesis es explorar estos temas con mayor detalle. En el capítulo 2 de esta tesis desarrollamos un nuevo formalismo para calcular las propiedades de la luz cuántica cuando interactúa con sistemas atómicos. El método consiste en utilizar un"`modelo de espines" que mapea un problema de propagación de luz cuasi unidimensional (1D) a la dinámica de un sistema abierto unidimensional de espines que interactúan entre sí, donde todas las correlaciones de fotones se obtienen a partir de las de los espines. La dinámica de los espines se puede resolver numéricamente utilizando la caja de herramientas de los estados producto de matrices (MPS), proporcionando así una técnica para estudiar los fotones que interactúan fuertemente en el regimen de la física de muchos cuerpos. En el capítulo 3 se investiga la posibilidad de crear fases exóticas de la materia utilizando la interfaz entre guía de ondas de cristales fotónicos (PCW) y átomos recientemente realizada experimentalmente, donde los modos de la banda de frecuencias prohibidas de la PCW se utilizan para mediar las interacciones de largo alcance entre los átomos. Encontramos un rico diagrama de fases de órdenes emergentes. En el capítulo 4 se investiga la posibilidad de implementar procesos ópticos cuánticos no lineales de segundo orden con nano-estructuras de grafeno, como una alternativa más robusta al uso de sistemas atómicos. Cuantificamos las propiedades no lineales de segundo orden, mostrando que el estrecho confinamiento da lugar a extraordinarias fuerzas de interacción a nivel de un solo fotón y predecimos que un diseño apropiado de las nano-estructuras del grafeno permitiría generar el segundo armónico con una eficiencia comparable a la de los cristales no lineales de última generación. En el capítulo 5, investigamos cómo la emisión cooperativa en memorias cuánticas realizadas con reticulos atómicos afecta su eficiencia, encontrando el impresionante resultado de que una memoria realizada con 16 átomos puede tener la misma eficiencia que un gas cuántico atómico de profundidad óptica mayor que 100.
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Mulansky, Mario. "Chaotic diffusion in nonlinear Hamiltonian systems". Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2013/6318/.
Testo completoAbstract (sommario):
This work investigates diffusion in nonlinear Hamiltonian systems.
The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''.
Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings.
The fundamental observation is the spreading of energy for localized initial conditions.
Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time.
This new quantity allows for a more precise analysis of the spreading than traditional methods.
Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation.
Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced.
The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE.
From this relation, exact spreading predictions are deduced.
Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE.
Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation.
All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy.
In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation.
For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments.
Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case.
Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.Diese Arbeit beschäftigt sich mit dem Phänomen der Diffusion in nichtlinearen Systemen. Unter Diffusion versteht man normalerweise die zufallsmäss ige Bewegung von Partikeln durch den stochastischen Einfluss einer thermodynamisch beschreibbaren Umgebung. Dieser Prozess ist mathematisch beschrieben durch die Diffusionsgleichung. In dieser Arbeit werden jedoch abgeschlossene Systeme ohne Einfluss der Umgebung betrachtet. Dennoch wird eine Art von Diffusion, üblicherweise bezeichnet als Subdiffusion, beobachtet. Die Ursache dafür liegt im chaotischen Verhalten des Systems. Vereinfacht gesagt, erzeugt das Chaos eine intrinsische Pseudo-Zufälligkeit, die zu einem gewissen Grad mit dem Einfluss einer thermodynamischen Umgebung vergleichbar ist und somit auch diffusives Verhalten provoziert. Zur quantitativen Beschreibung dieses subdiffusiven Prozesses wird eine Verallgemeinerung der Diffusionsgleichung herangezogen, die Nichtlineare Diffusionsgleichung. Desweiteren wird die mikroskopische Dynamik des Systems mit analytischen Methoden untersucht, und Schlussfolgerungen für den makroskopischen Diffusionsprozess abgeleitet. Die Technik der Verbindung von mikroskopischer Dynamik und makroskopischen Beobachtungen, die in dieser Arbeit entwickelt wird und detailliert beschrieben ist, führt zu einem tieferen Verständnis von hochdimensionalen chaotischen Systemen. Die mit mathematischen Mitteln abgeleiteten Ergebnisse sind darüber hinaus durch ausführliche Simulationen verifiziert, welche teilweise auf einem der leistungsfähigsten Supercomputer Europas durchgeführt wurden, dem sp6 in Bologna, Italien. Desweiteren können die in dieser Arbeit vorgestellten Erkenntnisse und Techniken mit Sicherheit auch in anderen Fällen bei der Untersuchung chaotischer Systeme Anwendung finden.
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Lemch, Ekaterina S. "Nonlinear and hierarchical hybrid control systems". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0032/NQ64600.pdf.
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Raj, Ashish. "Evolutionary Optimization Algorithms for Nonlinear Systems". DigitalCommons@USU, 2013. http://digitalcommons.usu.edu/etd/1520.
Testo completoAbstract (sommario):
Many real world problems in science and engineering can be treated as optimization problems with multiple objectives or criteria. The demand for fast and robust stochastic algorithms to cater to the optimization needs is very high. When the cost function for the problem is nonlinear and non-differentiable, direct search approaches are the methods of choice. Many such approaches use the greedy criterion, which is based on accepting the new parameter vector only if it reduces the value of the cost function. This could result in fast convergence, but also in misconvergence where it could lead the vectors to get trapped in local minima. Inherently, parallel search techniques have more exploratory power. These techniques discourage premature convergence and consequently, there are some candidate solution vectors which do not converge to the global minimum solution at any point of time. Rather, they constantly explore the whole search space for other possible solutions. In this thesis, we concentrate on benchmarking three popular algorithms: Real-valued Genetic Algorithm (RGA), Particle Swarm Optimization (PSO), and Differential Evolution (DE). The DE algorithm is found to out-perform the other algorithms in fast convergence and in attaining low-cost function values. The DE algorithm is selected and used to build a model for forecasting auroral oval boundaries during a solar storm event. This is compared against an established model by Feldstein and Starkov. As an extended study, the ability of the DE is further put into test in another example of a nonlinear system study, by using it to study and design phase-locked loop circuits. In particular, the algorithm is used to obtain circuit parameters when frequency steps are applied at the input at particular instances.
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Chryssochoos, Ioannis. "Optimization based control of nonlinear systems". Thesis, Imperial College London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.399165.
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Mathew, Michael Ian. "Design of nonlinear sampled-data systems". Thesis, Coventry University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.480606.
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Blake, Iain M. "Conjugated porphyrin systems for nonlinear optics". Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365889.
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Szpruch, Lukasz. "Numerical approximations of nonlinear stochastic systems". Thesis, University of Strathclyde, 2010. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=14439.
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Sincock, Paul. "Nonlinear compliant systems in irregular seas". Thesis, University College London (University of London), 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.490146.
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