Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
Mathematical Systems Theory : from Behaviors to Nonlinear Control
Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien
2015-01-01
This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...
Energy flow theory of nonlinear dynamical systems with applications
Xing, Jing Tang
2015-01-01
This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as ...
Nonlinear dynamical systems for theory and research in ergonomics.
Guastello, Stephen J
2017-02-01
Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.
Nonlinear closure relations theory for transport processes in nonequilibrium systems.
Sonnino, Giorgio
2009-05-01
A decade ago, a macroscopic theory for closure relations has been proposed for systems out of Onsager's region. This theory is referred to as the thermodynamic field theory (TFT). The aim of this work was to determine the nonlinear flux-force relations that respect the thermodynamic theorems for systems far from equilibrium. We propose a formulation of the TFT where one of the basic restrictions, namely, the closed-form solution for the skew-symmetric piece of the transport coefficients, has been removed. In addition, the general covariance principle is replaced by the De Donder-Prigogine thermodynamic covariance principle (TCP). The introduction of TCP requires the application of an appropriate mathematical formalism, which is referred to as the entropy-covariant formalism. By geometrical arguments, we prove the validity of the Glansdorff-Prigogine universal criterion of evolution. A new set of closure equations determining the nonlinear corrections to the linear ("Onsager") transport coefficients is also derived. The geometry of the thermodynamic space is non-Riemannian. However, it tends to be Riemannian for high values of the entropy production. In this limit, we recover the transport equations found by the old theory. Applications of our approach to transport in magnetically confined plasmas, materials submitted to temperature, and electric potential gradients or to unimolecular triangular chemical reactions can be found at references cited herein. Transport processes in tokamak plasmas are of particular interest. In this case, even in the absence of turbulence, the state of the plasma remains close to (but, it is not in) a state of local equilibrium. This prevents the transport relations from being linear.
An approximation theory for the identification of nonlinear distributed parameter systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1990-01-01
An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato appproximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.
Hybrid simulation theory for a classical nonlinear dynamical system
Drazin, Paul L.; Govindjee, Sanjay
2017-03-01
Hybrid simulation is an experimental and computational technique which allows one to study the time evolution of a system by physically testing a subset of it while the remainder is represented by a numerical model that is attached to the physical portion via sensors and actuators. The technique allows one to study large or complicated mechanical systems while only requiring a subset of the complete system to be present in the laboratory. This results in vast cost savings as well as the ability to study systems that simply can not be tested due to scale. However, the errors that arise from splitting the system in two requires careful attention, if a valid simulation is to be guaranteed. To date, efforts to understand the theoretical limitations of hybrid simulation have been restricted to linear dynamical systems. In this work we consider the behavior of hybrid simulation when applied to nonlinear dynamical systems. As a model problem, we focus on the damped, harmonically-driven nonlinear pendulum. This system offers complex nonlinear characteristics, in particular periodic and chaotic motions. We are able to show that the application of hybrid simulation to nonlinear systems requires a careful understanding of what one expects from such an experiment. In particular, when system response is chaotic we advocate the need for the use of multiple metrics to characterize the difference between two chaotic systems via Lyapunov exponents and Lyapunov dimensions, as well as correlation exponents. When system response is periodic we advocate the use of L2 norms. Further, we are able to show that hybrid simulation can falsely predict chaotic or periodic response when the true system has the opposite characteristic. In certain cases, we are able to show that control system parameters can mitigate this issue.
Correlations in complex nonlinear systems and quantum information theory
Energy Technology Data Exchange (ETDEWEB)
Guehne, Otfried [Institut fuer Quantenoptik und Quanteninformation, Oesterreichische Akademie der Wissenschaften, Innsbruck (Austria); Galla, Tobias [School of Physics and Astronomy, University of Manchester (United Kingdom)
2010-07-01
The dynamical evolution of classical complex systems such as coupled logistic maps or simple models of lattice gases and cellular automata can result in correlations between distant parts of the system. For the understanding of these systems, it is crucial to develop methods to characterize and quantify these multi-party correlations. On the other hand, the study of correlations between distant particles is also a central problem in the field of quantum information theory. There, correlations are often viewed as a resource and many tools have been developed for their characterization. In this talk, we explore the extent to which the tools from quantum information can be applied to study classical complex systems and whether they allow to study complex systems from a different perspective.
Classical and Quantum Nonlinear Integrable Systems: Theory and Application
Energy Technology Data Exchange (ETDEWEB)
Brzezinski, Tomasz [Department of Mathematics, University of Wales Swansea (United Kingdom)
2003-12-12
This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical
Research in Applied Mathematics Related to Nonlinear System Theory.
1985-08-01
IEEE Transactions on Automatic Control , AC-27: 196-198. J. C...P. KHARGONEKAR [1982] "Regulation of split linear systems over rings: coefficient assignment and observers", IEEE Transactions on Automatic Control , AC...Optimization, 20: 497-505. [1983a] "Linear dynamic output feedback: invariants and stability", IEEE Transactions on Automatic Control , AC-28: 489-496.
Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.
Perdigão, Rui A P; Hall, Julia
2016-01-01
We formulate a nonlinear synergistic theory of coevolutionary systems, disentangling and explaining dynamic complexity in terms of fundamental processes for optimised data analysis and dynamic model design: Dynamic Source Analysis (DSA). DSA provides a nonlinear dynamical basis for spatiotemporal datasets or dynamical models, eliminating redundancies and expressing the system in terms of the smallest number of fundamental processes and interactions without loss of information. This optimises model design in dynamical systems, expressing complex coevolution in simple synergistic terms, yielding physically meaningful spatial and temporal structures. These are extracted by spatiotemporal decomposition of nonlinearly interacting subspaces via the novel concept of a Spatiotemporal Coevolution Manifold. Physical consistency is ensured and mathematical ambiguities are avoided with fundamental principles on energy minimisation and entropy production. The relevance of DSA is illustrated by retrieving a non-redundant, ...
Nonlinear Theory of Light Speed Reduction in a Three-Level A System
Institute of Scientific and Technical Information of China (English)
王德重; 李代军; 刘夏姬; 李师群; 王育竹
2001-01-01
We present a nonlinear theory of light velocity reduction in a three-level A system based on electromagneticllyinduced transparency. Analysis shows that the probe field propagates with a velocity that is quite strongly dependent on its intensity instead of being merely approximately dependent on the coupling intensity. Moreover,the minimum group velocity of the probe field is analytically given for a given input power.
GA and Lyapunov theory-based hybrid adaptive fuzzy controller for non-linear systems
Roy, Ananya; Das Sharma, Kaushik
2015-02-01
In this present article, a new hybrid methodology for designing stable adaptive fuzzy logic controllers (AFLCs) for a class of non-linear system is proposed. The proposed design strategy exploits the features of genetic algorithm (GA)-based stochastic evolutionary global search technique and Lyapunov theory-based local adaptation scheme. The objective is to develop a methodology for designing AFLCs with optimised free parameters and guaranteed closed-loop stability. Simultaneously, the proposed method introduces automation in the design process. The stand-alone Lyapunov theory-based design, GA-based design and proposed hybrid GA-Lyapunov design methodologies are implemented for two benchmark non-linear plants in simulation case studies with different reference signals and one experimental case study. The results demonstrate that the hybrid design methodology outperforms the other control strategies on the whole.
On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics
DEFF Research Database (Denmark)
True, Hans
1999-01-01
We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined...... of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed....
Maj, Omar
2008-01-01
This is the second part of a work aimed to study complex-phase oscillatory solutions of nonlinear symmetric hyperbolic systems. We consider, in particular, the case of one space dimension. That is a remarkable case, since one can always satisfy the \\emph{naive} coherence condition on the complex phases, which is required in the construction of the approximate solution. Formally the theory applies also in several space dimensions, but the \\emph{naive} coherence condition appears to be too restrictive; the identification of the optimal coherence condition is still an open problem.
de Paor, A. M.
Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ɛ has the value 1 is proved via the Popov theorem from feedback system stability theory.
Nonlinear systems in medicine.
Higgins, John P
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.
Perdigão, Rui A. P.; Hall, Julia; Pires, Carlos A. L.; Blöschl, Günter
2017-04-01
Classical and stochastic dynamical system theories assume structural coherence and dynamic recurrence with invariants of motion that are not necessarily so. These are grounded on the unproven assumption of universality in the dynamic laws derived from statistical kinematic evaluation of non-representative empirical records. As a consequence, the associated formulations revolve around a restrictive set of configurations and intermittencies e.g. in an ergodic setting, beyond which any predictability is essentially elusive. Moreover, dynamical systems are fundamentally framed around dynamic codependence among intervening processes, i.e. entail essentially redundant interactions such as couplings and feedbacks. That precludes synergistic cooperation among processes that, whilst independent from each other, jointly produce emerging dynamic behaviour not present in any of the intervening parties. In order to overcome these fundamental limitations, we introduce a broad class of non-recursive dynamical systems that formulate dynamic emergence of unprecedented states in a fundamental synergistic manner, with fundamental principles in mind. The overall theory enables innovations to be predicted from the internal system dynamics before any a priori information is provided about the associated dynamical properties. The theory is then illustrated to anticipate, from non-emergent records, the spatiotemporal emergence of multiscale hyper chaotic regimes, critical transitions and structural coevolutionary changes in synthetic and real-world complex systems. Example applications are provided within the hydro-climatic context, formulating and dynamically forecasting evolving hydro-climatic distributions, including the emergence of extreme precipitation and flooding in a structurally changing hydro-climate system. Validation is then conducted with a posteriori verification of the simulated dynamics against observational records. Agreement between simulations and observations is
Directory of Open Access Journals (Sweden)
A. M. de Paor
1998-01-01
Full Text Available Hide (Nonlinear Processes in Geophysics, 1998 has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ε has the value 1 is proved via the Popov theorem from feedback system stability theory.
Nonlinearity and disorder: Theory and applications
DEFF Research Database (Denmark)
Bang, Ole; Sørensen, Mads Peter
Proceedings of the NATO Advanced Research Workshop (ARW) entitled Nonlinearity and Disorder: Theory and Applications, held in Tashkent, Uzbekistan, October 2-6, 2001. Phenomena of coherent structures in nonlinear systems and disorder are considered opposite in nature. For example one of the most...
Spectral theory and nonlinear functional analysis
Lopez-Gomez, Julian
2001-01-01
This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.
Directory of Open Access Journals (Sweden)
2007-01-01
Full Text Available Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A self-consistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Knight, Rona
2014-04-01
A focus on the latency phase is used to illustrate how theory and developmental research have influenced our psychoanalytic views of development over the past hundred years. Beginning with Freud's psychosexual theory and his conception of latency, an historical overview of the major psychoanalytic contributions bearing on this developmental period over the past century is presented. Recent longitudinal research in latency supports a nonlinear dynamic systems approach to development. This approach obliges us to reconsider our linear theories and how we think about and work with our patients.
Fuchs, Armin
2013-01-01
With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered by their particular education. Especially in the life- and neurosciences quantitative models based on nonlinear dynamics and complex systems are becoming as frequently implemented as traditional statistical analysis. Unfamiliarity with the terminology and rigorous mathematics may discourage many scientists to adopt these methods for their own work, even though such reluctance in most cases is not justified.This book bridges this gap by introducing the procedures and methods used for analyzing nonlinear dynamical systems. In Part I, the concepts of fixed points, phase space, stability and transitions, among others, are discussed in great detail and implemented on the basis of example elementary systems. Part II is devoted to specific, non-trivial applications: coordination of human limb movement (Haken-Kelso-Bunz ...
Badikyan, Karen
2016-01-01
The nonlinear theory of relyativistic strophotron is developed. Classical equations of motion are averaged over fast oscillations. The slow motion phase and saturation parameter are found different from usual undulator oscillation parameters. In the strong field approximation the analytical expression of gain is found on higher harmonics of main resonance frequency.
Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy
Rossberg, A G; Kramer, L; Pesch, W
1996-01-01
Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly nonlinear analysis leading to amplitude equations which couple the short-wavelength patterning mode with the Goldstone mode resulting from the broken isotropy. The new coefficients in these equations are calculated from the hydrodynamics. Simulations exhibit a new type of spatio-temporal chaos at onset. The results are compared with experiments.
Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman Operator Theory
2017-03-01
calculus, applied mathematics, Director’s Research Initiative 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...ARL-TR-7959 MAR 2017 US Army Research Laboratory Global Stability and Dynamics of Strongly Nonlinear Systems Using Koopman...report when it is no longer needed. Do not return it to the originator. ARL-TR-7959 ● MAR 2017 US Army Research Laboratory Global
Nonlinear Progressive Failure Analysis of Surrounding Rock System Based on Similarity Theory
Directory of Open Access Journals (Sweden)
Zhao Y.
2016-01-01
Full Text Available Nonlinear progressive failure study of surrounding rock is important for the stability analysis of underground engineering projects. Taking a deep-buried tunnel in Chongqing as an example, a three dimensional(3-D physical model was established based on similarity theory. To satisfy similarity requirement of physical–mechanical properties, such as elastic modulus, compressive strength and Poisson ratio, physical model materials were developed. Using full inner-spy photograph technology, the deformation and failure process of rock were studied under the situation of independent and combined action of anchor, shotcrete and reinforcing mesh. Based on experimental results, the interaction mechanism between rock and support structure under high stress was investigated.
The Nonlinear Field Space Theory
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
Energy Technology Data Exchange (ETDEWEB)
Mielczarek, Jakub, E-mail: jakub.mielczarek@uj.edu.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Trześniewski, Tomasz, E-mail: tbwbt@ift.uni.wroc.pl [Institute of Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków (Poland); Institute for Theoretical Physics, University of Wrocław, pl. Borna 9, 50-204 Wrocław (Poland)
2016-08-10
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
The Nonlinear Field Space Theory
Directory of Open Access Journals (Sweden)
Jakub Mielczarek
2016-08-01
Full Text Available In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the “Principle of finiteness” of physical theories, which once motivated the Born–Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity, as well as in condensed matter physics (e.g. continuous spin chains, and can shed new light on the issue of divergences in quantum field theories.
Nonlinearity and disorder: Theory and applications
DEFF Research Database (Denmark)
Bang, Ole; Sørensen, Mads Peter
Proceedings of the NATO Advanced Research Workshop (ARW) entitled Nonlinearity and Disorder: Theory and Applications, held in Tashkent, Uzbekistan, October 2-6, 2001. Phenomena of coherent structures in nonlinear systems and disorder are considered opposite in nature. For example one of the most...... fascinating nonlinear wave phenomenon - the soliton - is a highly coherent object, but in disordered linear media we know of the existence of the famous Anderson localization, which means the appearance of localized wave structures in disordered linear media. Investigations of wave phenomena in disordered...... of the photorefractive solitons. Another very fast growing area induced by the technological development is statistical phenomena in nonlinear pulse propagation in optical fibers. Intrinsic randomness of existing optical communication systems has an important impact on the performance of planned soliton communication...
Nonlinear theory of kinetic instabilities near threshold
Energy Technology Data Exchange (ETDEWEB)
Berk, H.L.; Pekker, M.S. [Univ. of Texas, Austin, TX (United States). Inst. for Fusion Studies; Breizman, B.N. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies]|[Budker Inst. of Nuclear Physics, Novosibirsk (Russian Federation)
1997-05-01
A new nonlinear equation has been derived and solved for the evolution of an unstable collective mode in a kinetic system close to the threshold of linear instability. The resonant particle response produces the dominant nonlinearity, which can be calculated iteratively in the near-threshold regime as long as the mode doe snot trap resonant particles. With sources and classical relaxation processes included, the theory describes both soft nonlinear regimes, where the mode saturation level is proportional to an increment above threshold, and explosive nonlinear regimes, where the mode grows to a level that is independent of the closeness to threshold. The explosive solutions exhibit mode frequency shifting. For modes that exist in the absence of energetic particles, the frequency shift is both upward and downward. For modes that require energetic particles for their existence, there is a preferred direction of the frequency shift. The frequency shift continues even after the mode traps resonant particles.
On balanced truncation for symmetric nonlinear systems
Fujimoto, K.; Scherpen, Jacqueline M.A.
2014-01-01
This paper is concerned with model order reduction based on balanced realization for symmetric nonlinear systems. A new notion of symmetry for nonlinear systems was characterized recently. It plays an important role in linear systems theory and is expected to provide new insights to nonlinear system
Time-dependent density functional theory for nonlinear properties of open-shell systems.
Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans
2007-09-21
This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.
Theory and design of nonlinear metamaterials
Rose, Alec Daniel
If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers
Introducing Nonlinear Pricing into Consumer Choice Theory.
DeSalvo, Joseph S.; Huq, Mobinul
2002-01-01
Describes and contrasts nonlinear and linear pricing in consumer choice theory. Discusses the types of nonlinear pricing: block-declining tariff, two-part tariff, three-part tariff, and quality discounts or premia. States that understanding nonlinear pricing enhances student comprehension of consumer choice theory. Suggests teaching the concept in…
National Research Council Canada - National Science Library
de Paor, A. M
1998-01-01
Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field...
Phase reduction theory for hybrid nonlinear oscillators
Shirasaka, Sho; Kurebayashi, Wataru; Nakao, Hiroya
2017-01-01
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of limit-cycle oscillations in rhythmic systems, has mostly been restricted to smooth dynamical systems. Here we develop a general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis, control, and optimization of nonlinear oscillators whose smooth models are unavailable or intractable. On the basis of the generalized theory, we analyze injection locking of hybrid limit-cycle oscillators by periodic forcing and reveal their characteristic synchronization properties, such as ultrafast and robust entrainment to the periodic forcing and logarithmic scaling at the synchronization transition. We also illustrate the theory by analyzing the synchronization dynamics of a simple physical model of biped locomotion.
Spectral theory and nonlinear analysis with applications to spatial ecology
Cano-Casanova, S; Mora-Corral , C
2005-01-01
This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis - from the most abstract developments up to the most concrete applications to population dynamics and socio-biology - in an effort to fill the existing gaps between these fields.
Complex motions and chaos in nonlinear systems
Machado, José; Zhang, Jiazhong
2016-01-01
This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.
Controllability in nonlinear systems
Hirschorn, R. M.
1975-01-01
An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.
A. M. de Paor
1998-01-01
International audience; Hide (Nonlinear Processes in Geophysics, 1998) has produced a new mathematical model of a self-exciting homopolar dynamo driving a series- wound motor, as a continuing contribution to the theory of the geomagnetic field. By a process of exact perturbation analysis, followed by combination and partial solution of differential equations, the complete nonlinear quenching of current fluctuations reported by Hide in the case that a parameter ? has the value 1 is proved via ...
Stability analysis of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatoly A
2015-01-01
The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners. Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.
Practical stability of nonlinear systems
Lakshmikantham, Vangipuram; Martynyuk, Anatolii Andreevich
1990-01-01
This is the first book that deals with practical stability and its development. It presents a systematic study of the theory of practical stability in terms of two different measures and arbitrary sets and demonstrates the manifestations of general Lyapunov's method by showing how this effective technique can be adapted to investigate various apparently diverse nonlinear problems including control systems and multivalued differential equations.
Lugiato, Luigi; Brambilla, Massimo
2015-01-01
Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.
An Adaptive Nonlinear Filter for System Identification
Directory of Open Access Journals (Sweden)
Tokunbo Ogunfunmi
2009-01-01
Full Text Available The primary difficulty in the identification of Hammerstein nonlinear systems (a static memoryless nonlinear system in series with a dynamic linear system is that the output of the nonlinear system (input to the linear system is unknown. By employing the theory of affine projection, we propose a gradient-based adaptive Hammerstein algorithm with variable step-size which estimates the Hammerstein nonlinear system parameters. The adaptive Hammerstein nonlinear system parameter estimation algorithm proposed is accomplished without linearizing the systems nonlinearity. To reduce the effects of eigenvalue spread as a result of the Hammerstein system nonlinearity, a new criterion that provides a measure of how close the Hammerstein filter is to optimum performance was used to update the step-size. Experimental results are presented to validate our proposed variable step-size adaptive Hammerstein algorithm given a real life system and a hypothetical case.
Nonlinear Ekman Layer Theories and Their Applications
Institute of Scientific and Technical Information of China (English)
TAN Zhemin; FANG Juan; WU Rongsheng
2006-01-01
Based on the classical Ekman theory, a series of intermediate boundary layer models, which retain the nonlinear advective process while discard embellishments, have been proposed with the intention to understand the complex nonlinear features of the atmospheric boundary layer and its interaction with the free atmosphere. In this paper, the recent advances in the intermediate boundary-layer dynamic models are reviewed. Several intermediate models such as the boundary-layer models incorporating geostrophic momentum approximation, Ekman momentum approximation, and the weak nonlinear Ekman-layer model are a major theme.With inspection of the theoretical frameworks, the physical meaning and the limitations of each intermediate model are discussed. It is found that the qualitative descriptions of the nonlinear nature in Ekman layer made by the intermediate models are fairly consistent though the details may be different. As the application of the intermediate models is concerned, the application of the intermediate models to the study of the topographic boundary layer, frontogenesis, low-level frontal structure, and low-level jet are especially summarized in this paper. It is shown that the intermediate boundary-layer models have great potential in illustrating the low-level structures of the weather and climate systems as they are coupled with the free atmospheric models.In addition, the important remaining scientific challenges and a prospectus for future research on the intermediate model are also discussed.
Linear and Nonlinear Theory of Eigenfunction Scars
Kaplan, L
1998-01-01
The theory of scarring of eigenfunctions of classically chaotic systems by short periodic orbits is extended in several ways. The influence of short-time linear recurrences on correlations and fluctuations at long times is emphasized. We include the contribution to scarring of nonlinear recurrences associated with homoclinic orbits, and treat the different scenarios of random and nonrandom long-time recurrences. The importance of the local classical structure around the periodic orbit is emphasized, and it is shown for an optimal choice of test basis in phase space, scars must persist in the semiclassical limit. The crucial role of symmetry is also discussed, which together with the nonlinear recurrences gives a much improved account of the actual strength of scars for given classical orbits and in individual wavefunctions. Quantitative measures of scarring are provided and comparisons are made with numerical data.
Observability and Controllability for Smooth Nonlinear Systems
Schaft, A.J. van der
1982-01-01
The definition of a smooth nonlinear system as proposed recently, is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input-output system. Minimality for such systems can be defined in a very direct geometric way, and already implies a usual notion of observability, namely, local weak observability. As an application of this theory, it is shown that observable nonlinear Hamiltonian systems are necessarily controllable, and vice versa.
DEFF Research Database (Denmark)
Jørgensen, Michael Finn
1995-01-01
It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...
Directory of Open Access Journals (Sweden)
Victor Kardashov
2002-01-01
Full Text Available This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion. The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients. The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions.
Using system theory and energy methods to prove existence of non-linear PDE's
Zwart, Hans
2015-01-01
Consider a network with linear dynamics on the edges, and observation and control in the nodes. Assume that on the edges there is no damping, and so the dynamics can be described by an infinite-dimensional, port-Hamiltonian system. For general infinite-dimensional systems, the zero dynamics can be d
Nonlinear dynamics of a pseudoelastic shape memory alloy system - theory and experiment
DEFF Research Database (Denmark)
Enemark, Søren; A Savi, M.; Santos, Ilmar
2014-01-01
In this work, a helical spring made from a pseudoelastic shape memory alloy was embedded in a dynamic system also composed of a mass, a linear spring and an excitation system. The mechanical behaviour of shape memory alloys is highly complex, involving hysteresis, which leads to damping...... capabilities and varying stiffness. Besides, these properties depend on the temperature and pretension conditions. Because of these capabilities, shape memory alloys are interesting in relation to engineering design of dynamic systems. A theoretical model based on a modification of the 1D Brinson model...... and forced vibrations of the system setup under different temperature conditions. The experiments give a thorough insight into dynamic systems involving pseudoelastic shape memory alloys. Comparison between experimental results and the proposed model shows that the model is able to explain and predict...
Geometric nonlinearities in field theory, condensed matter and analytical mechanics
Directory of Open Access Journals (Sweden)
J.J. Sławianowski
2010-01-01
Full Text Available There are two very important subjects in physics: Symmetry of dynamical models and nonlinearity. All really fundamental models are invariant under some particular symmetry groups. There is also no true physics, no our Universe and life at all, without nonlinearity. Particularly interesting are essential, non-perturbative nonlinearities which are not described by correction terms imposed on some well-defined linear background. Our idea in this paper is that there exists some mysterious, still incomprehensible link between essential, physically relevant nonlinearity and dynamical symmetry, first of all, of large symmetry groups. In some sense the problem is known even in soliton theory, where the essential nonlinearity is often accompanied by the infinite system of integrals of motion, thus, by infinite-dimensional symmetry groups. Here we discuss some more familiar problems from the realm of field theory, condensed matter physics, and analytical mechanics, where the link between essential nonlinearity and high symmetry is obvious, although not fully understandable.
The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications
Andreasen, Martin Møller; Fernández-Villaverde, Jesús; Juan F Rubio-Ramírez
2013-01-01
This paper studies the pruned state-space system for higher-order approximations to the solutions of DSGE models. For second- and third-order approximations, we derive the statistical properties of this system and provide closed-form expressions for first and second unconditional moments and impulse response functions. Thus, our analysis introduces GMM estimation for DSGE models approximated up to third-order and provides the foundation for indirect inference and SMM when simulation is requir...
Gauge theories of gravity: the nonlinear framework
Tiemblo, A
2004-01-01
Nonlinear realizations of spacetime groups are presented as a versatile mathematical tool providing a common foundation for quite different formulations of gauge theories of gravity. We apply nonlinear realizations in particular to both the Poincar\\'e and the affine group in order to develop Poincar\\'e gauge theory (PGT) and metric-affine gravity (MAG) respectively. Regarding PGT, two alternative nonlinear treatments of the Poincar\\'e group are developed, one of them being suitable to deal with the Lagrangian and the other one with the Hamiltonian version of the same gauge theory. We argue that our Hamiltonian approach to PGT is closely related to Ashtekar's approach to gravity. On the other hand, a brief survey on MAG clarifies the role played by the metric--affine metric tensor as a Goldsone field. All gravitational quantities in fact --the metric as much as the coframes and connections-- are shown to acquire a simple gauge--theoretical interpretation in the nonlinear framework.
Quantum theory of nonlocal nonlinear Schrodinger equation
Vyas, Vivek M
2015-01-01
Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.
A Geometrically—Nonlinear Plate Theory 12
Institute of Scientific and Technical Information of China (English)
AlbertC.J.LUO
1999-01-01
An approximate plate theory developed in this paper is based on an assumed displacement field,the strains described by a Taylor series in the normal distance from the middle surface,the exact strains of the middle surface and the equations of equilibrium governing the exact configuration of the deformed middle surface,In this theory the exact geometry of the deformed middle surface is used to derive the strains and equilibrium of the plate.Application of this theory does not depend on the constitutive law.THis theory can reduce to some existing nonlinear theories through imposition of constraints.
The quantum theory of nonlinear optics
Drummond, Peter D
2014-01-01
Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamic...
Lattice Theories with Nonlinearly Realized Chiral Symmetry
Chandrasekharan, S; Steffen, F D; Wiese, U J
2003-01-01
We present the lattice formulation of effective Lagrangians in which chiral symmetry is realized nonlinearly on the fermion fields. In this framework both the Wilson term removing unphysical doubler fermions and the fermion mass term do not break chiral symmetry. Our lattice formulation allows us to address non-perturbative questions in effective theories of baryons interacting with pions and in models involving constitutent quarks interacting with pions and gluons. With the presented methods, a system containing a non-zero density of static baryons interacting with pions can be studied on the lattice without encountering a complex action problem. This might lead to new insights into the phase diagram of strongly interacting matter at non-zero chemical potential.
Energy Technology Data Exchange (ETDEWEB)
Elton, A.B.H.
1990-09-24
A numerical theory for the massively parallel lattice gas and lattice Boltzmann methods for computing solutions to nonlinear advective-diffusive systems is introduced. The convergence theory is based on consistency and stability arguments that are supported by the discrete Chapman-Enskog expansion (for consistency) and conditions of monotonicity (in establishing stability). The theory is applied to four lattice methods: Two of the methods are for some two-dimensional nonlinear diffusion equations. One of the methods is for the one-dimensional lattice method for the one-dimensional viscous Burgers equation. And one of the methods is for a two-dimensional nonlinear advection-diffusion equation. Convergence is formally proven in the L{sub 1}-norm for the first three methods, revealing that they are second-order, conservative, conditionally monotone finite difference methods. Computational results which support the theory for lattice methods are presented. In addition, a domain decomposition strategy using mesh refinement techniques is presented for lattice gas and lattice Boltzmann methods. The strategy allows concentration of computational resources on regions of high activity. Computational evidence is reported for the strategy applied to the lattice gas method for the one-dimensional viscous Burgers equation. 72 refs., 19 figs., 28 tabs.
An Asymptotic Derivation of Weakly Nonlinear Ray Theory
Indian Academy of Sciences (India)
Phoolan Prasad
2000-11-01
Using a method of expansion similar to Chapman–Enskog expansion, a new formal perturbation scheme based on high frequency approximation has been constructed. The scheme leads to an eikonal equation in which the leading order amplitude appears. The transport equation for the amplitude has been deduced with an error (2) where is the small parameter appearing in the high frequency approximation. On a length scale over which Choquet–Bruhat's theory is valid, this theory reduces to the former. The theory is valid on a much larger length scale and the leading order terms give the weakly nonlinear ray theory (WNLRT) of Prasad, which has been very successful in giving physically realistic results and also in showing that the caustic of a linear theory is resolved when nonlinear effects are included. The weak shock ray theory with infinite system of compatibility conditions also follows from this theory.
Rigorous theory of molecular orientational nonlinear optics
Directory of Open Access Journals (Sweden)
Chong Hoon Kwak
2015-01-01
Full Text Available Classical statistical mechanics of the molecular optics theory proposed by Buckingham [A. D. Buckingham and J. A. Pople, Proc. Phys. Soc. A 68, 905 (1955] has been extended to describe the field induced molecular orientational polarization effects on nonlinear optics. In this paper, we present the generalized molecular orientational nonlinear optical processes (MONLO through the calculation of the classical orientational averaging using the Boltzmann type time-averaged orientational interaction energy in the randomly oriented molecular system under the influence of applied electric fields. The focal points of the calculation are (1 the derivation of rigorous tensorial components of the effective molecular hyperpolarizabilities, (2 the molecular orientational polarizations and the electronic polarizations including the well-known third-order dc polarization, dc electric field induced Kerr effect (dc Kerr effect, optical Kerr effect (OKE, dc electric field induced second harmonic generation (EFISH, degenerate four wave mixing (DFWM and third harmonic generation (THG. We also present some of the new predictive MONLO processes. For second-order MONLO, second-order optical rectification (SOR, Pockels effect and difference frequency generation (DFG are described in terms of the anisotropic coefficients of first hyperpolarizability. And, for third-order MONLO, third-order optical rectification (TOR, dc electric field induced difference frequency generation (EFIDFG and pump-probe transmission are presented.
Lectures in nonlinear mechanics and chaos theory
Stetz, Albert W
2016-01-01
This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...
Controllability of nonlinear systems.
Sussmann, H. J.; Jurdjevic, V.
1972-01-01
Discussion of the controllability of nonlinear systems described by the equation dx/dt - F(x,u). Concepts formulated by Chow (1939) and Lobry (1970) are applied to establish criteria for F and its derivatives to obtain qualitative information on sets which can be obtained from x which denotes a variable of state in an arbitrary, real, analytical manifold. It is shown that controllability implies strong accessibility for a large class of manifolds including Euclidean spaces.-
2007-03-01
IEEE Transactions on Automatic Control , AC- 48, pp. 1712-1723, (2003). [14] C.I. Byrnes, A. Isidori...Nonlinear internal models for output regulation,” IEEE Transactions on Automatic Control , AC-49, pp. 2244-2247, (2004). [15] C.I. Byrnes, F. Celani, A...approach,” IEEE Transactions on Automatic Control , 48 (Dec. 2003), 2172–2190. 2. C. I. Byrnes, “Differential Forms and Dynamical Systems,” to appear
Fault Detection for Nonlinear Systems
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, H.H.
1998-01-01
The paper describes a general method for designing fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension of methods based...
Primary exploration of nonlinear information fusion control theory
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By introducing information fusion techniques into a control field, a new theory of information fusion control (IFC) is proposed. Based on the theory of information fusion estimation, optimal control of nonlinear discrete control system is investigated. All information on control strategy, including ideal control strategy, expected object trajectory and dynamics of system, are regarded as measuring information of control strategy. Therefore, the problem of optimal control is transferred into the one of information fusion estimation. Firstly, the nonlinear information fusion estimation theorems are described. Secondly, an algorithm of nonlinear IFC theory is detailedly deduced. Finally, the simulation results of manipulator shift control are given, which show the feasibility and effectiveness of the presented algorithm.
Directory of Open Access Journals (Sweden)
DJAIRO G. DEFIGUEIREDO
2000-12-01
Full Text Available In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv, - deltav = g(x, u, v, Ñu, Ñv, in omega, We discuss several classes of such systems using both variational and topological methods. The notion of criticality takes into consideration the coupling, which plays important roles in both a priori estimates for the solutions and Palais-Smale conditions for the associated functional in the variational case.
Analysis and design of nonlinear resonances via singularity theory
Cirillo, G I; Kerschen, G; Sepulchre, R
2016-01-01
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurcations reveals the qualitative changes in the behaviour, tracking singularities reveals how structural changes are themselves organised in parameter space. The complementarity of that information is demonstrated in the analysis of detached resonance curves in a two-degree-of-freedom system.
Analysis and design of nonlinear resonances via singularity theory
Cirillo, G. I.; Habib, G.; Kerschen, G.; Sepulchre, R.
2017-03-01
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter. While tracking bifurcations reveals the qualitative changes in the behaviour, tracking singularities reveals how structural changes are themselves organised in parameter space. The complementarity of that information is demonstrated in the analysis of detached resonance curves in a two-degree-of-freedom system.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Theory and application of nonlinear river dynamics
Institute of Scientific and Technical Information of China (English)
Yu-chuan BAI; Zhao-yin WANG
2014-01-01
A theoretical model for river evolution including riverbed formation and meandering pattern formation is presented in this paper. Based on nonlinear mathematic theory, the nonlinear river dynamic theory is set up for river dynamic process. Its core content includes the stability and tropism characteristics of flow motion in river and river selves’ evolution. The stability of river dynamic process depends on the response of river selves to the external disturbance, if the disturbance and the resulting response will eventually attenuate, and the river dynamics process can be restored to new equilibrium state, the river dynamic process is known as stable;otherwise, the river dynamic process is unstable. The river dynamic process tropism refers to that the evolution tendency of river morphology after the disturbance. As an application of this theory, the dynamical stability of the constant curvature river bend is calculated for its coherent vortex disturbance and response. In addition, this paper discusses the nonlinear evolution of the river peristaltic process under a large-scale disturbance, showing the nonlinear tendency of river dynamic processes, such as river filtering and butterfly effect.
A nonlinear theory of generalized functions
1990-01-01
This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
ON NONLINEAR DIFFERENTIAL GALOIS THEORY
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Let X denote a complex analytic manifold, and let Aut(X) denote the space of invertible maps of a germ (X, a) to a germ (X, b); this space is obviously a groupoid; roughly speaking, a "Lie groupoid" is a subgroupoid of Aut(X) defined by a system of partial differential equations.To a foliation with singularities on X one attaches such a groupoid, e.g. the smallest one whose Lie algebra contains the vector fields tangent to the foliation. It is called "the Galois groupoid of the foliation". Some examples are considered, for instance foliations of codimension one, and foliations defined by linear differential equations; in this last case one recuperates the usual differential Galois group.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Balancing for unstable nonlinear systems
Scherpen, J.M.A.
1993-01-01
A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By c
Modal analysis of nonlinear mechanical systems
2014-01-01
The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.
NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM
Institute of Scientific and Technical Information of China (English)
A.Y.T.Leung; WuGuorong; ZhongWeifang
2004-01-01
The nonlinear dynamic equations of a multibody system composed of flexible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation effect is employed and its deformation field is described by exact vibration modes. A numerical procedure for solving the dynamic equations is presented based on the Newmark direct integration method combined with Newton-Raphson iterative method. The results of numerical examples prove the correctness and efficiency of the method proposed.
Nonlinear and Variable Structure Excitation Controller for Power System Stability
Institute of Scientific and Technical Information of China (English)
Wang Ben; Ronnie Belmans
2006-01-01
A new nonlinear variable structure excitation controller is proposed. Its design combines the differential geometry theory and the variable structure controlling theory. The mathematical model in the form of "an affine nonlinear system" is set up for the control of a large-scale power system. The static and dynamic performances of the nonlinear variable structure controller are simulated. The response of system with the controller proposed is compared to that of the nonlinear optimal controller when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure excitation controller gives more satisfactorily static and dynamic performance and better robustness.
Nonlinear system compound inverse control method
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Peng YANG; Zhuzhi YUAN
2005-01-01
A compound neural network is utilized to identify the dynamic nonlinear system.This network is composed of two parts: one is a linear neural network,and the other is a recurrent neural network.Based on the inverse theory a compound inverse control method is proposed.The controller has also two parts:a linear controller and a nonlinear neural network controller.The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated based on the Lyapunov theory.Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
Synchronization between two different chaotic systems with nonlinear feedback control
Institute of Scientific and Technical Information of China (English)
Lü Ling; Guo Zhi-An; Zhang Chao
2007-01-01
This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback controller is designed on the basis of stability theory, and the area of feedback gain is determined. The artificial simulation results show that this control method is commendably effective and feasible.
Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.
2015-01-01
Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential
Nonlinear analysis approximation theory, optimization and applications
2014-01-01
Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Meyer, George
1997-01-01
The paper describes a method for guiding a dynamic system through a given set of points. The paradigm is a fully automatic aircraft subject to air traffic control (ATC). The ATC provides a sequence of way points through which the aircraft trajectory must pass. The way points typically specify time, position, and velocity. The guidance problem is to synthesize a system state trajectory which satisfies both the ATC and aircraft constraints. Complications arise because the controlled process is multi-dimensional, multi-axis, nonlinear, highly coupled, and the state space is not flat. In addition, there is a multitude of possible operating modes, which may number in the hundreds. Each such mode defines a distinct state space model of the process by specifying the state space coordinatization, the partition of the controls into active controls and configuration controls, and the output map. Furthermore, mode transitions must be smooth. The guidance algorithm is based on the inversion of the pure feedback approximations, which is followed by iterative corrections for the effects of zero dynamics. The paper describes the structure and modules of the algorithm, and the performance is illustrated by several example aircraft maneuvers.
SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics
Energy Technology Data Exchange (ETDEWEB)
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-09-01
This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.
Properties of some nonlinear Schroedinger equations motivated through information theory
Energy Technology Data Exchange (ETDEWEB)
Yuan, Liew Ding; Parwani, Rajesh R, E-mail: parwani@nus.edu.s [Department of Physics, National University of Singapore, Kent Ridge (Singapore)
2009-06-01
We update our understanding of nonlinear Schroedinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q = 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value eta = 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, eta might be encoding relativistic effects.
The K-Stability of Nonlinear Delay Systems
Institute of Scientific and Technical Information of China (English)
章毅; 张毅; 王联
1994-01-01
In this paper,we study the K-stability theory of nonlinear delay systems.In the more general case,we establish two nonlinear delay differential inequalities.Therefore,to study the X-stability,a powerful method is provided.By making use of the foregoing inequalities,we analyse and investigate some K-stabiiity conditions of nonlinear delay systems.Finally,some examples are given to illustrate our theory.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
DEFF Research Database (Denmark)
Enemark, Søren; Santos, Ilmar F.
2016-01-01
In this work, the nonlinear dynamic behaviour of a vertical rigid rotor interacting with a flexible foundation by means of two passive magnetic bearings is quantified and evaluated. The quantification is based on theoretical and experimental investigation of the non-uniformity (anisotropy) of the...
Loop Quantum Theory Applied to Biology and Nonlinear Whole Biology
Chang, Yi-Fang
2008-01-01
The loop quantum theory, which constitutes a very small discontinuous space, as new method is applied to biology. The model of protein folding and lungs is proposed. In the model, some known results are used, and four approximate conclusions are obtained: their structures are quantized, their space regions are finite, various singularities correspond to folding and crossed points, and different types of catastrophe exist. Further, based on the inseparability and correlativity of the biological systems, the nonlinear whole biology is proposed, and four basic hypotheses are formed. It may unify reductionism and holism, structuralism and functionalism. Finally, the medical meaning of the theory is discussed briefly.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
2009-11-18
analytic semigroup T(t) ~ eAl is exponentially stable (Notice that it is also a contraction semigroup ). 3. Be 3(U, Z) and P e £(W, 2) are bounded. 4. Ce...quite often in practice, .4 is self-adjoint. We also note that, since we assume (—A) is sectorial, we work with the semigroup exp(.4f) rather than...Uniform Output Regulation of Nonlinear Sys- tems: A convergent Dynamics Approach, Birkhauser, Boston, 2006. 23 135] A. Pazy, Semigroups of Linear
Periodicity of a class of nonlinear fuzzy systems with delays
Energy Technology Data Exchange (ETDEWEB)
Yu Jiali [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: yujiali@uestc.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: zhangyi@uestc.edu.cn; Zhang Lei [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: leilazhang@uestc.edu.cn
2009-05-15
The well known Takagi-Sugeno (T-S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T-S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T-S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Asymptotic stability and stabilizability of nonlinear systems with delay.
Srinivasan, V; Sukavanam, N
2016-11-01
This paper is concerned with asymptotic stability and stabilizability of a class of nonlinear dynamical systems with fixed delay in state variable. New sufficient conditions are established in terms of the system parameters such as the eigenvalues of the linear operator, delay parameter, and bounds on the nonlinear parts. Finally, examples are given to testify the effectiveness of the proposed theory.
Nonlinear robust hierarchical control for nonlinear uncertain systems
Directory of Open Access Journals (Sweden)
Leonessa Alexander
1999-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
Can weakly nonlinear theory explain Faraday wave patterns near onset?
Skeldon, A C
2015-01-01
The Faraday problem is an important pattern-forming system that provides some middle ground between systems where the initial instability involves just a single mode and in which complexity then results from mode interactions or secondary bifurcations, and cases where a system is highly turbulent and many spatial and temporal modes are excited. It has been a rich source of novel patterns and of theoretical work aimed at understanding how and why such patterns occur. Yet it is particularly challenging to tie theory to experiment: the experiments are difficult to perform; the parameter regime of interest (large box, moderate viscosity) along with the technical difficulties of solving the free boundary Navier--Stokes equations make numerical solution of the problem hard; and the fact that the instabilities result in an entire circle of unstable wavevectors presents considerable theoretical difficulties. In principle, weakly nonlinear theory should be able to predict which patterns are stable near pattern onset. ...
A nonlinear variable structure stabilizer for power system stability
Energy Technology Data Exchange (ETDEWEB)
Cao, Y.; Jiang, L.; Cheng, S.; Chen, D. (Huazhong Univ. of Science and Technology, Wuhan (China). Dept. of Electrical Power Engineering); Malik, O.P.; Hope, G.S. (Univ. of Calgary, Alberta (Canada). Dept. of Electrical and Computer Engineering)
1994-09-01
A nonlinear variable structure stabilizer is proposed in this paper. Design of this stabilizer involves the nonlinear transformation technique, the variable structure control technique and the linear system theory. Performance of the proposed nonlinear variable structure controller in a single machine connected to an infinite bus power and a multi-machine system with multi-mode oscillations is simulated. The responses of the system with the proposed stabilizer are compared with those obtained with some other kinds of stabilizers when the system is subjected to a variety of disturbances. Simulation results show that the nonlinear variable structure stabilizer gives satisfactory dynamic performance and good robustness.
Nonlinear solar cycle forecasting: theory and perspectives
Directory of Open Access Journals (Sweden)
A. L. Baranovski
2008-02-01
Full Text Available In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters – the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
Exact Controllability for a Class of Nonlinear Evolution Control Systems
Institute of Scientific and Technical Information of China (English)
L¨u Yue; Li Yong
2015-01-01
In this paper, we study the exact controllability of the nonlinear control systems. The controllability results by using the monotone operator theory are es-tablished. No compactness assumptions are imposed in the main results.
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
Institute of Scientific and Technical Information of China (English)
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Nonlinear effective-medium theory of disordered spring networks.
Sheinman, M; Broedersz, C P; MacKintosh, F C
2012-02-01
Disordered soft materials, such as fibrous networks in biological contexts, exhibit a nonlinear elastic response. We study such nonlinear behavior with a minimal model for networks on lattice geometries with simple Hookian elements with disordered spring constant. By developing a mean-field approach to calculate the differential elastic bulk modulus for the macroscopic network response of such networks under large isotropic deformations, we provide insight into the origins of the strain stiffening and softening behavior of these systems. We find that the nonlinear mechanics depends only weakly on the lattice geometry and is governed by the average network connectivity. In particular, the nonlinear response is controlled by the isostatic connectivity, which depends strongly on the applied strain. Our predictions for the strain dependence of the isostatic point as well as the strain-dependent differential bulk modulus agree well with numerical results in both two and three dimensions. In addition, by using a mapping between the disordered network and a regular network with random forces, we calculate the nonaffine fluctuations of the deformation field and compare them to the numerical results. Finally, we discuss the limitations and implications of the developed theory.
Shahnazi, Reza
2015-01-01
An adaptive fuzzy output feedback controller is proposed for a class of uncertain MIMO nonlinear systems with unknown input nonlinearities. The input nonlinearities can be backlash-like hysteresis or dead-zone. Besides, the gains of unknown input nonlinearities are unknown nonlinear functions. Based on universal approximation theorem, the unknown nonlinear functions are approximated by fuzzy systems. The proposed method does not need the availability of the states and an observer based on strictly positive real (SPR) theory is designed to estimate the states. An adaptive robust structure is used to cope with fuzzy approximation error and external disturbances. The semi-global asymptotic stability of the closed-loop system is guaranteed via Lyapunov approach. The applicability of the proposed method is also shown via simulations.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2).
Zhang, Ruoxun; Tian, Gang; Yang, Shiping; Cao, Hefei
2015-05-01
This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.
Nonlinear input-output systems
Hunt, L. R.; Luksic, Mladen; Su, Renjeng
1987-01-01
Necessary and sufficient conditions that the nonlinear system dot-x = f(x) + ug(x) and y = h(x) be locally feedback equivalent to the controllable linear system dot-xi = A xi + bv and y = C xi having linear output are found. Only the single input and single output case is considered, however, the results generalize to multi-input and multi-output systems.
Deterministic nonlinear systems a short course
Anishchenko, Vadim S; Strelkova, Galina I
2014-01-01
This text is a short yet complete course on nonlinear dynamics of deterministic systems. Conceived as a modular set of 15 concise lectures it reflects the many years of teaching experience by the authors. The lectures treat in turn the fundamental aspects of the theory of dynamical systems, aspects of stability and bifurcations, the theory of deterministic chaos and attractor dimensions, as well as the elements of the theory of Poincare recurrences.Particular attention is paid to the analysis of the generation of periodic, quasiperiodic and chaotic self-sustained oscillations and to the issue of synchronization in such systems. This book is aimed at graduate students and non-specialist researchers with a background in physics, applied mathematics and engineering wishing to enter this exciting field of research.
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
Nonlinear dynamics in biological systems
Carballido-Landeira, Jorge
2016-01-01
This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...
Super Yang-Mills theory from nonlinear supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Shima, Kazunari, E-mail: shima@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology Fukaya, Saitama 369-0293 (Japan); Tsuda, Motomu, E-mail: tsuda@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology Fukaya, Saitama 369-0293 (Japan)
2010-04-05
The relation between a nonlinear supersymmetric (NLSUSY) theory and a SUSY Yang-Mills (SYM) theory is studied for N=3 SUSY in two-dimensional space-time. We explicitly show the NL/L SUSY relation for the (pure) SYM theory by means of cancellations among Nambu-Goldstone fermion self-interaction terms.
Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion
Directory of Open Access Journals (Sweden)
Jun Wang
2013-01-01
Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.
Nonlinear theory of magnetic Landau damping
Energy Technology Data Exchange (ETDEWEB)
Kirpichnikov, A.P.; Yusupov, I.U.
1978-05-01
The nonlinear Cerenkov damping of helical electromagnetic waves in a magnetized plasma is analyzed. The nonlinear mechanism which leads to oscillations in the wave amplitude and limits the damping is the trapping of resonant particles in the potential well of the wave, as in the O'Neil problem. The factors of the type exp (-..cap alpha..t/sup 2/) in the expression for the nonlinear damping rate for a Maxwellian particle distribution lead to a damping of the amplitude oscillations of the helical wave which is much more rapid than for a plasma wave.
Nonlinear elliptic systems with exponential nonlinearities
Directory of Open Access Journals (Sweden)
Said El Manouni
2002-12-01
Full Text Available In this paper we investigate the existence of solutions for {gather*} -mathop{m div}( a(| abla u | ^N| abla u |^{N-2}u = f(x,u,v quad mbox{in } Omega -mathop{m div}(a(| abla v| ^N| abla v |^{N-2}v = g(x,u,v quad mbox{in } Omega u(x = v(x = 0 quad mbox{on }partial Omega. end{gather*} Where $Omega$ is a bounded domain in ${mathbb{R}}^N$, $Ngeq 2$, $f$ and $g$ are nonlinearities having an exponential growth on $Omega$ and $a$ is a continuous function satisfying some conditions which ensure the existence of solutions.
VARIANCE OF NONLINEAR PHASE NOISE IN FIBER-OPTIC SYSTEM
RANJU KANWAR; SAMEKSHA BHASKAR
2013-01-01
In communication system, the noise process must be known, in order to compute the system performance. The nonlinear effects act as strong perturbation in long- haul system. This perturbation effects the signal, when interact with amplitude noise, and results in random motion of the phase of the signal. Based on the perturbation theory, the variance of nonlinear phase noise contaminated by both self- and cross-phase modulation, is derived analytically for phase-shift- keying system. Through th...
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Directory of Open Access Journals (Sweden)
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
Theory of nonlinear elastic behavior in rock
Energy Technology Data Exchange (ETDEWEB)
McCall, K.R.
1993-04-01
We study plane wave propagation in an isotropic, homogeneous solid with cubic and quartic anharmonicity. Attenuation is introduced through use of a retarded displacement response. We develop a Green function technique to exhibit the solution for the displacement field as a systematic hierarchy in the nonlinear parameters. This solution is applied to three problems: propagation from monochromatic and broadband sources, and the shape of nonlinear stress curves.
Theory of nonlinear elastic behavior in rock
Energy Technology Data Exchange (ETDEWEB)
McCall, K.R.
1993-01-01
We study plane wave propagation in an isotropic, homogeneous solid with cubic and quartic anharmonicity. Attenuation is introduced through use of a retarded displacement response. We develop a Green function technique to exhibit the solution for the displacement field as a systematic hierarchy in the nonlinear parameters. This solution is applied to three problems: propagation from monochromatic and broadband sources, and the shape of nonlinear stress curves.
Spectral decomposition of nonlinear systems with memory.
Svenkeson, Adam; Glaz, Bryan; Stanton, Samuel; West, Bruce J
2016-02-01
We present an alternative approach to the analysis of nonlinear systems with long-term memory that is based on the Koopman operator and a Lévy transformation in time. Memory effects are considered to be the result of interactions between a system and its surrounding environment. The analysis leads to the decomposition of a nonlinear system with memory into modes whose temporal behavior is anomalous and lacks a characteristic scale. On average, the time evolution of a mode follows a Mittag-Leffler function, and the system can be described using the fractional calculus. The general theory is demonstrated on the fractional linear harmonic oscillator and the fractional nonlinear logistic equation. When analyzing data from an ill-defined (black-box) system, the spectral decomposition in terms of Mittag-Leffler functions that we propose may uncover inherent memory effects through identification of a small set of dynamically relevant structures that would otherwise be obscured by conventional spectral methods. Consequently, the theoretical concepts we present may be useful for developing more general methods for numerical modeling that are able to determine whether observables of a dynamical system are better represented by memoryless operators, or operators with long-term memory in time, when model details are unknown.
A nonlinear theory of tensor distributions
Vickers, J A
1998-01-01
The coordinate invariant theory of generalised functions of Colombeau and Meril is reviewed and extended to enable the construction of multi-index generalised tensor functions whose transformation laws coincide with their counterparts in classical distribution theory.
Dynamical Systems On Weighted Lattices: General Theory
Maragos, Petros
2016-01-01
In this work a theory is developed for unifying large classes of nonlinear discrete-time dy- namical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces which we call complete weighted lat- tices and include as special cases the nonlinear vector spaces of minimax algebra. Their algebraic structure has a polygonal geometry. Some of the special cases unified include max-plus, max- product, and probabilistic...
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
Nonlinearity of colloid systems oxyhydrate systems
Sucharev, Yuri I
2008-01-01
The present monograph is the first systematic study of the non-linear characteristic of gel oxy-hydrate systems involving d- and f- elements. These are the oxyhydrates of rare-earth elements and oxides - hydroxides of d- elements (zirconium, niobium, titanium, etc.) The non-linearity of these gel systems introduces fundamental peculiarities into their structure and, consequently, their properties. The polymer-conformational diversity of energetically congenial gel fragments, which continu-ously transform under the effect of, for instance, system dissipation heat, is central to the au-thor's hy
Control of nonlinear systems with applications
Pan, Haizhou
In practical applications of feedback control, most actuators exhibit physical constraints that limit the control amplitude and/or rate. The principal challenge of control design problem for linear systems with input constraints is to ensure closed-loop stability and yield a good transient performance in the presence of amplitude and/or rate-limited control. Since actuator saturation manifests itself as a nonlinear behavior in an otherwise linear system, the development of a nonconservative saturation control design methodology poses a significant challenge. In particular, it is well known that unstable linear systems can be stabilized using smooth controllers only in a local sense in the presence of actuator saturation. Thus, it is of paramount importance to develop a saturation control design methodology that yields a nonconservative estimate of the stability domain for closed-loop system. The first part of this research focuses on a numerically tractable formulation of the control synthesis problem for linear systems with actuator amplitude and rate saturation nonlinearity using a linear-matrix-inequality (LMI) framework. Following the recent trend in the actuator saturation control research, we (i) utilize absolute stability theory to ensure closed-loop stability and (ii) minimize a quadratic cost to account for the closed-loop system performance degradation. In order to reduce the inherent conservatism of the absolute stability based saturation control framework, we exploit stability multipliers (of, e.g., weighted circle criterion, Popov criterion, etc.). For the control of linear systems with simultaneous actuator amplitude and rate saturation nonlinearities, by virtue of a rate limiter that is predicated on designing the control amplitude and then computing the control rates, we directly account for rate constraints. Both continuous- and discrete-time systems with actuator saturation are considered. A number of design examples are presented to demonstrate
Nonlinear Galerkin Optimal Truncated Low—dimensional Dynamical Systems
Institute of Scientific and Technical Information of China (English)
ChuijieWU
1996-01-01
In this paper,a new theory of constructing nonlinear Galerkin optimal truncated Low-Dimensional Dynamical Systems(LDDSs) directly from partial differential equations has been developed.Applying the new theory to the nonlinear Burgers' equation,it is shown that a nearly perfect LDDS can be gotten,and the initial-boundary conditions are automatically included in the optimal bases.The nonlinear Galerkin method does not have advantages within the optimization process,but it can significantly improve the results,after the Galerkin optimal bases have been gotten.
A Stability Theory in Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We propose a new method for finding the local optimal points ofthe constrained nonlinear programming by Ordinary Differential Equations (ODE), and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
Nonlinear theory of autooscillations of quasiplanar interface during directional solidification
Lubashevsky, I A; Keijan, M G
1998-01-01
Within the framework of the frozen temperature approximation we develop a strongly-nonlinear theory of one-dimensional pattern formation during directional solidification of binary mixture under nonequilibrium segregation. In the case of small partition coefficient the full problem is reduced to the system of two ordinary differential equations describing the interface motion in terms of its velocity and position coordinate. The type of the oscillatory instability bifurcation is studied in detail in different limits. For the subcrytical bifurcaton relaxation interface oscillations are analyzed analytically and numerically. We show that these oscillation exibit a number of anomalous properies. In particular, such oscillations can be weakly- or strongly-dissipative depending on the physical parameters and the amplitude of the strongly-dissipative oscillations is determined not only by the form of the corresponding nullcline but also by the behavior of the system for small values of the interface velocity. Chara...
On SL(2,R) symmetry in nonlinear electrodynamics theories
Babaei Velni, Komeil; Babaei-Aghbolagh, H.
2016-12-01
Recently, it has been observed that the Noether-Gaillard-Zumino (NGZ) identity holds order by order in α‧ expansion in nonlinear electrodynamics theories as Born-Infeld (BI) and Bossard-Nicolai (BN). The nonlinear electrodynamics theory that couples to an axion field is invariant under the SL (2 , R) duality in all orders of α‧ expansion in the Einstein frame. In this paper we show that there are the SL (2 , R) invariant forms of the energy momentum tensors of axion-nonlinear electrodynamics theories in the Einstein frame. These SL (2 , R) invariant structures appear in the energy momentum tensors of BI and BN theories at all orders of α‧ expansion. The SL (2 , R) symmetry appears in the BI and BN Lagrangians as a multiplication of Maxwell Lagrangian and a series of SL (2 , R) invariant structures.
On SL(2;R) symmetry in nonlinear electrodynamics theories
Velni, Komeil Babaei
2016-01-01
Recently, it has been observed that the Noether-Gaillard-Zumino (NGZ) identity holds order by order in $\\alpha'$ expansion in nonlinear electrodynamics theories as Born-Infeld (BI) and Bossard-Nicolai (BN). The nonlinear electrodynamics theory that couples to an axion field is invariant under the $SL(2,R)$ duality in all orders of $\\alpha'$ expansion in the Einstein frame. In this paper we show that there are the $SL(2,R)$ invariant forms of the energy momentum tensors of axion-nonlinear electrodynamics theories in the Einstein frame. These $SL(2,R)$ invariant structures appear in the energy momentum tensors of BI and BN theories at all orders of $\\alpha'$ expansion. The $SL(2,R)$ symmetry appears in the BI and BN Lagrangians as a multiplication of Maxwell Lagrangian and a series of $SL(2,R)$ invariant structures.
Non-linear Systems and Educational Development in Europe.
Reilly, David H.
1999-01-01
European educational systems are under immense pressure to change, develop, improve, and satisfy many conflicting demands. Educational development and improvement in these countries is unlikely to progress in a neat, orderly, and linear fashion. Applying nonlinear (chaos) theory to development theory may aid understanding of educational…
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Nonlinear physical systems spectral analysis, stability and bifurcations
Kirillov, Oleg N
2013-01-01
Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems.Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynam
Nonlinear systems techniques for dynamical analysis and control
Lefeber, Erjen; Arteaga, Ines
2017-01-01
This treatment of modern topics related to the control of nonlinear systems is a collection of contributions celebrating the work of Professor Henk Nijmeijer and honoring his 60th birthday. It addresses several topics that have been the core of Professor Nijmeijer’s work, namely: the control of nonlinear systems, geometric control theory, synchronization, coordinated control, convergent systems and the control of underactuated systems. The book presents recent advances in these areas, contributed by leading international researchers in systems and control. In addition to the theoretical questions treated in the text, particular attention is paid to a number of applications including (mobile) robotics, marine vehicles, neural dynamics and mechanical systems generally. This volume provides a broad picture of the analysis and control of nonlinear systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participan...
Nonlinear cross Gramians and gradient systems
Ionescu, T. C.; Scherpen, J.M.A.
2007-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain linearization results that precisely correspond to the notion of a cross Gramian for symmetric linear systems. Furthermore, first steps towards relations with the singular value functions of the nonlinear Han...
Introduction to the theory of nonlinear optimization
Jahn, Johannes
2007-01-01
This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba
A Nonlinear Theory for Smart Composite Structures
Chattopadhyay, Aditi
2002-01-01
The paper discusses the following: (1) Development of a completely coupled thermo-piezoelectric-mechanical theory for the analysis of composite shells with segmented and distributed piezoelectric sensor/actuators and shape memory alloys. The higher order displacement theory will be used to capture the transverse shear effects in anisotropic composites. The original theory will be modified to satisfy the stress continuity at ply interfaces. (2) Development of a finite element technique to implement the mathematical model. (3) Investigation of the coupled structures/controls interaction problem to study the complex trade-offs associated with the coupled problem.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
Peterson, D.
1979-01-01
Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.
Numerical studies of identification in nonlinear distributed parameter systems
Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.
1989-01-01
An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.
Computing abstractions of nonlinear systems
Reißig, Gunther
2009-01-01
We present an efficient algorithm for computing discrete abstractions of arbitrary memory span for nonlinear discrete-time and sampled systems, in which, apart from possibly numerically integrating ordinary differential equations, the only nontrivial operation to be performed repeatedly is to distinguish empty from non-empty convex polyhedra. We also provide sufficient conditions for the convexity of attainable sets, which is an important requirement for the correctness of the method we propose. It turns out that requirement can be met under rather mild conditions, which essentially reduce to sufficient smoothness in the case of sampled systems. Practicability of our approach in the design of discrete controllers for continuous plants is demonstrated by an example.
Nonlinear Control for SVG Based On Generalized Hamiltonian System Theory%基于广义Hamilton系统理论的SVG非线性控制
Institute of Scientific and Technical Information of China (English)
张敏; 黄强
2013-01-01
Considering nonlinear and energy dissipation characteristics of SVG,the nonlinear controller is designed based on generalized Hamiltonian system realization for the model of SVG.The paper discusses the generalized Hamiltonian system and its realization,establishes nonlinear dynamic model accordingto the principle of SVG.Based on the characteristics of system model,the appropriate structure matrix and function of Hamilton are selected and realization of the generalized Hamiltonian system is carried on.In accordance with the generalized Hamiltonian system of SVG,the paper quotes control method of L2 interference rejection,and designs nonlinear controller for SVG operating in one-load-infinite-bus system.Digital simulation results realized by PSASP show that designed controller of different load obtains better compensation effect and be able to maintain the stability of the bus voltage.%考虑静止无功发生器(static var generator,SVG)的非线性和能量耗散特性,基于系统模型的广义Hamilton系统实现,设计非线性控制器.论述了广义Hamilton系统及其实现问题.针对SVG的工作原理建立其非线性动态模型,依据系统模型特性,选取适当的结构矩阵和Hamilton函数,完成了系统的广义Hamilton实现.针对SVG模型的广义Hamilton实现,引用L2干扰抑制控制方法,设计单负荷-无穷大系统中运行的SVG非线性控制器,并利用电力系统分析综合软件(PSASP)对所设计的控制器进行不同负载情况下的仿真,数字仿真结果表明了控制器有较好的补偿效果,并能够维持负载母线电压的稳定.
Rigatos, Gerasimos G
2015-01-01
This monograph presents recent advances in differential flatness theory and analyzes its use for nonlinear control and estimation. It shows how differential flatness theory can provide solutions to complicated control problems, such as those appearing in highly nonlinear multivariable systems and distributed-parameter systems. Furthermore, it shows that differential flatness theory makes it possible to perform filtering and state estimation for a wide class of nonlinear dynamical systems and provides several descriptive test cases. The book focuses on the design of nonlinear adaptive controllers and nonlinear filters, using exact linearization based on differential flatness theory. The adaptive controllers obtained can be applied to a wide class of nonlinear systems with unknown dynamics, and assure reliable functioning of the control loop under uncertainty and varying operating conditions. The filters obtained outperform other nonlinear filters in terms of accuracy of estimation and computation speed. The bo...
Nonlinear Acoustics -- Perturbation Theory and Webster's Equation
Jorge, Rogério
2013-01-01
Webster's horn equation (1919) offers a one-dimensional approximation for low-frequency sound waves along a rigid tube with a variable cross-sectional area. It can be thought as a wave equation with a source term that takes into account the nonlinear geometry of the tube. In this document we derive this equation using a simplified fluid model of an ideal gas. By a simple change of variables, we convert it to a Schr\\"odinger equation and use the well-known variational and perturbative methods to seek perturbative solutions. As an example, we apply these methods to the Gabriel's Horn geometry, deriving the first order corrections to the linear frequency. An algorithm to the harmonic modes in any order for a general horn geometry is derived.
Nonlinear Control and Discrete Event Systems
Meyer, George; Null, Cynthia H. (Technical Monitor)
1995-01-01
As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.
Nonlinear cross Gramians and gradient systems
Ionescu, T. C.; Scherpen, J. M. A.
2007-01-01
We study the notion of cross Gramians for nonlinear gradient systems, using the characterization in terms of prolongation and gradient extension associated to the system. The cross Gramian is given for the variational system associated to the original nonlinear gradient system. We obtain
First order devices, hybrid memristors, and the frontiers of nonlinear circuit theory
Riaza, Ricardo
2010-01-01
Several devices exhibiting memory effects have shown up in nonlinear circuit theory in recent years. Among others, these circuit elements include Chua's memristors, as well as memcapacitors and meminductors. These and other related devices seem to be beyond the, say, classical scope of circuit theory, which is formulated in terms of resistors, capacitors, inductors, and voltage and current sources. We explore in this paper the potential extent of nonlinear circuit theory by classifying such mem-devices in terms of the variables involved in their constitutive relations and the notions of the differential- and the state-order of a device. Within this framework, the frontier of first order circuit theory is defined by so-called hybrid memristors, which are proposed here to accommodate a characteristic relating all four fundamental circuit variables. Devices with differential order two and mem-systems are discussed in less detail. We allow for fully nonlinear characteristics in all circuit elements, arriving at a...
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...
Annual Progress Report. [Linear and nonlinear instability theory
Energy Technology Data Exchange (ETDEWEB)
Simon, A.; Catto, P.J.
1978-09-11
A number of topics in nonlinear and linear instability theory are covered in this report. The nonlinear saturation of the dissipative trapped electron instability is evaluated and its amplitude compares well with existing experimental observations. The nonlinear saturation of the drift cyclotron loss-cone mode is carried out for a variety of empty loss-cone distributions. The saturation amplitude is predicted to be small and stable. An improved linear theory of the collisionless drift instability in sheared magnetic fields yields the surprising result that no instability occurs for a wide range of parameters. Finally, the bump-on-tail calculation is shown to be unchanged by some recent results of Case and Siewart, and a rough time scale is established for the transition from the O'Neil trapping regime to the final time-asymptotic result.
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
Nonlinear Hyperbolic-Parabolic System Modeling Some Biological Phenomena
Institute of Scientific and Technical Information of China (English)
WU Shaohua; CHEN Hua
2011-01-01
In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.
Ordinary matter in nonlinear affine gauge theories of gravitation
Tiemblo, A; Tiemblo, A; Tresguerres, R
1994-01-01
We present a general framework to include ordinary fermionic matter in the metric--affine gauge theories of gravity. It is based on a nonlinear gauge realization of the affine group, with the Lorentz group as the classification subgroup of the matter and gravitational fields.
Major open problems in chaos theory and nonlinear dynamics
Li, Y Charles
2013-01-01
Nowadays, chaos theory and nonlinear dynamics lack research focuses. Here we mention a few major open problems: 1. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4. the paradox of enrichment, 5. the paradox of pesticides, 6. the paradox of plankton.
Nonlinear density fluctuation field theory for large scale structure
Institute of Scientific and Technical Information of China (English)
Yang Zhang; Hai-Xing Miao
2009-01-01
We develop an effective field theory of density fluctuations for a Newtonian self-gravitating N-body system in quasi-equilibrium and apply it to a homogeneous uni-verse with small density fluctuations. Keeping the density fluctuations up to second or-der, we obtain the nonlinear field equation of 2-pt correlation ξ(r), which contains 3-pt correlation and formal ultra-violet divergences. By the Groth-Peebles hierarchical ansatz and mass renormalization, the equation becomes closed with two new terms beyond the Gaussian approximation, and their coefficients are taken as parameters. The analytic solu-tion is obtained in terms of the hypergeometric functions, which is checked numerically.With one single set of two fixed parameters, the correlation ξ(r) and the corresponding power spectrum P(k) simultaneously match the results from all the major surveys, such as APM, SDSS, 2dfGRS, and REFLEX. The model gives a unifying understanding of several seemingly unrelated features of large scale structure from a field-theoretical per-spective. The theory is worth extending to study the evolution effects in an expanding universe.
Discontinuity and complexity in nonlinear physical systems
Baleanu, Dumitru; Luo, Albert
2014-01-01
This unique book explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fractional dynamics and Lie group analysis for nonlinear partial differential equations. Part II covers chaos and complexity in nonlinear Hamiltonian systems, important to understand the resonance interactions in nonlinear dynamical systems, such as Tsunami waves and wildfire propagations; as well as Lev flights in chaotic trajectories, dynamical system synchronization and DNA information complexity analysis. Part III examines chaos and periodic motions in discontinuous dynamical systems, extensively present in a range of systems, including piecewise linear systems, vibro-impact systems and drilling systems in engineering. And in Part IV, engineering and financial nonlinearity are discussed. The mechanism of shock wave with saddle-node bifurcation and rotating disk stability will be presented, and the financial nonlinear models will be discussed....
Non-linear theory of elasticity
Lurie, AI
2012-01-01
This book examines in detail the Theory of Elasticity which is a branch of the mechanics of a deformable solid. Special emphasis is placed on the investigation of the process of deformation within the framework of the generally accepted model of a medium which, in this case, is an elastic body. A comprehensive list of Appendices is included providing a wealth of references for more in depth coverage. The work will provide both a stimulus for future research in this field as well as useful reference material for many years to come.
Nonlinear control for dual quaternion systems
Price, William D.
The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE(3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is
Reconstructing the Nonlinear Dynamical Systems by Evolutionary Computation Techniques
Institute of Scientific and Technical Information of China (English)
LIU Minzhong; KANG Lishan
2006-01-01
We introduce a new dynamical evolutionary algorithm(DEA) based on the theory of statistical mechanics and investigate the reconstruction problem for the nonlinear dynamical systems using observation data. The convergence of the algorithm is discussed. We make the numerical experiments and test our model using the two famous chaotic systems (mainly the Lorenz and Chen systems ). The results show the relatively accurate reconstruction of these chaotic systems based on observational data can be obtained. Therefore we may conclude that there are broad prospects using our method to model the nonlinear dynamical systems.
Research on Nonlinear Dynamical Systems.
1983-01-10
investigated fundamental aspects of functional differential equations, including qualitative questions (stability, nonlinear oscillations ), in 142,45,47,52...Bifurcation in the Duffing equation with several parameters, II. Proc. of the Royal Society of Edinburgh, Series A, 79A (1977), pp.317-326. 1I.J (with ;Ibtoas...Lecture Notes in Mathematics, Vol. 730 (1979). [54] Nonlinear oscillations in equations with delays. Proc. at A.M.S. 10th Summer Seminar on Nonlinear
Iterative Solution for Systems of Nonlinear Two Binary Operator Equations
Institute of Scientific and Technical Information of China (English)
ZHANGZhi-hong; LIWen-feng
2004-01-01
Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are imnroved and generalized.
Robust stabilization for a class of nonlinear networked control systems
Institute of Scientific and Technical Information of China (English)
Jinfeng GAO; Hongye SU; Xiaofu JI; Jian CHU
2008-01-01
The problem of robust stabilization for a class of uncertain networked control systems(NCSs)with nonlinearities satisfying a given sector condition is investigated in this paper.By introducing a new model of NCSs with parameter uncertainty,network.induced delay,nonlinearity and data packet dropout in the transmission,a strict linear matrix inequality(LMI)criterion is proposed for robust stabilization of the uncenmn nonlinear NCSs based on the Lyapunov stability theory.The maximum allowable transfer interval(MATI)can be derived by solving the feasibility problem of the corresponding LMI.Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.
Stability of fractional positive nonlinear systems
Directory of Open Access Journals (Sweden)
Kaczorek Tadeusz
2015-12-01
Full Text Available The conditions for positivity and stability of a class of fractional nonlinear continuous-time systems are established. It is assumed that the nonlinear vector function is continuous, satisfies the Lipschitz condition and the linear part is described by a Metzler matrix. The stability conditions are established by the use of an extension of the Lyapunov method to fractional positive nonlinear systems.
Hruška, Vlastimil; Svobodová, Jana; Beneš, Martin; Gaš, Bohuslav
2012-12-07
We introduce a new nonlinear electrophoretic model for complex-forming systems with a fully charged analyte and a neutral ligand. The background electrolyte is supposed to be composed of two constituents, which do not interact with the ligand. In order to characterize the electromigration dispersion (EMD) of the analyte zone we define a new parameter, the nonlinear electromigration mobility slope, S(EMD,A). The parameter can be easily utilized for quantitative prediction of the EMD and for comparisons of the model with the simulated and experimental profiles. We implemented the model to the new version of PeakMaster 5.3 Complex that can calculate some characteristic parameters of the electrophoretic system and can plot the dependence of S(EMD,A) on the concentration of the ligand. Besides S(EMD,A), also the relative velocity slope, S(X), can be calculated. It is commonly used as a measure of EMD in electrophoretic systems. PeakMaster 5.3 Complex software can be advantageously used for optimization of the separation conditions to avoid high EMD in complexing systems. Based on the theoretical model we analyze the S(EMD,A) and reveal that this parameter is composed of six terms. We show that the major factor responsible for the electromigration dispersion in complex-forming electrophoretic systems is the complexation equilibrium and particularly its impact on the effective mobility of the analyte. To prove the appropriateness of the model we showed that there is a very good agreement between peak shapes calculated by PeakMaster 5.3 Complex (plotted using the HVLR function) and the profiles simulated by means of Simul 5 Complex. The detailed experimental verification of the new mode of PeakMaster 5.3 Complex is in the next part IV of the series.
Backward stochastic differential equations from linear to fully nonlinear theory
Zhang, Jianfeng
2017-01-01
This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Stability Analysis and Design for Nonlinear Singular Systems
Yang, Chunyu; Zhou, Linna
2013-01-01
Singular systems which are also referred to as descriptor systems, semi-state systems, differential- algebraic systems or generalized state-space systems have attracted much attention because of their extensive applications in the Leontief dynamic model, electrical and mechanical models, etc. This monograph presented up-to-date research developments and references on stability analysis and design of nonlinear singular systems. It investigated the problems of practical stability, strongly absolute stability, input-state stability and observer design for nonlinear singular systems and the problems of absolute stability and multi-objective control for nonlinear singularly perturbed systems by using Lyapunov stability theory, comparison principle, S-procedure and linear matrix inequality (LMI), etc. Practical stability, being quite different from stability in the sense of Lyapunov, is a significant performance specification from an engineering point of view. The basic concepts and results on practical stability f...
Stability analysis of nonlinear systems with slope restricted nonlinearities.
Liu, Xian; Du, Jiajia; Gao, Qing
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Directory of Open Access Journals (Sweden)
Xian Liu
2014-01-01
Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
DISTURBANCE ATTENUATION FOR UNCERTAIN NONLINEAR CASCADED SYSTEMS
Institute of Scientific and Technical Information of China (English)
BI Weiping; MU Xiaowu; SUN Yuqiang
2004-01-01
In present paper, the disturbance attenuation problem of uncertain nonlinear cascaded systems is studied. Based on the adding one power integrator technique and recursive design, a feedback controller that solves the disturbance attenuation problem is constructed for uncertain nonlinear cascaded systems with internal stability.
Stamovlasis, Dimitrios
2011-04-01
In this study, an attempt is made to integrate Nonlinear Dynamical Systems theory and neo-Piagetian theories applied to creative mental processes, such as problem solving. A catastrophe theory model is proposed, which implements three neo-Piagetian constructs as controls: the functional M-capacity as asymmetry and logical thinking and the degree of field dependence independence as bifurcation. Data from achievement scores of students in tenth grade physics were analyzed using dynamic difference equations and statistical regression techniques. The cusp catastrophe model proved superior comparing to the pre-post linear counterpart and demonstrated nonlinearity at the behavioral level. The nonlinear phenomenology, such as hysteresis effects and bifurcation, is explained by an analysis, which provides a causal interpretation via the mathematical theory of self-organization and thus building bridges between NDS-theory concepts and neo-Piagetian theories. The contribution to theory building is made, by also addressing the emerging philosophical, - ontological and epistemological- questions about the processes of problem solving and creativity.
Non-linearities in Theory-of-Mind Development
Blijd-Hoogewys, Els M. A.; van Geert, Paul L. C.
2017-01-01
Research on Theory-of-Mind (ToM) has mainly focused on ages of core ToM development. This article follows a quantitative approach focusing on the level of ToM understanding on a measurement scale, the ToM Storybooks, in 324 typically developing children between 3 and 11 years of age. It deals with the eventual occurrence of developmental non-linearities in ToM functioning, using smoothing techniques, dynamic growth model building and additional indicators, namely moving skewness, moving growth rate changes and moving variability. The ToM sum-scores showed an overall developmental trend that leveled off toward the age of 10 years. Within this overall trend two non-linearities in the group-based change pattern were found: a plateau at the age of around 56 months and a dip at the age of 72–78 months. These temporary regressions in ToM sum-score were accompanied by a decrease in growth rate and variability, and a change in skewness of the ToM data, all suggesting a developmental shift in ToM understanding. The temporary decreases also occurred in the different ToM sub-scores and most clearly so in the core ToM component of beliefs. It was also found that girls had an earlier growth spurt than boys and that the underlying developmental path was more salient in girls than in boys. The consequences of these findings are discussed from various theoretical points of view, with an emphasis on a dynamic systems interpretation of the underlying developmental paths. PMID:28101065
Nonlinear Robust Control Theory and Applications
1997-01-18
IEEE Transactions on Automatic Control , pp. 228-238...34Robustness in the presence of mixed parametric uncertainty and unmodelled dynamics," IEEE Transactions on Automatic Control , pp. 25-38, 1991. 8 [10...Letter, 1994. [14] B. Moore, "Principal component analysis of linear systems: Controllability, observ- ability and model reduction," IEEE Transactions on Automatic Control ,
Quantum Dynamics of Nonlinear Cavity Systems
Nation, Paul D.
2010-01-01
We investigate the quantum dynamics of three different configurations of nonlinear cavity systems. To begin, we carry out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector comprised of a SQUID with a mechanically compliant loop segment. The SQUID is approximated by a nonlinear current-dependent inductor, inducing a flux tunable nonlinear Duffing term in the cavity equation of motion. Expressions are derived for the detector signal ...
On global asymptotic controllability of planar affine nonlinear systems
Institute of Scientific and Technical Information of China (English)
SUN Yimin; GUO Lei
2005-01-01
In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input.This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.
Observability analysis of nonlinear systems using pseudo-linear transformation
Kawano, Yu; Ohtsuka, Toshiyuki
2013-01-01
In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear system
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Nonlinear dynamics non-integrable systems and chaotic dynamics
Borisov, Alexander
2017-01-01
This monograph reviews advanced topics in the area of nonlinear dynamics. Starting with theory of integrable systems – including methods to find and verify integrability – the remainder of the book is devoted to non-integrable systems with an emphasis on dynamical chaos. Topics include structural stability, mechanisms of emergence of irreversible behaviour in deterministic systems as well as chaotisation occurring in dissipative systems.
Finite-time disturbance attenuation of nonlinear systems
Institute of Scientific and Technical Information of China (English)
MO LiPo; JIA YingMin; ZHENG ZhiMing
2009-01-01
This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems.Based on the finite time Lyapunov stability theory,some finite-time H_∞ performance criterions are derived.Then the state-feedback control law is designed and the structure of such a controller is investigated.Furthermore,it is shown that the H_∞ controller can also make the closed-loop system satisfy finite-time H_∞ performance for nonlinear homogeneous systems.An example is provided to demonstrate the effectiveness of the presented results.
Applying linguistic theory to speech-language pathology: the case for nonlinear phonology.
Bernhardt, B; Gilbert, J
1992-01-01
Application of knowledge from many related fields benefits the practice of speech-language pathology. In the past 20 years, linguistic theory has provided a rich knowledge base for application. Phonological theories have provided frameworks for the description of the speech of unintelligible children in terms of coherent phonological systems, thus facilitating logical goal-setting for intervention. In this paper we suggest some of the possible implications of current nonlinear phonological frameworks for developmental phonology, and give an example of clinical application.
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
FORCED OSCILLATIONS IN NONLINEAR FEEDBACK CONTROL SYSTEM
Since a nonlinear feedback control system may possess more than one type of forced oscillations, it is highly desirable to investigate the type of...method for finding the existence of forced oscillations and response curve characteristics of a nonlinear feedback control system by means of finding the...second order feedback control system are investigated; the fundamental frequency forced oscillation for a higher order system and the jump resonance
Nonlinear identification of power electronic systems
Chau, KT; Chan, CC
1995-01-01
This paper presents a new approach to modelling power electronic systems using nonlinear system identification. By employing the nonlinear autoregressive moving average with exogenous input (NARMAX) technique, the parametric model of power electronic systems can be derived from the time-domain data. This approach possesses some advantages over available circuit-oriented modelling approaches, such as no small-signal approximation, no circuit idealization and no detailed knowledge of system ope...
Symmetries and semi-invariants in the analysis of nonlinear systems with control applications
Menini, Laura
2014-01-01
This volume details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations. The theory is developed for general nonlinear systems and specialized for the class of Hamiltonian systems.
Nonlinear electrodynamics coupled to teleparallel theory of gravity
Institute of Scientific and Technical Information of China (English)
Gamal G. L. Nashed
2011-01-01
Using nonlinear electrodynamics coupled to teleparallel theory of gravity, regular charged spherically symmetric solutions are obtained. The nonlinear theory is reduced to the Maxwell one in the weak limit and the solutions correspond to charged spacetimes. One of the obtained solutions contains an arbitrary function which we call general solution since we can generate from it the other solutions. The metric associated with these spacetimes is the same, i.e., regular charged static spherically symmetric black hole. In calculating the energy content of the general solution using the gravitational energy-momentum within the framework of the teleparallel geometry, we find that the resulting form depends on the arbitrary function. Using the regularized expression of the gravitational energy-momentum we obtain the value of energy.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [Theory Division, CERN, 1211 Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas, E-mail: diego.blas@cern.ch, E-mail: mathias.garny@desy.de, E-mail: Thomas.Konstandin@desy.de [DESY, Notkestr. 85, 22607 Hamburg (Germany)
2013-09-01
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Quadratic stabilization of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
DONG YaLi; FAN JiaoJiao; MEI ShengWei
2009-01-01
In this paper, the problem of quadratic stabilization of multi-input multi-output switched nonlinear systems under an arbitrary switching law is investigated. When switched nonlinear systems have uniform normal form and the zero dynamics of uniform normal form is asymptotically stable under an arbitrary switching law, state feedbacks are designed and a common quadratic Lyapunov function of all the closed-loop subsystems is constructed to realize quadratic stabilizability of the class of switched nonlinear systems under an arbitrary switching law. The results of this paper are also applied to switched linear systems.
Advances and applications in nonlinear control systems
Volos, Christos
2016-01-01
The book reports on the latest advances and applications of nonlinear control systems. It consists of 30 contributed chapters by subject experts who are specialized in the various topics addressed in this book. The special chapters have been brought out in the broad areas of nonlinear control systems such as robotics, nonlinear circuits, power systems, memristors, underwater vehicles, chemical processes, observer design, output regulation, backstepping control, sliding mode control, time-delayed control, variables structure control, robust adaptive control, fuzzy logic control, chaos, hyperchaos, jerk systems, hyperjerk systems, chaos control, chaos synchronization, etc. Special importance was given to chapters offering practical solutions, modeling and novel control methods for the recent research problems in nonlinear control systems. This book will serve as a reference book for graduate students and researchers with a basic knowledge of electrical and control systems engineering. The resulting design proce...
A Geometrically Nonlinear Phase Field Theory of Brittle Fracture
2014-10-01
tension. Int J Fract Mech 4:257–266 Voyiadjis G, Mozaffari N (2013) Nonlocal damage model using the phase field method: theory and applications. Int J... model of fracture. Computer simula- tions enable descriptions of fracture in brittle solids under complex loading conditions and for nonlinear and...Simple models based on the notion of theo- retical strength (Gilman1960;Clayton 2009, 2010) can provide insight into directionality of fracture
Microscopic theory of linear and nonlinear terahertz spectroscopy of semiconductors
Energy Technology Data Exchange (ETDEWEB)
Steiner, Johannes
2008-12-09
This Thesis presents a fully microscopic theory to describe terahertz (THz)-induced processes in optically-excited semiconductors. The formation process of excitons and other quasi-particles after optical excitation has been studied in great detail for a variety of conditions. Here, the formation process is not modelled but a realistic initial many-body state is assumed. In particular, the linear THz response is reviewed and it is demonstrated that correlated quasi-particles such as excitons and plasmons can be unambiguously detected via THz spectroscopy. The focus of the investigations, however, is on situations where the optically-excited many-body state is excited by intense THz fields. While weak pulses detect the many-body state, strong THz pulses control and manipulate the quasi-particles in a way that is not accessible via conventional techniques. The nonlinear THz dynamics of exciton populations is especially interesting because similarities and differences to optics with atomic systems can be studied. (orig.)
Nonlinear Integral Sliding Mode Control for a Second Order Nonlinear System
Directory of Open Access Journals (Sweden)
Xie Zheng
2015-01-01
Full Text Available A nonlinear integral sliding-mode control (NISMC scheme is proposed for second order nonlinear systems. The new control scheme is characterized by a nonlinear integral sliding manifold which inherits the desired properties of the integral sliding manifold, such as robustness to system external disturbance. In particular, compared with four kinds of sliding mode control (SMC, the proposed control scheme is able to provide better transient performances. Furthermore, the proposed scheme ensures the zero steady-state error in the presence of a constant disturbance or an asymptotically constant disturbance is proved by Lyapunov stability theory and LaSalle invariance principle. Finally, both the theoretical analysis and simulation examples demonstrate the validity of the proposed scheme.
Nonlinear dynamic theory for photorefractive phase hologram formation
Kim, D. M.; Shah, R. R.; Rabson, T. A.; Tittle, F. K.
1976-01-01
A nonlinear dynamic theory is developed for the formation of photorefractive volume phase holograms. A feedback mechanism existing between the photogenerated field and free-electron density, treated explicitly, yields the growth and saturation of the space-charge field in a time scale characterized by the coupling strength between them. The expression for the field reduces in the short-time limit to previous theories and approaches in the long-time limit the internal or photovoltaic field. Additionally, the phase of the space charge field is shown to be time-dependent.
Synthesis of robust nonlinear autopilots using differential game theory
Menon, P. K. A.
1991-01-01
A synthesis technique for handling unmodeled disturbances in nonlinear control law synthesis was advanced using differential game theory. Two types of modeling inaccuracies can be included in the formulation. The first is a bias-type error, while the second is the scale-factor-type error in the control variables. The disturbances were assumed to satisfy an integral inequality constraint. Additionally, it was assumed that they act in such a way as to maximize a quadratic performance index. Expressions for optimal control and worst-case disturbance were then obtained using optimal control theory.
Wan, W. M. V.; Lee, H. C.; Hui, P. M.; Yu, K. W.
1996-08-01
The effective response of random media consisting of two different kinds of strongly nonlinear materials with strong power-law nonlinearity is studied. Each component satisfies current density and electric-field relation of the form J=χ\\|E\\|βE. A simple self-consistent mean-field theory, which leads to a simple way in determining the average local electric field in each constituent, is introduced. Each component is assumed to have a conductivity depending on the averaged local electric field. The averaged local electric field is then determined self-consistently. Numerical simulations of the system are carried out on random nonlinear resistor networks. Theoretical results are compared with simulation data, and excellent agreements are found. Results are also compared with the Hashin-Shtrikman lower bound proposed by Ponte Castaneda et al. [Phys. Rev. B 46, 4387 (1992)]. It is found that the present theory, at small contrasts of χ between the two components, gives a result identical to that of Ponte Castaneda et al. up to second order of the contrast. The crossover and scaling behavior of the effective response near the percolation threshold as suggested by the present theory are discussed and demonstrated.
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Projective synchronization of chaotic systems with bidirectional nonlinear coupling
Indian Academy of Sciences (India)
Mohammada Ali Khan; Swarup Poria
2013-09-01
This paper presents a new scheme for constructing bidirectional nonlinear coupled chaotic systems which synchronize projectively. Conditions necessary for projective synchronization (PS) of two bidirectionally coupled chaotic systems are derived using Lyapunov stability theory. The proposed PS scheme is discussed by taking as examples the so-called unified chaotic model, the Lorenz–Stenflo system and the nonautonomous chaotic Van der Pol oscillator. Numerical simulation results are presented to show the efficiency of the proposed synchronization scheme.
Variable universe stable adaptive fuzzy control of nonlinear system
Institute of Scientific and Technical Information of China (English)
李洪兴; 苗志宏; 王加银
2002-01-01
A kind of stable adaptive fuzzy control of nonlinear system is implemented using variable universe method. First of all, the basic structure of variable universe adaptive fuzzy controllers is briefly introduced. Then the contraction-expansion factor that is a key tool of variable universe method is defined by means of integral regulation idea, and a kind of adaptive fuzzy controllers is designed by using such a contraction-expansion factor. The simulation on first order nonlinear system is done. Secondly, it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of Lyapunov theory. The simulation on the second order nonlinear system shows that its simulation effect is also quite good. Finally a useful tool, called symbolic factor, is proposed, which may be of universal significance. It can greatly reduce the settling time and enhance the robustness of the system.
Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay
Directory of Open Access Journals (Sweden)
Wenli Zhu
2013-01-01
Full Text Available Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to an n-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our results.
Linearization of Systems of Nonlinear Diffusion Equations
Institute of Scientific and Technical Information of China (English)
KANG Jing; QU Chang-Zheng
2007-01-01
We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...
Boundary Controllability of Nonlinear Fractional Integrodifferential Systems
Directory of Open Access Journals (Sweden)
Ahmed HamdyM
2010-01-01
Full Text Available Sufficient conditions for boundary controllability of nonlinear fractional integrodifferential systems in Banach space are established. The results are obtained by using fixed point theorems. We also give an application for integropartial differential equations of fractional order.
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...
Interactive optomechanical coupling with nonlinear polaritonic systems
Bobrovska, N; Liew, T C H; Kyriienko, O
2016-01-01
We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of the mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, being distinct from the previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, being quartic in the polariton number. We consider particular systems of exciton-polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to the interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher order terms give...
Chaotification for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Liu Na; Guan Zhi-Hong
2009-01-01
More and more attention has been focused on effectively generating chaos via simple physical devices. The problem of creating chaotic attractors is considered for a class of nonlinear systems with backlash function in this paper. By utilizing the Silnikov heteroclinic and homoclinic theorems, some sufficient conditions are established to guarantee that the nonlinear system has horseshoe-type chaos. Examples and simulations are given to verify the effectiveness of the theoretical results.
APPROXIMATE OUTPUT REGULATION FOR AFFINE NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Yali DONG; Daizhan CHENG; Huashu QIN
2003-01-01
Output regulation for affine nonlinear systems driven by an exogenous signal is investigated in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law.For affine nonlinear systems, the necessary and sufficient conditions of the solvability of approximate output regulation problem are obtained. The precise form of the control law is presented under some suitable assumptions.
Qualitative stability of nonlinear networked systems
Angulo, Marco Tulio; Slotine, Jean-Jacques
2016-01-01
In many large systems, such as those encountered in biology or economics, the dynamics are nonlinear and are only known very coarsely. It is often the case, however, that the signs (excitation or inhibition) of individual interactions are known. This paper extends to nonlinear systems the classical criteria of linear sign stability introduced in the 70's, yielding simple sufficient conditions to determine stability using only the sign patterns of the interactions.
Nonlinear electrodynamics as a symmetric hyperbolic system
Abalos, Fernando; Goulart, Érico; Reula, Oscar
2015-01-01
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the point-wise values of the electromagnetic field. These effective Lorentzian metrics share the null (generically two) directions of the electromagnetic field. We show that, the theory is symmetric hyperbolic if and only if the cones these metrics give rise to have a non-empty intersection. Namely that there exist families of symmetrizers in the sense of Geroch which are positive definite for all covectors in the interior of the cones intersection. Thus, for these theories, the initial value problem is well-posed. We illustrate the power of this approach with several nonlinear models of physical interest such as Born-Infeld, Gauss-Bonnet and Euler-Heisenberg.
Analysis and control of nonlinear systems a flatness-based approach
Levine, Jean
2009-01-01
This book examines control of nonlinear systems. Coverage ranges from mathematical system theory to practical industrial control applications. The author offers web-based videos illustrating some dynamical aspects and case studies in simulation.
MULTIPLE POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR HAMMERSTEIN TYPE INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Wang Feng; Zhang Fang; Liu Chunhan
2009-01-01
In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system is discussed.
Maslov-type index and brake orbits in nonlinear Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.
Analyses of non-linear systems and their application to biology: a review.
Sato, S
1994-01-01
In this review article, Wiener's analyses of non-linear systems and other topics on non-linear noise and non-stationary signals are introduced. Firstly, application and limitation of linear aspects on a biological system and a background of introduction of the Wiener's theory to non-linear analysis are briefly mentioned. The practical applications, however, were not so successful for several reasons. We shall see how these problems are solved under collaboration between biologists and engineers who have a knowledge of the subject and utilizing computational facility. Several aspects of the methodology involving non-linear systems, non-linear noise and non-stationary signals are also reviewed.
Application of the Hori Method in the Theory of Nonlinear Oscillations
Directory of Open Access Journals (Sweden)
Sandro da Silva Fernandes
2012-01-01
Full Text Available Some remarks on the application of the Hori method in the theory of nonlinear oscillations are presented. Two simplified algorithms for determining the generating function and the new system of differential equations are derived from a general algorithm proposed by Sessin. The vector functions which define the generating function and the new system of differential equations are not uniquely determined, since the algorithms involve arbitrary functions of the constants of integration of the general solution of the new undisturbed system. Different choices of these arbitrary functions can be made in order to simplify the new system of differential equations and define appropriate near-identity transformations. These simplified algorithms are applied in determining second-order asymptotic solutions of two well-known equations in the theory of nonlinear oscillations: van der Pol equation and Duffing equation.
Adaptive Observer-Based Fault Estimate for Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
ZONG Qun; LIU Wenjing; LIU Li
2006-01-01
An approach for adaptive observer-based fault estimate for nonlinear system is proposed.H-infinity theory is applied to analyzing the design method and stable conditions of the adaptive observer,from which both system state and fault can be estimated.It is proved that the fault estimate error is related to the given H-infinity track performance indexes,as well as to the changing rate of the fault and the Lipschitz constant of the nonlinear item.The design steps of the adaptive observer are proposed.The simulation results show that the observer has good performance for fault estimate even when the system includes nonlinear terms,which confirms the effectiveness of the method.
Applications of equivalent linearization approaches to nonlinear piping systems
Energy Technology Data Exchange (ETDEWEB)
Park, Y.; Hofmayer, C. [Brookhaven National Lab., Upton, NY (United States); Chokshi, N. [Nuclear Regulatory Commission, Washington, DC (United States)
1997-04-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA`s are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations.
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
On the non-linear scale of cosmological perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-04-15
We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
VARIANCE OF NONLINEAR PHASE NOISE IN FIBER-OPTIC SYSTEM
Directory of Open Access Journals (Sweden)
RANJU KANWAR
2013-04-01
Full Text Available In communication system, the noise process must be known, in order to compute the system performance. The nonlinear effects act as strong perturbation in long- haul system. This perturbation effects the signal, when interact with amplitude noise, and results in random motion of the phase of the signal. Based on the perturbation theory, the variance of nonlinear phase noise contaminated by both self- and cross-phase modulation, is derived analytically for phase-shift- keying system. Through this work, it is investigated that for longer transmission distance, 40-Gb/s systems are more sensitive to nonlinear phase noise as compared to 50-Gb/s systems. Also, when transmitting the data through the fiber optic link, bit errors are produced due to various effects such as noise from optical amplifiers and nonlinearity occurring in fiber. On the basis of the simulation results , we have compared the bit error rate based on 8-PSK with theoretical results, and result shows that in real time approach, the bit error rate is high for the same signal to noise ratio. MATLAB software is used to validate the analytical expressions for the variance of nonlinear phase noise.
Further studies of a simple gyrotron equation: nonlinear theory
Energy Technology Data Exchange (ETDEWEB)
Shi Meixuan, E-mail: meixuan@cims.nyu.ed [Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185 (United States)
2010-11-05
A nonlinear version of a standard system of gyrotron model equations is studied using asymptotic analysis and variational methods. The condition for obtaining a high-amplitude wave is achieved in the study. A simple method for obtaining the patterns and amplitude of the wave based on the given free-space wave-number pattern is shown.
Nonlinear Differential Systems with Prescribed Invariant Sets
DEFF Research Database (Denmark)
Sandqvist, Allan
1999-01-01
We present a class of nonlinear differential systems for which invariant sets can be prescribed.Moreover,we show that a system in this class can be explicitly solved if a certain associated linear homogeneous system can be solved.As a simple application we construct a plane autonomous system having...
Hyperchaos in fractional order nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. [Electrical and Computer Engineering Department, University of Sharjah, P.O. Box 27272 Sharjah (United Arab Emirates)] e-mail: wajdi@sharjah.ac.ae
2005-12-01
We numerically investigate hyperchaotic behavior in an autonomous nonlinear system of fractional order. It is demonstrated that hyperchaotic behavior of the integer order nonlinear system is preserved when the order becomes fractional. The system under study has been reported in the literature [Murali K, Tamasevicius A, Mykolaitis G, Namajunas A, Lindberg E. Hyperchaotic system with unstable oscillators. Nonlinear Phenom Complex Syst 3(1);2000:7-10], and consists of two nonlinearly coupled unstable oscillators, each consisting of an amplifier and an LC resonance loop. The fractional order model of this system is obtained by replacing one or both of its capacitors by fractional order capacitors. Hyperchaos is then assessed by studying the Lyapunov spectrum. The presence of multiple positive Lyapunov exponents in the spectrum is indicative of hyperchaos. Using the appropriate system control parameters, it is demonstrated that hyperchaotic attractors are obtained for a system order less than 4. Consequently, we present a conjecture that fourth-order hyperchaotic nonlinear systems can still produce hyperchaotic behavior with a total system order of 3 + {epsilon}, where 1 > {epsilon} > 0.
Callier, Frank M.; Desoer, Charles A.
1991-01-01
The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Nonlinear characteristics of an autoparametric vibration system
Yan, Zhimiao; Taha, Haithem E.; Tan, Ting
2017-03-01
The nonlinear characteristics of an autoparametric vibration system are investigated. This system consists of a base structure and a cantilever beam with a tip mass. The dynamic equations for the system are derived using the extended Hamilton's principle. The method of multiple scales (MMS) is used to determine an approximate analytical solution of the nonlinear governing equations and, hence, analyze the stability and bifurcation of the system. Compared with the numerical simulation, the first-order MMS is not sufficient. A Lagrangian-based approach is proposed to perform a second-order analysis, which is applicable to a large class of nonlinear systems. The effects of the amplitude and frequency of the external force, damping and frequency of the attached cantilever beam, and the tip mass on the nonlinear responses of the autoparametric vibration system are determined. The results show that this system exhibits many interesting nonlinear phenomena including saturation, jumps, hysteresis and different kinds of bifurcations, such as saddle-node, supercritical pitchfork and subcritical pitchfork bifurcations. Power spectra, phase portraits and Poincare maps are employed to analyze the unstable behavior and the associated Hopf bifurcation and chaos. Depending on the application of such a system, its dynamical behaviors could be exploited or avoided.
Nonlinear vibrating system identification via Hilbert decomposition
Feldman, Michael; Braun, Simon
2017-02-01
This paper deals with the identification of nonlinear vibration systems, based on measured signals for free and forced vibration regimes. Two categories of time domain signal are analyzed, one of a fast inter-modulation signal and a second as composed of several mono-components. To some extent, this attempts to imitate analytic studies of such systems, with its two major analysis groups - the perturbation and the harmonic balance methods. Two appropriate signal processing methods are then investigated, one based on demodulation and the other on signal decomposition. The Hilbert Transform (HT) has been shown to enable effective and simple methods of analysis. We show that precise identification of the nonlinear parameters can be obtained, contrary to other average HT based methods where only approximation parameters are obtained. The effectiveness of the proposed methods is demonstrated for the precise nonlinear system identification, using both the signal demodulation and the signal decomposition methods. Following the exposition of the tools used, both the signal demodulation as well as decomposition are applied to classical examples of nonlinear systems. Cases of nonlinear stiffness and damping forces are analyzed. These include, among other, an asymmetric Helmholtz oscillator, a backlash with nonlinear turbulent square friction, and a Duffing oscillator with dry friction.
Non-linear theory of elasticity and optimal design
Ratner, LW
2003-01-01
In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it
NONLINEAR BENDING THEORY OF DIAGONAL SQUARE PYRAMID RETICULATED SHALLOW SHELLS
Institute of Scientific and Technical Information of China (English)
肖潭; 刘人怀
2001-01-01
Double-deck reticulated shells are a main form of large space structures. One of the shells is the diagonal square pyramid reticulated shallow shell, whose its upper and lower faces bear most of the load but its core is comparatively flexible. According to its geometrical and mechanical characteristics, the diagonal square pyramid reticulated shallow shell is treated as a shallow sandwich shell on the basis of three basic assumptions. Its constitutive relations are analyzed from the point of view of energy and internal force equivalence. Basic equations of the geometrically nonlinear bending theory of the diagonal square pyramid reticulated shallow shell are established by means of the virtual work principle .
A convergence theory for a class of nonlinear programming problems.
Rauch, S. W.
1973-01-01
A recent convergence theory of Elkin concerning methods for unconstrained minimization is extended to a certain class of nonlinear programming problems. As in Elkin's original approach, the analysis of a variety of step-length algorithms is treated entirely separately from that of several direction algorithms. This allows for their combination into many different methods for solving the constrained problem. These include some of the methods of Rosen and Zoutendijk. We also extend the results of Topkis and Veinott to nonconvex sets and drop their requirement of the uniform feasibility of a subsequence of the search directions.
de Sitter limit of inflation and nonlinear perturbation theory
Jarnhus, Philip R
2007-01-01
We study the fourth order action of comoving curvature perturbations in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbations to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of comoving curvature perturbations and discuss the slow-roll order of the n-point correlation function.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint
Martínez-Guerra, Rafael
2017-01-01
This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.
Gradient realization of nonlinear control systems
Cortes monforte, J.; Cortés, J.; Crouch, P.E.; Astolfi, A.; van der Schaft, Arjan; Gordillo, F.
2003-01-01
We investigate necessary and su?cient conditions under which a nonlinear afine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with
Doria, Gino; Koch, Giorgio; Strom, Roberto
1979-01-01
This volume collects the contributions presented at the "Working Conference on System Theory in Immunology", held in Rome, May 1978. The aim of the Conference was to bring together immunologists on one side and experts in system theory and applied mathematics on the other, in order to identify problems of common interest and to establish a network of joint effort toward their solution. The methodologies of system theory for processing experimental data and for describing dynamical phenomena could indeed contribute significantly to the under standing of basic immunological facts. Conversely, the complexity of experimental results and of interpretative models should stimulate mathematicians to formulate new problems and to design appropriate procedures of analysis. The multitude of scientific publications in theoretical biology, appeared in recent years, confirms this trend and calls for extensive interaction between mat- matics and immunology. The material of this volume is divided into five sections, along ...
Damage detection in initially nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Bornn, Luke [Los Alamos National Laboratory; Farrar, Charles [Los Alamos National Laboratory; Park, Gyuhae [Los Alamos National Laboratory
2009-01-01
The primary goal of Structural Health Monitoring (SHM) is to detect structural anomalies before they reach a critical level. Because of the potential life-safety and economic benefits, SHM has been widely studied over the past decade. In recent years there has been an effort to provide solid mathematical and physical underpinnings for these methods; however, most focus on systems that behave linearly in their undamaged state - a condition that often does not hold in complex 'real world' systems and systems for which monitoring begins mid-lifecycle. In this work, we highlight the inadequacy of linear-based methodology in handling initially nonlinear systems. We then show how the recently developed autoregressive support vector machine (AR-SVM) approach to time series modeling can be used for detecting damage in a system that exhibits initially nonlinear response. This process is applied to data acquired from a structure with induced nonlinearity tested in a laboratory environment.
Controller Design of Complex System Based on Nonlinear Strength
Directory of Open Access Journals (Sweden)
Rongjun Mu
2015-01-01
Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.
Nonlinear magnetotransport theory and Hall induced resistance oscillations in graphene.
Gutiérrez-Jáuregui, R; Torres, M
2014-06-11
The quantum oscillations of nonlinear magnetoresistance in graphene that occur in response to a dc current bias are investigated. We present a theoretical model for the nonlinear magnetotransport of graphene carriers. The model is based on the exact solution of the effective Dirac equation in crossed electric and magnetic fields, while the effects of randomly distributed impurities are perturbatively added. To compute the nonlinear current effects, we develop a covariant formulation of the migration center theory. The current is calculated for short- and large-range scatterers. The analysis of the differential resistivity in the large magnetic field region, shows that the extrema of the Shubnikov de Hass oscillations invert when the dc currents exceed a threshold value. These results are in good agreement with experimental observations. In the small magnetic field regime, corresponding to large filling factors, the existence of Hall induced resistance oscillations are predicted for ultra clean graphene samples. These oscillations originate from Landau-Zener tunneling between Landau levels, that are tilted by the strong electric Hall field.
Nonlinear System Identification and Behavioral Modeling
Huq, Kazi Mohammed Saidul; Kabir, A F M Sultanul
2010-01-01
The problem of determining a mathematical model for an unknown system by observing its input-output data pair is generally referred to as system identification. A behavioral model reproduces the required behavior of the original analyzed system, such as there is a one-to-one correspondence between the behavior of the original system and the simulated system. This paper presents nonlinear system identification and behavioral modeling using a work assignment.
Theory of nonlinear phononics for coherent light control of solids
Subedi, Alaska; Cavalleri, Andrea; Georges, Antoine
2014-06-01
We present a microscopic theory for ultrafast control of solids with high-intensity terahertz frequency optical pulses. When resonant with selected infrared-active vibrations, these pulses transiently modify the crystal structure and lead to new collective electronic properties. The theory predicts the dynamical path taken by the crystal lattice using first-principles calculations of the energy surface and classical equations of motion, as well as symmetry considerations. Two classes of dynamics are identified. In the perturbative regime, displacements along the normal mode coordinate of symmetry-preserving Raman active modes can be achieved by cubic anharmonicities. This explains the light-induced insulator-to-metal transition reported experimentally in manganites. We predict a regime in which ultrafast instabilities that break crystal symmetry can be induced. This nonperturbative effect involves a quartic anharmonic coupling and occurs above a critical threshold, below which the nonlinear dynamics of the driven mode displays softening and dynamical stabilization.
Institute of Scientific and Technical Information of China (English)
邹文学; 庞兵; 陈庆国
2011-01-01
The 3-phase non-sinusoidal asymmetrical source voltage and 3-line unbalanced load current that were transformed in Furrier transformation would be analyzed with symmetrical component method in the paper, and then compared with current physical components theory and instantaneous reactive power theory. It is reasonable that the symmetrical component method is best among the theories on the 3-phase 4-line power system. For the asymmetrical source voltage and non-linear load current power system, it cut the system into two linear sub-systems according to it' s direction of active power flow and decomposed the voltage and current with symmetrical component method to obtaine more detailed electrical data. However there are some problems of compensating reactive power in the 3-phase asymmetrical voltage 3-line nonlinear unbalanced load power system.%运用对称分量法原理对经过Furrier变换后的三相不对称,非正弦电压和三相线性不平衡负载电流进行分解,并与其他功率理论方法如电流物理份量法和瞬时无功功率理论对系统的功率现象和定义进行分析和比较.通过比较可见在频域上,对于线性负载系统,应用对称分量法对所有三相四线电压不对称,负载不平衡的线性系统的分解与定义较其他的功率方法更合理.对于三相三线电压不对称,负载为非线性不平衡系统可以先按有功功率潮流方向将系统分拆为2个线性子系统再应用对称分量法分解即可得到最多的电量参数.同时也证明了对该类系统的补偿存在一些难以解决的问题.
Directory of Open Access Journals (Sweden)
Mingzhu Song
2016-01-01
Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.
Identification of Nonlinear Nonautonomous State Space Systems from Input-Output Measurements
Verdult, Vincent; Verhaegen, Michel; Scherpen, Jacquelien
2000-01-01
This paper presents a method to determine a nonlinear state space model from a finite number of measurements of the inputs and outputs. The method is based on embedding theory for nonlinear systems, and can be viewed as an extension of the subspace identification method for linear systems. The paper
On the estimation of the attainability set of nonlinear control systems
Energy Technology Data Exchange (ETDEWEB)
Ekimov, A.V.; Balykina, Yu.E.; Svirkin, M.V. [Saint Petersburg State University, 198504, Universitetskii pr., 35, Saint Petersburg (Russian Federation)
2015-03-10
Analysis of the attainability set and construction of its estimates greatly facilitates the solution of a variety of problems in mathematical control theory. In the paper, the problem of boundedness of the integral funnel of nonlinear controlled system is considered. Some estimates of the attainability sets for a nonlinear controlled system are presented. Theorems on the boundedness of considered integral funnels are proved.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Discrete time learning control in nonlinear systems
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Theoretical aspects of nonlinear echo image system
Institute of Scientific and Technical Information of China (English)
ZHANG Ruiquan; FENG Shaosong
2003-01-01
In order to develop the nonlinear echo image system to diagnose pathological changes in biological tissue , a simple physical model to analyse the character of nonlinear reflected wave in biological medium is postulated. The propagation of large amplitude plane sound wave in layered biological media is analysed for the one dimensional case by the method of successive approximation and the expression for the second order wave reflected from any interface of layered biological media is obtained. The relations between the second order reflection coefficients and the nonlinear parameters of medium below the interface are studied in three layers interfaces. Finally, the second order reflection coefficients of four layered media are calculated numerically. The results indicate that the nonlinear parameter B/A of each layer of biological media can be determined by the reflection method.
Nonlinear system identification in offshore structural reliability
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corporation, Houston, TX (United States)
1995-08-01
Nonlinear forces acting on offshore structures are examined from a system identification perspective. The nonlinearities are induced by ocean waves and may become significant in many situations. They are not necessarily in the form of Morison`s equation. Various wave force models are examined. The force function is either decomposed into a set of base functions or it is expanded in terms of the wave and structural kinematics. The resulting nonlinear system is decomposed into a number of parallel no-memory nonlinear systems, each followed by a finite-memory linear system. A conditioning procedure is applied to decouple these linear sub-systems; a frequency domain technique involving autospectra and cross-spectra is employed to identify the linear transfer functions. The structural properties and those force transfer parameters are determine with the aid of the coherence functions. The method is verified using simulated data. It provides a versatile and noniterative approach for dealing with nonlinear interaction problems encountered in offshore structural analysis and design.
BINARY NONLINEARIZATION FOR THE DIRAC SYSTEMS
Institute of Scientific and Technical Information of China (English)
MAWENXIU
1997-01-01
A Bargmann symmetry constraint is proposed for the Lax pairs and the adjoint Lax pairs of the Dirac systems. It is shown that the spatial part of the nonlinearized Lax pairs and adjoint Lax pairs is a finite dimensional Linuville integrable Hamiltonian system and that under the control of the spatial part, the time parts of the nonlinearized Lax pairs and adjoint Lax pairs are interpreted as a hierarchy of commutative, finite dimensional Linuville integrable Hamiltoian systems whose Hamiltonian functions consist of a series of integrals of motion for the spatial part. Moreover an invaiutive representation of solutions of the Dirac systems exhibits their integrability by quadratures. This kind of symmetry constraint procedure involving thespectral problem and the adjoint spectral problem is referred to as a binary nonlinearization technique like a binary Darhoux transformation.
Applied multidimensional systems theory
Bose, Nirmal K
2017-01-01
Revised and updated, this concise new edition of the pioneering book on multidimensional signal processing is ideal for a new generation of students. Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with applications in biomedicine, X-ray technology and satellite communications. Serving as a firm basis for graduate engineering students and researchers seeking applications in mathematical theories, this edition eschews detailed mathematical theory not useful to students. Presentation of the theory has been revised to make it more readable for students, and introduce some new topics that are emerging as multidimensional DSP topics in the interdisciplinary fields of image processing. New topics include Groebner bases, wavelets, and filter banks.
Ontology of Earth's nonlinear dynamic complex systems
Babaie, Hassan; Davarpanah, Armita
2017-04-01
As a complex system, Earth and its major integrated and dynamically interacting subsystems (e.g., hydrosphere, atmosphere) display nonlinear behavior in response to internal and external influences. The Earth Nonlinear Dynamic Complex Systems (ENDCS) ontology formally represents the semantics of the knowledge about the nonlinear system element (agent) behavior, function, and structure, inter-agent and agent-environment feedback loops, and the emergent collective properties of the whole complex system as the result of interaction of the agents with other agents and their environment. It also models nonlinear concepts such as aperiodic, random chaotic behavior, sensitivity to initial conditions, bifurcation of dynamic processes, levels of organization, self-organization, aggregated and isolated functionality, and emergence of collective complex behavior at the system level. By incorporating several existing ontologies, the ENDCS ontology represents the dynamic system variables and the rules of transformation of their state, emergent state, and other features of complex systems such as the trajectories in state (phase) space (attractor and strange attractor), basins of attractions, basin divide (separatrix), fractal dimension, and system's interface to its environment. The ontology also defines different object properties that change the system behavior, function, and structure and trigger instability. ENDCS will help to integrate the data and knowledge related to the five complex subsystems of Earth by annotating common data types, unifying the semantics of shared terminology, and facilitating interoperability among different fields of Earth science.
Robustness analysis for a class of nonlinear descriptor systems
Institute of Scientific and Technical Information of China (English)
吴敏; 张凌波; 何勇
2004-01-01
The robustness analysis problem of a class of nonlinear descriptor systems is studied. Nonlinear matrix inequality which has the good computation property of convex feasibility is employed to derive some sufficient conditions to guarantee that the nonlinear descriptor systems have robust disturbance attenuation performance, which avoids the computational difficulties in conversing nonlinear matrix and Hamilton-Jacobi inequality. The computation property of convex feasibility of nonlinear matrix inequality makes it possible to apply the results of nonlinear robust control to practice.
Nonlinear Control of Delay and PDE Systems
Bekiaris-Liberis, Nikolaos
In this dissertation we develop systematic procedures for the control and analysis of general nonlinear systems with delays and of nonlinear PDE systems. We design predictor feedback laws (i.e., feedback laws that use the future, rather than the current state of the system) for the compensation of delays (i.e., after the control signal reaches the system for the first time, the system behaves as there were no delay at all) that can be time-varying or state-dependent, on the input and on the state of nonlinear systems. We also provide designs of predic- tor feedback laws for linear systems with constant distributed delays and known or unknown plant parameters, and for linear systems with simultaneous known or unknown constant delays on the input and the state. Moreover, we intro- duce infinite-dimensional backstepping transformations for each particular prob-lem, which enables us to construct Lyapunov-Krasovskii functionals. With the available Lyapunov-Krasovskii functionals we study stability, as well as, robust- ness of our control laws to plant uncertainties. We deal with coupled PDE-ODE systems. We consider nonlinear systems with wave actuator dynamics, for which we design a predictor inspired feedback law. We study stability of the closed-loop system either by constructing Lyapunov functionals, or using arguments of explicit solutions. We also consider linear sys- tems with distributed actuator and sensor dynamics governed by diffusion or wave PDEs, for which we design stabilizing feedback laws. We study stability of the closed-loop systems using Lyapunov functionals that we construct with the intro- duction of infinite-dimensional transformations of forwarding type. Finally, we develop a control design methodology for coupled nonlinear first-order hyperbolic PDEs through an application to automotive catalysts.
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting m
Dynamic disturbance decoupling for nonlinear systems
Huijberts, H.J.C.; Nijmeijer, H.; Wegen, van der L.L.M.
1992-01-01
In analogy with the dynamic input-output decoupling problem the dynamic disturbance decoupling problem for nonlinear systems is introduced. A local solution of this problem is obtained in the case that the system under consideration is invertible. The solution is given in algebraic as well as in geo
Can there be a general nonlinear PDE theory for the existence of solutions ?
2004-01-01
Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the respective PDEs. The method can also deal with associated initial and/or boundary value problems. The solutions obtained can be assimilated with usual ...
Fault detection for nonlinear systems - A standard problem approach
DEFF Research Database (Denmark)
Stoustrup, Jakob; Niemann, Hans Henrik
1998-01-01
The paper describes a general method for designing (nonlinear) fault detection and isolation (FDI) systems for nonlinear processes. For a rich class of nonlinear systems, a nonlinear FDI system can be designed using convex optimization procedures. The proposed method is a natural extension...
Nonlinear polarization of ionic liquids: theory, simulations, experiments
Kornyshev, Alexei
2010-03-01
Room temperature ionic liquids (RTILs) composed of large, often asymmetric, organic cations and simple or complex inorganic or organic anions do not freeze at ambient temperatures. Their rediscovery some 15 years ago is widely accepted as a ``green revolution'' in chemistry, offering an unlimited number of ``designer'' solvents for chemical and photochemical reactions, homogeneous catalysis, lubrication, and solvent-free electrolytes for energy generation and storage. As electrolytes they are non-volatile, some can sustain without decomposition up to 6 times higher voltages than aqueous electrolytes, and many are environmentally friendly. The studies of RTILs and their applications have reached a critical stage. So many of them can be synthesized - about a thousand are known already - their mixtures can further provide ``unlimited'' number of combinations! Thus, establishing some general laws that could direct the best choice of a RTIL for a given application became crucial; guidance is expected from theory and modelling. But for a physical theory, RTILs comprise a peculiar and complex class of media, the description of which lies at the frontier line of condensed matter theoretical physics: dense room temperature ionic plasmas with ``super-strong'' Coulomb correlations, which behave like glasses at short time-scale, but like viscous liquids at long-time scale. This talk will introduce RTILs to physicists and overview the current understanding of the nonlinear response of RTILs to electric field. It will focus on the theory, simulations, and experimental characterisation of the structure and nonlinear capacitance of the electrical double layer at a charged electrode. It will also discuss pros and contras of supercapacitor applications of RTILs.
Nonlinear Theory of Anomalous Diffusion and Application to Fluorescence Correlation Spectroscopy
Boon, Jean Pierre; Lutsko, James F.
2015-12-01
The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result of competitive effects between attractive and repulsive interactions. We present the explicit analytical solution to the nonlinear diffusion equation which we then use to compute the correlation function which is experimentally measured by correlation spectroscopy. The theoretical results are applicable in particular to the analysis of fluorescence correlation spectroscopy of marked molecules in biological systems. More specifically we consider the cases of fluorescently labeled lipids in the plasma membrane and of fluorescent apoferritin (a spherically shaped oligomer) in a crowded dextran solution and we find that the nonlinear correlation spectra reproduce very well the experimental data indicating sub-diffusive molecular motion.
Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings
Institute of Scientific and Technical Information of China (English)
JING Hui; TIAN Li-Jun
2002-01-01
We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.
Network science, nonlinear science and infrastructure systems
2007-01-01
Network Science, Nonlinear Science and Infrastructure Systems has been written by leading scholars in these areas. Its express purpose is to develop common theoretical underpinnings to better solve modern infrastructural problems. It is felt by many who work in these fields that many modern communication problems, ranging from transportation networks to telecommunications, Internet, supply chains, etc., are fundamentally infrastructure problems. Moreover, these infrastructure problems would benefit greatly from a confluence of theoretical and methodological work done with the areas of Network Science, Dynamical Systems and Nonlinear Science. This book is dedicated to the formulation of infrastructural tools that will better solve these types of infrastructural problems. .
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Controllability of non-linear systems: generic singularities and their stability
Energy Technology Data Exchange (ETDEWEB)
Davydov, Alexey A; Zakalyukin, Vladimir M
2012-04-30
This paper presents an overview of the state of the art in applications of singularity theory to the analysis of generic singularities of controllability of non-linear systems on manifolds. Bibliography: 40 titles.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
Institute of Scientific and Technical Information of China (English)
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
Institute of Scientific and Technical Information of China (English)
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Sustained small oscillations in nonlinear control systems. [launch vehicle dynamics
George, J. H.; Gunderson, R. W.; Hahn, H.
1975-01-01
Some results of bifurcation theory were used to study the existence of small-amplitude periodic behavior in launch vehicle dynamics, assuming that nonlinearity exists as a cubic term in the rudder response. The analysis follows closely Sattinger's (1973) approach to the theory of periodic bifurcations. The conditions under which a bifurcating branch of orbitally stable periodic solutions will exist are determined. It is shown that in more complicated cases, the conditions under which the system matrix has a pair of simple purely imaginary eigenvalues can be determined with the aid of linear stability techniques.
Bifurcation criterion of faults in complex nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yagang, E-mail: yagangzhang@gmail.com [State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206 (China); Department of Mathematics and Interdisciplinary Mathematics Institute, University of South Carolina, Columbia, SC 29208 (United States); Wang, Zengping [State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206 (China)
2014-03-01
In this paper, we introduce bifurcation theory into complex nonlinear systems. We adopt a novel approach to identify faults in electric circuit systems. After accidents occur without warning, with large numbers of complicated and high-precision calculations, we use bifurcation results of corresponding amplitude and frequency (period) to analyze their universal characteristics. Based on super attractive parameters, we have got the universal constant 4.6692… . The results from the present investigation imply that each fault in an electric circuit system must correspond to one or more bifurcation locations, which will provide a bifurcation criterion of faults in complex nonlinear systems. This research will have a significant theoretical value and engineering practical significance.
Simplified nonlinear theory of the dielectric loaded rectangular Cerenkov maser
Institute of Scientific and Technical Information of China (English)
Zhao Ding; Ding Yao-Gen
2012-01-01
To rapidly and accurately investigate the performance of the dielectric loaded rectangular Cerenkov maser,a simplified nonlinear theory is proposed,in which the variations of wave amplitude and wave phase are determined by two coupled first-order differential equations.Through combining with the relativistic equation of motion and adopting the forward wave assumption,the evolutions of the forward wave power,the power growth rate,the axial wave number,the accumulated phase offset,and the information of the particle movement can be obtained in a single-pass calculation.For an illustrative example,this method is used to study the influences of the beam current,the gap distance between the beam and the dielectric surface,and the momentum spread on the forward wave.The variations of the saturated power and the saturation length with the working frequency for the beams with different momentum spreads have also been studied.The result shows that the beam-wave interaction is very sensitive to the electron beam state.To further verify this simplified theory,a comparison with the result produced from a rigorous method is also provided,we find that the evolution curves of the forward wave power predicted by the two methods exhibit excellent agreement.In practical applications,the developed theory can be used for the design and analysis of the rectangular Cerenkov maser.
Nonlinear relaxation field in charged systems under high electric fields
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K
2000-07-01
The influence of an external electric field on the current in charged systems is investigated. The results from the classical hierarchy of density matrices are compared with the results from the quantum kinetic theory. The kinetic theory yields a systematic treatment of the nonlinear current beyond linear response. To this end the dynamically screened and field-dependent Lenard-Balescu equation is integrated analytically and the nonlinear relaxation field is calculated. The classical linear response result known as Debye - On-Sager relaxation effect is only obtained if asymmetric screening is assumed. Considering the kinetic equation of one specie the other species have to be screened dynamically while the screening with the same specie itself has to be performed statically. Different other approximations are discussed and compared. (author)
Evolutionary quantitative genetics of nonlinear developmental systems.
Morrissey, Michael B
2015-08-01
In quantitative genetics, the effects of developmental relationships among traits on microevolution are generally represented by the contribution of pleiotropy to additive genetic covariances. Pleiotropic additive genetic covariances arise only from the average effects of alleles on multiple traits, and therefore the evolutionary importance of nonlinearities in development is generally neglected in quantitative genetic views on evolution. However, nonlinearities in relationships among traits at the level of whole organisms are undeniably important to biology in general, and therefore critical to understanding evolution. I outline a system for characterizing key quantitative parameters in nonlinear developmental systems, which yields expressions for quantities such as trait means and phenotypic and genetic covariance matrices. I then develop a system for quantitative prediction of evolution in nonlinear developmental systems. I apply the system to generating a new hypothesis for why direct stabilizing selection is rarely observed. Other uses will include separation of purely correlative from direct and indirect causal effects in studying mechanisms of selection, generation of predictions of medium-term evolutionary trajectories rather than immediate predictions of evolutionary change over single generation time-steps, and the development of efficient and biologically motivated models for separating additive from epistatic genetic variances and covariances.
Extremal Black Hole in a Nonlinear Newtonian Theory of Gravity
Good, Michael R R
2008-01-01
This work investigates an upper-limit of charge for a black hole in a nonlinear Newtonian theory of gravity. The charge is accumulated via protons fired isotropically at the black hole. This theoretical study of gravity (known as `pseudo-Newtonian') is a forced merger of special relativity and Newtonian gravity. Whereas the source of Newton's gravity is purely mass, pseudo-Newtonian gravity includes effects of fields around the mass, giving a more complete picture of how gravity behaves. Interestingly, pseudo-Newtonian gravity predicts such relativistic phenomena as black holes and deviations from Kepler's laws, but of course, provides a less accurate picture than general relativity. Though less accurate, it offers an easier approach to understanding some results of general relativity, and merits interest due to its simplicity. The method of study applied here examines the predictions of pseudo-Newtonian gravity for a particle interacting with a highly charged black hole. A black hole with a suitable charge w...
Theory of weakly nonlinear self-sustained detonations
Faria, Luiz M.
2015-11-03
We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.
History of nonlinear oscillations theory in France (1880-1940)
Ginoux, Jean-Marc
2017-01-01
This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own...
Workshop on Nonlinear Phenomena in Complex Systems
1989-01-01
This book contains a thorough treatment of neural networks, cellular-automata and synergetics, in an attempt to provide three different approaches to nonlinear phenomena in complex systems. These topics are of major interest to physicists active in the fields of statistical mechanics and dynamical systems. They have been developed with a high degree of sophistication and include the refinements necessary to work with the complexity of real systems as well as the more recent research developments in these areas.
Design Theory in Information Systems
Directory of Open Access Journals (Sweden)
Shirley Gregor
2002-11-01
Full Text Available The aim of this paper is to explore an important category of information systems knowledge that is termed “design theory”. This knowledge is distinguished as the fifth of five types of theory: (i theory for analysing and describing, (ii theory for understanding, (iii theory for predicting, (iv theory for explaining and predicting, and (v theory for design and action. Examples of design theory in information systems are provided, with associated research methods. The limited understanding and recognition of this type of theory in information systems indicates that further debate concerning its nature and role in our discipline is needed.
New results in global stabilization for stochastic nonlinear systems
Institute of Scientific and Technical Information of China (English)
Tao BIAN; Zhong-Ping JIANG
2016-01-01
This paper presents new results on the robust global stabilization and the gain assignment problems for stochastic nonlinear systems. Three stochastic nonlinear control design schemes are developed. Furthermore, a new stochastic gain assignment method is developed for a class of uncertain interconnected stochastic nonlinear systems. This method can be combined with the nonlinear small-gain theorem to design partial-state feedback controllers for stochastic nonlinear systems. Two numerical examples are given to illustrate the effectiveness of the proposed methodology.
Nonlinear distortion in wireless systems modeling and simulation with Matlab
Gharaibeh, Khaled M
2011-01-01
This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems
Exploring Nonlinearities in Financial Systemic Risk
Wolski, M.
2013-01-01
We propose a new methodology of assessing the effects of individual institution's risk on the others and on the system as a whole. We build upon the Conditional Value-at-Risk approach, however, we introduce the explicit Granger causal linkages and we account for possible nonlinearities in the
Oscillatority Conditions for Nonlinear Systems with Delay
Directory of Open Access Journals (Sweden)
Denis V. Efimov
2007-01-01
Full Text Available Sufficient conditions for oscillatority in the sense of Yakubovich for a class of time delay nonlinear systems are proposed. Under proposed conditions, upper and lower bounds for oscillation amplitude are given. Examples illustrating analytical results by computer simulation are presented.
A polynomial approach to nonlinear system controllability
Zheng, YF; Willems, JC; Zhang, CH
2001-01-01
This note uses a polynomial approach to present a necessary and sufficient condition for local controllability of single-input-single-output (SISO) nonlinear systems. The condition is presented in terms of common factors of a noncommutative polynomial expression. This result exposes controllability
Periodic Solutions for Highly Nonlinear Oscillation Systems
DEFF Research Database (Denmark)
Ghadimi, M; Barari, Amin; Kaliji, H.D
2012-01-01
In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams...
Optimized spectral estimation for nonlinear synchronizing systems.
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
Statistical mechanics of a discrete nonlinear system
Rasmussen; Cretegny; Kevrekidis; Gronbech-Jensen
2000-04-24
Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.
Nonlinear dynamics in distributed systems
Adjali, I; Gell-Mann, Murray; Iqbal Adjali; Jose-Luis Fernandez-Villacanas; Michael Gell
1994-01-01
formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a systematic way using Van Kanpen's expansion method for Markov processes. We present some results for both stationary and time-dependent states. Our approach allows the effect of fluctuations to be explored, particularly in finite systems where such processes assume increasing importance.
Impulsive control for synchronization of nonlinear R(o)ssler chaotic systems
Institute of Scientific and Technical Information of China (English)
Li Yang; Liao Xiao-Feng; Li Chuan-Dong; Chen Guo
2006-01-01
This paper reports that an impulsive control theory for synchronization of nonlinear R(o)ssler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear R(o)ssler chaotic systems and the simulation results demonstrate the effectiveness of the method.
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Adaptive Fuzzy Containment Control for Uncertain Nonlinear Multiagent Systems
Directory of Open Access Journals (Sweden)
Yang Yu
2014-01-01
Full Text Available This paper considers the containment control problem for uncertain nonlinear multiagent systems under directed graphs. The followers are governed by nonlinear systems with unknown dynamics while the multiple leaders are neighbors of a subset of the followers. Fuzzy logic systems (FLSs are used to identify the unknown dynamics and a distributed state feedback containment control protocol is proposed. This result is extended to the output feedback case, where observers are designed to estimate the unmeasurable states. Then, an output feedback containment control scheme is presented. The developed state feedback and output feedback containment controllers guarantee that the states of all followers converge to the convex hull spanned by the dynamic leaders. Based on Lyapunov stability theory, it is proved that the containment control errors are uniformly ultimately bounded (UUB. An example is provided to show the effectiveness of the proposed control method.
Application of non-linear control theory to a model of deep brain stimulation.
Davidson, Clare M; Lowery, Madeleine M; de Paor, Annraoi M
2011-01-01
Deep brain stimulation (DBS) effectively alleviates the pathological neural activity associated with Parkinson's disease. Its exact mode of action is not entirely understood. This paper explores theoretically the optimum stimulation parameters necessary to quench oscillations in a neural-mass type model with second order dynamics. This model applies well established nonlinear control system theory to DBS. The analysis here determines the minimum criteria in terms of amplitude and pulse duration of stimulation, necessary to quench the unwanted oscillations in a closed loop system, and outlines the relationship between this model and the actual physiological system.
Dekkers, Rob
2017-01-01
Offering an up-to-date account of systems theories and its applications, this book provides a different way of resolving problems and addressing challenges in a swift and practical way, without losing overview and grip on the details. From this perspective, it offers a different way of thinking in order to incorporate different perspectives and to consider multiple aspects of any given problem. Drawing examples from a wide range of disciplines, it also presents worked cases to illustrate the principles. The multidisciplinary perspective and the formal approach to modelling of systems and processes of ‘Applied Systems Theory’ makes it suitable for managers, engineers, students, researchers, academics and professionals from a wide range of disciplines; they can use this ‘toolbox’ for describing, analysing and designing biological, engineering and organisational systems as well as getting a better understanding of societal problems. This revised, updated and expanded second edition includes coverage of a...
Interplay between dissipation and driving in nonlinear quantum systems
Energy Technology Data Exchange (ETDEWEB)
Vierheilig, Carmen
2011-07-01
In this thesis we investigate the interplay between dissipation and driving in nonlinear quantum systems for a special setup: a flux qubit read out by a DC-SQUID - a nonlinear quantum oscillator. The latter is embedded in a harmonic bath, thereby mediating dissipation to the qubit. Two different approaches are elaborated: First we consider a composite qubit-SQUID system and add the bath afterwards. We derive analytical expressions for its eigenstates beyond rotating wave approximation (RWA), by applying Van Vleck perturbation theory (VVPT) in the qubit-oscillator coupling. The second approach is an effective bath approach based on a mapping procedure, where SQUID and bath form an effective bath seen by the qubit. Here the qubit dynamics is obtained by applying standard procedures established for the spin-boson problem. This approach requires the knowledge of the steady-state response of the dissipative Duffing oscillator, which is studied within a resonant and an offresonant approach: The first is applicable near and at an N-photon resonance using VVPT beyond a RWA. The second is based on the exact Floquet states of the nonlinear driven oscillator. The dissipative qubit dynamics is described analytically for weak system-bath coupling and agrees well for both approaches. We derive the effect of the nonlinearity on the qubit dynamics, on the Bloch-Siegert shift and on the vacuum Rabi splitting. (orig.)
Variable Separation Approach to Solve Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
SHEN Shou-Feng; PAN Zu-Liang; ZHANG Jun
2004-01-01
The variable separation approach method is very useful to solving (2+ 1 )-dimensional integrable systems. But the (1+1)-dimensional and (3+ 1 )-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1+1) dimensions by taking the Redekopp system as a simple example and (3+1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3+ 1 )-dimensional universal formula obtained from many (2+ 1 )-dimensional systems is extended.
Variable Separation Approach to Solve Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
SHENShou-Feng; PANZu-Liang; ZHANGJun
2004-01-01
The variable separation approach method is very useful to solving (2+1)-dimensional integrable systems.But the (1+1)-dimensional and (3+1)-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1+1) dimensions by taking the Redekopp system as a simp!e example and (3+1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3+1)-dimensional universal formula obtained from many (2+1)-dimensional systems is extended.
Long Time Behavior for a System of Differential Equations with Non-Lipschitzian Nonlinearities
Directory of Open Access Journals (Sweden)
Nasser-Eddine Tatar
2014-01-01
Full Text Available We consider a general system of nonlinear ordinary differential equations of first order. The nonlinearities involve distributed delays in addition to the states. In turn, the distributed delays involve nonlinear functions of the different variables and states. An explicit bound for solutions is obtained under some rather reasonable conditions. Several special cases of this system may be found in neural network theory. As a direct application of our result it is shown how to obtain global existence and, more importantly, convergence to zero at an exponential rate in a certain norm. All these nonlinearities (including the activation functions may be non-Lipschitz and unbounded.
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method
Directory of Open Access Journals (Sweden)
Qiang Ma
2011-03-01
Full Text Available In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
Institute of Scientific and Technical Information of China (English)
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
Nonlinear System Control Using Neural Networks
Directory of Open Access Journals (Sweden)
Jaroslava Žilková
2006-10-01
Full Text Available The paper is focused especially on presenting possibilities of applying off-linetrained artificial neural networks at creating the system inverse models that are used atdesigning control algorithm for non-linear dynamic system. The ability of cascadefeedforward neural networks to model arbitrary non-linear functions and their inverses isexploited. This paper presents a quasi-inverse neural model, which works as a speedcontroller of an induction motor. The neural speed controller consists of two cascadefeedforward neural networks subsystems. The first subsystem provides desired statorcurrent components for control algorithm and the second subsystem providescorresponding voltage components for PWM converter. The availability of the proposedcontroller is verified through the MATLAB simulation. The effectiveness of the controller isdemonstrated for different operating conditions of the drive system.
Consensus tracking for multiagent systems with nonlinear dynamics.
Dong, Runsha
2014-01-01
This paper concerns the problem of consensus tracking for multiagent systems with a dynamical leader. In particular, it proposes the corresponding explicit control laws for multiple first-order nonlinear systems, second-order nonlinear systems, and quite general nonlinear systems based on the leader-follower and the tree shaped network topologies. Several numerical simulations are given to verify the theoretical results.
Family systems theory, attachment theory, and culture.
Rothbaum, Fred; Rosen, Karen; Ujiie, Tatsuo; Uchida, Nobuko
2002-01-01
Family systems theory and attachment theory have important similarities and complementarities. Here we consider two areas in which the theories converge: (a) in family system theorists' description of an overly close, or "enmeshed," mother-child dyad, which attachment theorists conceptualize as the interaction of children's ambivalent attachment and mothers' preoccupied attachment; (b) in family system theorists' description of the "pursuer-distance cycle" of marital conflict, which attachment theorists conceptualize as the interaction of preoccupied and dismissive partners. We briefly review family systems theory evidence, and more extensively review attachment theory evidence, pertaining to these points of convergence. We also review cross-cultural research, which leads us to conclude that the dynamics described in both theories reflect, in part, Western ways of thinking and Western patterns of relatedness. Evidence from Japan suggests that extremely close ties between mother and child are perceived as adaptive, and are more common, and that children experience less adverse effects from such relationships than do children in the West. Moreover, in Japan there is less emphasis on the importance of the exclusive spousal relationship, and less need for the mother and father to find time alone to rekindle romantic, intimate feelings and to resolve conflicts by openly communicating their differences. Thus, the "maladaptive" pattern frequently cited by Western theorists of an extremely close mother-child relationship, an unromantic, conflictual marriage characterized by little verbal communication and a peripheral, distant father, may function very differently in other cultures. While we believe that both theories will be greatly enriched by their integration, we caution against the application of either theory outside the cultures in which they were developed.
Zhang, Hou-Dao; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing
2015-01-14
We consider the hybrid system-bath dynamics, based on the Yan's dissipaton formalism [Y. J. Yan, J. Chem. Phys. 140, 054105 (2014)]. This theory provides a unified quasi-particle treatment on three distinct classes of quantum bath, coupled nonperturbatively to arbitrary quantum systems. In this work, to study the entangled system and bath polarization and nonlinear Fano interference, we incorporate further the time-dependent light field, which interacts with both the molecular system and the collective bath dipoles directly. Numerical demonstrations are carried out on a two-level system, with comparison between phonon and exciton baths, in both linear and nonlinear Fano interference regimes.
Dekkers, Rob
2014-01-01
Offering an up-to-date account of systems theories and its applications, this book provides a different way of resolving problems and addressing challenges in a swift and practical way, without losing overview and not having a grip on the details. From this perspective, it offers a different way of thinking in order to incorporate different perspectives and to consider multiple aspects of any given problem. Drawing examples from a wide range of disciplines, it also presents worked cases to illustrate the principles. The multidisciplinary perspective and the formal approach to modelling of syst
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
Application of dynamic recurrent neural networks in nonlinear system identification
Du, Yun; Wu, Xueli; Sun, Huiqin; Zhang, Suying; Tian, Qiang
2006-11-01
An adaptive identification method of simple dynamic recurrent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteristics of system can reflect the dynamic characteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNN, and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topological structure in usual dynamic recurrent neural network.
Small-scale nonlinear dynamics of K-mouflage theories
Brax, Philippe; Valageas, Patrick
2014-12-01
We investigate the small-scale static configurations of K-mouflage models defined by a general function K (χ ) of the kinetic terms. The fifth force is screened by the nonlinear K-mouflage mechanism if K'(χ ) grows sufficiently fast for large negative χ . In the general nonspherically symmetric case, the fifth force is not aligned with the Newtonian force. For spherically symmetric static matter density profiles, we show that the results depend on the potential function W-(y )=y K'(-y2/2 ) ; i.e., W-(y ) must be monotonically increasing to +∞ for y ≥0 to guarantee the existence of a single solution throughout space for any matter density profile. Small radial perturbations around these static profiles propagate as travelling waves with a velocity greater than the speed of light. Starting from vanishing initial conditions for the scalar field and for a time-dependent matter density corresponding to the formation of an overdensity, we numerically check that the scalar field converges to the static solution. If W- is bounded, for high-density objects there are no static solutions throughout space, but one can still define a static solution restricted to large radii. Our dynamical study shows that the scalar field relaxes to this static solution at large radii, whereas spatial gradients keep growing with time at smaller radii. If W- is not bounded but nonmonotonic, there is an infinite number of discontinuous static solutions. However, the Klein-Gordon equation is no longer a well-defined hyperbolic equation, which leads to complex characteristic speeds and exponential instabilities. Therefore, these discontinuous static solutions are not physical, and these models are not theoretically sound. Such K-mouflage scenarios provide an example of theories that can appear viable at the cosmological level, for the cosmological background and perturbative analysis, while being meaningless at a nonlinear level for small-scale configurations. This shows the importance of
Nonlinear dynamic macromodeling techniques for audio systems
Ogrodzki, Jan; Bieńkowski, Piotr
2015-09-01
This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.
IMPULSIVE CONTROL OF CHAOTIC ATTRACTORS IN NONLINEAR CHAOTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
马军海; 任彪; 陈予恕
2004-01-01
Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented.By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, and with it, the upper bond of the impulse interval for asymptotically stable control was given. Numerical results are presented, which are considered with important reference value for control of chaotic attractors.
Model reduction of systems with localized nonlinearities.
Energy Technology Data Exchange (ETDEWEB)
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
Nonlinear Filtering Preserves Chaotic Synchronization via Master-Slave System
Directory of Open Access Journals (Sweden)
J. S. González-Salas
2013-01-01
Full Text Available We present a study on a class of interconnected nonlinear systems and give some criteria for them to behave like a filter. Some chaotic systems present this kind of interconnected nonlinear structure, which enables the synchronization of a master-slave system. Interconnected nonlinear filters have been defined in terms of interconnected nonlinear systems. Furthermore, their behaviors have been studied numerically and theoretically on different input signals.
Coordinated formation control of multiple nonlinear systems
Institute of Scientific and Technical Information of China (English)
Wei KANG; Ning XI; Jindong TAN; Yiwen ZHAO; Yuechao WANG
2005-01-01
A general method of controller design is developed for the purpose of formation keeping and reconfiguration of nonlinear systems with multiple subsystems,such as the formation of multiple aircraft,ground vehicles,or robot arms.The model consists of multiple nonlinear systems.Controllers are designed to keep the subsystems in a required formation and to coordinate the subsystems in the presence of environmental changes.A step-by-step algorithm of controller design is developed.Sufficient conditions for the stability of formation tracking are proved.Simulations and experiments are conducted to demonstrate some useful coordination strategies such as movement with a leader,simultaneous movement,series connection of formations,and human-machine interaction.
Nonlinear Energy Collimation System for Linear Colliders
Resta-Lopez, Javier
2011-01-01
The post-linac energy collimation system of multi-TeV linear colliders is designed to fulfil an important function of protection of the Beam Delivery System (BDS) against miss-steered beams likely generated by failure modes in the main linac. For the case of the Compact Linear Collider (CLIC), the energy collimators are required to withstand the impact of a full bunch train in case of failure. This is a very challenging task, assuming the nominal CLIC beam parameters at 1.5 TeV beam energy. The increase of the transverse spot size at the collimators using nonlinear magnets is a potential solution to guarantee the survival of the collimators. In this paper we present an alternative nonlinear optics based on a skew sextupole pair for energy collimation. Performance simulation results are also presented.
Adaptive stabilization for cascade nonlinear systems
Institute of Scientific and Technical Information of China (English)
陈岚萍; 王洪元; 吴波
2004-01-01
An adaptive controller of full state feedback for certain cascade nonlinear systems achieving input-to-state stability with respect to unknown bounded disturbance is designed using backstepping and control Lyapunov function (CLF)techniques. We show that unknown bounded disturbance can be estimated by update laws, which requires less information on unknown disturbance, as a part of stabilizing control. The design method achieves the desired property: global robust stability. Our contribution is illustrated with the example of a disturbed pendulum.
Inverse Problems for Nonlinear Delay Systems
2011-03-15
Ba82]. For nonlinear delay systems such as those discussed here, approximation in the context of a linear semigroup framework as presented [BBu1, BBu2...linear part generates a linear semigroup as in [BBu1, BBu2, BKap]. One then uses the linear semigroup in a vari- ation of parameters implicit...BBu2, BKap] (for the linear semigroup ) plus a Gronwall inequality. An alternative (and more general) approach given in [Ba82] eschews use of the Trotter
Adaptive Control of Nonlinear Flexible Systems
1994-05-26
Proceedings of the American Control Conference , pp. 547-551, San Francisco, June 1993. 3 2 1.3 Personnel Dr. Robert Kosut and Dr. M. Giintekin Kabuli worked on...Control of Nonlinear Systems Under Matching Conditions," Proceedings of the American Control Conference , pp. 549-555, San Diego, CA, May 1990. [10] I...Poolla, P. Khargonekar, A. Tikku, J. Krause and K. Nagpal, "A time-domain ap- proach to model validation," Proceedings
Controllability of nonlinear degenerate parabolic cascade systems
Directory of Open Access Journals (Sweden)
Mamadou Birba
2016-08-01
Full Text Available This article studies of null controllability property of nonlinear coupled one dimensional degenerate parabolic equations. These equations form a cascade system, that is, the solution of the first equation acts as a control in the second equation and the control function acts only directly on the first equation. We prove positive null controllability results when the control and a coupling set have nonempty intersection.
Nonlinear dynamics analysis of a new autonomous chaotic system
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further, to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nuchaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.
Nonabelian sine-Gordon theory and its application to nonlinear optics
Park, Q H; Park, Q Han
1996-01-01
Using a field theory generalization of the spinning top motion, we construct nonabelian generalizations of the sine-Gordon theory according to each symmetric spaces. A Lagrangian formulation of these generalized sine-Gordon theories is given in terms of a deformed gauged Wess-Zumino-Witten action which also accounts for integrably perturbed coset conformal field theories. As for physical applications, we show that they become precisely the effective field theories of self-induced transparency in nonlinear optics. This provides a dictionary between field theory and nonlinear optics.
Identification of Nonlinear Systems Using Neurofuzzy Networks
Institute of Scientific and Technical Information of China (English)
LI Ying; JIAO Licheng
2001-01-01
This paper presents a compound neu-ral network model, I.e., adaptive neurofuzzy network(ANFN), which can be used for identifying the com-plicated nonlinear system. The proposed ANFN has asimple structure and exploits a hybrid algorithm com-bining supervised learning and unsupervised learning.In addition, ANFN is capable of overcoming the errorof system identification due to the existence of somechanging points and improving the accuracy of identi-fication of the whole system. The effectiveness of themodel and its algorithm are tested on the identifica-tion results of missile attacking area.
Sliding Mode Control for Nonlinear System Based on T-S Model
Institute of Scientific and Technical Information of China (English)
WU Zhong-qiang
2002-01-01
Using T-S model as an approximation for nonlinear system, the nonlinear system has been fuzzy into local linear model. The variable structure controller designed by using Lyapunov theory insures the stability of system. The sliding mode controller is designed by using unit vector style, and it suit the uncertain elements satisfying matching condition or do not satisfy matching condition. The effect of the scheme has been tasted with a simulation of an inverted pendulum.
Design for robust stabilization of nonlinear systems with uncertain parameters
Institute of Scientific and Technical Information of China (English)
赖旭芝; 文静; 吴敏
2004-01-01
Based on Lyapunov stability theory, a design method for the robust stabilization problem of a class of nonlinear systems with uncertain parameters is presented. The design procedure is divided into two steps: the first is to design controllers for the nominal system and make the system asymptotically stabilize at the expected equilibrium point; the second is to construct closed-loop nominal system based on the first step, then design robust controller to make the error of state between the original system and the nominal system converge to zero, thereby a dynamic controller with the constructed closed-loop nominal system served as interior dynamic is obtained. A numerical simulation verifies the correctness of the design method.
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
Stabilization of nonlinear system using uniform eigenvalue assignment in linear model
Siahaan, Sahat P.; Pangaribuan, Timbang
2017-09-01
Some plant in control system has nonlinear dynamic, so it is not easy to do in analysis to see its behavior using eigenstructure assignment. From many observations which have been made, some literature give methods to design nonlinear control system. The modern control theory uses state-space method to explain the behaviour on stability of a plant. To improve the stability of the closed-loop system, designer commonly use the state feedback control law. For the case inverted pendulum plant with the nonlinear dynamics, its need to perform the nonlinear control law with the concepts of modern control theory to satisfy the closed-loop system characteristic, and all the behaviour of the closed-loop system only determined from the given linear pole specifications.
Nonlinear optimization of load allocation in a manufacturing system
Institute of Scientific and Technical Information of China (English)
GUO Cai-fen; WANG Ning-sheng
2006-01-01
Based on the queuing theory, a nonlinear optimization model is proposed in this paper. A novel transformation of optimization variables is devised and the constraints are properly combined so as to make this model into a convex one, from which the Lagrangian function and the KKT conditions are derived. The interiorpoint method for convex optimization is presented here as a computationally efficient tool. Finally, this model is evaluated on a real example, from which such conclusions are drawn that the optimum result can ensure the full utilization of machines and the least amount of WIP in manufacturing systems; the interior-point method for convex optimization needs fewer iterations with significant computational savings. It appears that many non-linear optimization problems in the industrial engineering field would be amenable to this method of solution.
One-dimensional nonlinear theory for rectangular helix traveling-wave tube
Energy Technology Data Exchange (ETDEWEB)
Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong; Ju, Yongfeng [Faculty of Electronic Information Engineering, Huaiyin Institute of Technology, Huai' an 223003 (China); Wei, Yanyu [School of Physical Electronics, University of Electronic and Technology of China, Chengdu 610054 (China)
2016-08-15
A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numerically using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.
One-dimensional nonlinear theory for rectangular helix traveling-wave tube
Fu, Chengfang; Wei, Yanyu; Zhao, Bo; Yang, Yudong; Ju, Yongfeng
2016-08-01
A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numerically using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.
Tracking Control for Switched Cascade Nonlinear Systems
Directory of Open Access Journals (Sweden)
Xiaoxiao Dong
2015-01-01
Full Text Available The issue of H∞ output tracking for switched cascade nonlinear systems is discussed in this paper, where not all the linear parts of subsystems are stabilizable. The conditions of the solvability for the issue are given by virtue of the structural characteristics of the systems and the average dwell time method, in which the total activation time for stabilizable subsystems is longer than that for the unstabilizable subsystems. At last, a simulation example is used to demonstrate the validity and advantages of the proposed approach.
Dynamics of Nonlinear Time-Delay Systems
Lakshmanan, Muthusamy
2010-01-01
Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant. This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics. Special attention is devoted to scalar chaotic/hyperchaotic time-delay systems, and some higher order models, occurring in different bran...
Control of self-organizing nonlinear systems
Klapp, Sabine; Hövel, Philipp
2016-01-01
The book summarizes the state-of-the-art of research on control of self-organizing nonlinear systems with contributions from leading international experts in the field. The first focus concerns recent methodological developments including control of networks and of noisy and time-delayed systems. As a second focus, the book features emerging concepts of application including control of quantum systems, soft condensed matter, and biological systems. Special topics reflecting the active research in the field are the analysis and control of chimera states in classical networks and in quantum systems, the mathematical treatment of multiscale systems, the control of colloidal and quantum transport, the control of epidemics and of neural network dynamics.
On stability of randomly switched nonlinear systems
Chatterjee, Debasish
2007-01-01
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure global asymptotic stability using Lyapunov-based methods when individual subsystems are stable and a certain ``slow switching'' condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results therefore hold for Markov jump systems in particular. For systems with control inputs we provide explicit control s...
Simplified non-linear time-history analysis based on the Theory of Plasticity
DEFF Research Database (Denmark)
Costa, Joao Domingues
2005-01-01
is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation......This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...
Simplified non-linear time-history analysis based on the Theory of Plasticity
DEFF Research Database (Denmark)
Costa, Joao Domingues
2005-01-01
is based on the Theory of Plasticity. Firstly, the formulation and the computational procedure to perform time-history analysis of a rigid-plastic single degree of freedom (SDOF) system are presented. The necessary conditions for the method to incorporate pinching as well as strength degradation......This paper aims at giving a contribution to the problem of developing simplified non-linear time-history (NLTH) analysis of structures which dynamical response is mainly governed by plastic deformations, able to provide designers with sufficiently accurate results. The method to be presented...
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
Field theory of unification in nonlinear and linear network (I)——Theoretical grounds of field theory
Institute of Scientific and Technical Information of China (English)
陈燊年; 何煜光; 王建成
1995-01-01
A field theory has been proposed. The laws of conservation of charge and energy can be obtained from the Maxwell’s equations, which are placed in nonlinear network for simultaneous solution, and therefore the Kirchhoff’s law with its most fundamental integral formulae in nonlinear network can be obtained. Thus, it will strictly push forward the total basic equations from non-linear network to linear network as well as other important new relationships to provide the theoretical grounds for the field theory.
Korteweg-de Vries and nonlinear Schrödinger equations qualitative theory
Zhidkov, Peter E
2001-01-01
The emphasis of this book is on questions typical of nonlinear analysis and qualitative theory of PDEs. The selection of the material is related to the author's attempt to illuminate those particularly interesting questions not yet covered in other monographs though they have been the subject of published articles. One chapter, for example, is devoted to the construction of invariant measures for dynamical systems generated by certain equations and a result from a recent paper on basic properties of a system of eigenfunctions of a stationary problem. Also considered is an application of the method of qualitative theory of ODes to proving the existence of radial solutions of stationary problems and stability of solutions of NLSE nonvanishing as the spatial variable tends to infinity. Finally a recent result on the existence of an infinite sequence of invariant measures for the inegrable KdV equation is presented.
Random perturbations of nonlinear parabolic systems
Beck, Lisa
2011-01-01
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when strict parabolicity is assumed, presents both classes of systems where all weak solutions are in fact more regular, and examples of systems with weak solutions which develop singularities in finite time. Our main result is the extension of a regularity result due to Kalita to the stochastic case. Concerning the examples with singular solutions (outside the setting of Kalita's regularity result), we do not know whether stochastic noise may prevent the emergence of singularities, as it happens for easier PDEs. We can only prove that, for a linear stochastic parabolic system with coefficients outside the previous regularity theory, the expected value of the solution is not singular.
Hankel Operators and Gramians for Nonlinear Systems
Gray, W. Steven; Scherpen, Jacquelien M.A.
1998-01-01
In the theory for continuous-time linear systems, the system Hankel operator plays an important role in a number of realization problems ranging from providing an abstract notion of state to yielding tests for state space minimality and algorithms for model reduction. But in the case of continuous-t
μ Synthesis Method for Robust Control of Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
μ synthesis method for robust control of uncertain nonlinear systems is propored, which is based on feedback linearization. First, nonlinear systems are linearized as controllable linear systems by I/O linearization,such that uncertain nonlinear systems are expressed as the linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty.Then,linear robust controllers are obtained for the LFTs usingμsynthesis method based on H∞ optimization.Finally,the nonlinear robust controllers are constructed by combining the linear robust controllers and the nonlinear feedback.An example is given to illustrate the design.
Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory
DEFF Research Database (Denmark)
Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher
1998-01-01
A non-linear time-domain strip theory for vertical wave loads and ship responses is presented. The theory is generalized from a rigorous linear time-domain strip theory representaton. The hydrodynamic memory effect due to the free surface is approximated by a higher order differential equation...
EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM
Institute of Scientific and Technical Information of China (English)
XU Zi-xiang; ZHOU De-yun; DENG Zi-chen
2006-01-01
To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control,multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.
Some Problems in Nonlinear Dynamic Instability and Bifurcation Theory for Engineering Structures
Institute of Scientific and Technical Information of China (English)
彭妙娟; 程玉民
2005-01-01
In civil engineering, the nonlinear dynamic instability of structures occurs at a bifurcation point or a limit point. The instability at a bifurcation point can be analyzed with the theory of nonlinear dynamics, and that at a limit point can be discussed with the theory of elastoplasticity. In this paper, the nonlinear dynamic instability of structures was treated with mathematical and mechanical theories. The research methods for the problems of structural nonlinear dynamic stability were discussed first, and then the criterion of stability or instability of structures, the method to obtain the bifurcation point and the limit point, and the formulae of the directions of the branch solutions at a bifurcation point were elucidated. These methods can be applied to the problems of nonlinear dynamic instability of structures such as reticulated shells, space grid structures, and so on.
Dwivedi, Yogesh K; Schneberger, Scott L
2011-01-01
The overall mission of this book is to provide a comprehensive understanding and coverage of the various theories and models used in IS research. Specifically, it aims to focus on the following key objectives: To describe the various theories and models applicable to studying IS/IT management issues. To outline and describe, for each of the various theories and models, independent and dependent constructs, reference discipline/originating area, originating author(s), seminal articles, level of analysis (i.e. firm, individual, industry) and links with other theories. To provide a critical revie
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
Institute of Scientific and Technical Information of China (English)
SUN WeiJie; HUANG Jie
2009-01-01
In this paper,we consider the global robust output regulation problem for a class of uncertain nonlinear systems with nonlinear exosystems.By employing the internal model approach,we show that this problem boils down to a global robust stabilization problem of a time-varying nonlinear system in lower triangular form,the solution of which will lead to the solution of the global robust output regulation problem.An example shows the effectiveness of the proposed approach.
Origin of Soft Limits from Nonlinear Supersymmetry in Volkov--Akulov Theory
Kallosh, Renata; Murli, and Divyanshu
2016-01-01
We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov--Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries.
Observability and Information Structure of Nonlinear Systems,
1985-10-01
defined by Shannon and used as a measure of mut.:al infor-mation between event x. and y4. If p(x.l IY.) I I(x., y.) xil -in (1/p(x.)) =- JInp (x.) (2...entropy H(x,y) in a similar way as H(x,y) = - fx,yp(xiy)lnp(x,y)cdlY, = -E[ JInp (x,y)]. (3-13) With the above definitions, mutual information between x...Observabiity of Nonlinear Systems, Eng. Cybernetics, Volume 1, pp 338-345, 1972. 18. Sen , P., Chidambara, M.R., Observability of a Class of Nonli-.ear
Identification methods for nonlinear stochastic systems.
Fullana, Jose-Maria; Rossi, Maurice
2002-03-01
Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
A Master Equation for Multi-Dimensional Non-Linear Field Theories
Park, Q H
1992-01-01
A master equation ( $n$ dimensional non--Abelian current conservation law with mutually commuting current components ) is introduced for multi-dimensional non-linear field theories. It is shown that the master equation provides a systematic way to understand 2-d integrable non-linear equations as well as 4-d self-dual equations and, more importantly, their generalizations to higher dimensions.
Nonlinear Coherent Directional Coupler: Coupled Mode Theory and BPM Simulation
National Research Council Canada - National Science Library
Kumbhakar, Dharmadas
2012-01-01
.... The coupling lengths derived from this simulation are compared with coupled mode theories. BPM results for the critical power follow the trend of the coupled mode theories, but it lies in between two coupled mode theories...
Kyriakos, Alexander G.
2004-01-01
The present paper is the continuity of the previous papers "Non-linear field theory" I and II. Here on the basis of the electromagnetic representation of Dirac's electron theory we consider the geometrical distribution of the electromagnetic fields of the electron-positron. This gives the posibility to obtain the explanation and solution of many fundamental problems of the QED.
Farantos, Stavros C
2014-01-01
This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.
Nonlinear Systems of Second-Order ODEs
Directory of Open Access Journals (Sweden)
Patricio Cerda
2008-02-01
Full Text Available We study existence of positive solutions of the nonlinear system Ã¢ÂˆÂ’(p1(t,u,vuÃ¢Â€Â²Ã¢Â€Â²=Ã¢Â€Â…h1(tf1(t,u,v in (0,1; Ã¢ÂˆÂ’(p2(t,u,vvÃ¢Â€Â²Ã¢Â€Â²=h2(tf2(t,u,v in (0,1; u(0=u(1=v(0=v(1=0, where p1(t,u,v=1/(a1(t+c1g1(u,v and p2(t,u,v=1/(a2(t+c2g2(u,v. Here, it is assumed that g1, g2 are nonnegative continuous functions, a1(t, a2(t are positive continuous functions, c1,c2Ã¢Â‰Â¥0, h1,h2Ã¢ÂˆÂˆL1(0,1, and that the nonlinearities f1,Ã¢Â€Â…f2 satisfy superlinear hypotheses at zero and +Ã¢ÂˆÂž. The existence of solutions will be obtained using a combination among the method of truncation, a priori bounded and Krasnosel'skii well-known result on fixed point indices in cones. The main contribution here is that we provide a treatment to the above system considering differential operators with nonlinear coefficients. Observe that these coefficients may not necessarily be bounded from below by a positive bound which is independent of u and v.
Coordinated nonlinear robust control of TCSC and excitation for multi-machine systems
Institute of Scientific and Technical Information of China (English)
Shengwei MEI; Juming CHEN; Qiang LU; Akihiko YOKOYAMA; Masuo GOTO
2004-01-01
An advanced nonlinear robust control scheme is proposed for multi-machine power systems equipped with thyristor-controlled series compensation (TCSC). First, a decentralized nonlinear robust control approach based on the feedback linearization and H∞ theory is introduced to eliminate the nonlinearities and interconnections of the studied system, and to attenuate the exogenous disturbances that enter the system. Then, a system model uilt up, which has considered all the generators' and TCSC's dynamics, and the effects of uncertainties such as disturbances. Next, a decentralized nonlinear robust coordinated control law is developed based on this model. Simulation results on a six-machine power system show that the transient stability of the power system is obviously improved and the power transfer capacity of long distance transmission lines is enhanced regardless of fault locahons and system operation points. In addition, the control law has engineering practicality since all the variables in the expression of he control strategy can be measured locally.
Minimax theory for a class of nonlinear statistical inverse problems
Ray, Kolyan; Schmidt-Hieber, Johannes
2016-06-01
We study a class of statistical inverse problems with nonlinear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the nonlinearity. This reduces the initial nonlinear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of Hölder smoothness scales that are natural in this setting.
Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems
Directory of Open Access Journals (Sweden)
Ewelina Seroka
2015-01-01
Full Text Available The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control with state dependent, Markovian, and any switching rule is considered in the paper. To solve the issue, the Lyapunov technique, including a common, single, and multiple Lyapunov function, the hybrid control theory, and some results for stochastic nonhybrid systems are used. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations.
Impulse position control algorithms for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Sesekin, A. N., E-mail: sesekin@list.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation); Institute of Mathematics and Mechanics, Ural Division of Russian Academy of Sciences, 16 S. Kovalevskaya, Ekaterinburg, 620990 (Russian Federation); Nepp, A. N., E-mail: anepp@urfu.ru [Ural Federal University, 19 S. Mira, Ekaterinburg, 620002 (Russian Federation)
2015-11-30
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
Impulse position control algorithms for nonlinear systems
Sesekin, A. N.; Nepp, A. N.
2015-11-01
The article is devoted to the formalization and description of impulse-sliding regime in nonlinear dynamical systems that arise in the application of impulse position controls of a special kind. The concept of trajectory impulse-sliding regime formalized as some limiting network element Euler polygons generated by a discrete approximation of the impulse position control This paper differs from the previously published papers in that it uses a definition of solutions of systems with impulse controls, it based on the closure of the set of smooth solutions in the space of functions of bounded variation. The need for the study of such regimes is the fact that they often arise when parry disturbances acting on technical or economic control system.
A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM(Ⅰ)--THEORY
Institute of Scientific and Technical Information of China (English)
Jian-jun Zhang; De-ren Wang
2002-01-01
In this paper, we extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory,we prove the existence and the continuation of the following path for the corresponding homotopy equations. Therefore the basic theory of the numerical embedding method for solving the nonlinear complementarity problem is established. In part Ⅱ of this paper, we will further study the implementation of the method and give some numerical exapmles.
Stability of the Shallow Axisymmetric Parabolic-Conic Bimetallic Shell by Nonlinear Theory
Directory of Open Access Journals (Sweden)
M. Jakomin
2011-01-01
Full Text Available In this contribution, we discuss the stress, deformation, and snap-through conditions of thin, axi-symmetric, shallow bimetallic shells of so-called parabolic-conic and plate-parabolic type shells loaded by thermal loading. According to the theory of the third order that takes into account the balance of forces on a deformed body, we present a model with a mathematical description of the system geometry, displacements, stress, and thermoelastic deformations. The equations are based on the large displacements theory. We numerically calculate the deformation curve and the snap-through temperature using the fourth-order Runge-Kutta method and a nonlinear shooting method. We show how the temperature of both snap-through depends on the point where one type of the rotational curve transforms into another.
Nonlinear Mixing in Optical Multicarrier Systems
Hameed, Mahmood Abdul
Although optical fiber has a vast spectral bandwidth, efficient use of this bandwidth is still important in order to meet the ever increased capacity demand of optical networks. In addition to wavelength division multiplexing, it is possible to partition multiple low-rate subcarriers into each high speed wavelength channel. Multicarrier systems not only ensure efficient use of optical and electrical components, but also tolerate transmission impairments. The purpose of this research is to understand the impact of mixing among subcarriers in Radio-Over-Fiber (RoF) and high speed optical transmission systems, and experimentally demonstrate techniques to minimize this impact. We also analyze impact of clipping and quantization on multicarrier signals and compare bandwidth efficiency of two popular multiplexing techniques, namely, orthogonal frequency division multiplexing (OFDM) and Nyquist modulation. For an OFDM-RoF system, we present a novel technique that minimizes the RF domain signal-signal beat interference (SSBI), relaxes the phase noise limit on the RF carrier, realizes the full potential of optical heterodyne-based RF carrier generation, and increases the performance-to-cost ratio of RoF systems. We demonstrate a RoF network that shares the same RF carrier for both downlink and uplink, avoiding the need of an additional RF oscillator in the customer unit. For multi-carrier optical transmission, we first experimentally compare performance degradations of coherent optical OFDM and single-carrier Nyquist pulse modulated systems in a nonlinear environment. We then experimentally evaluate SSBI compensation techniques in the presence of semiconductor optical amplifier (SOA) induced nonlinearities for a multicarrier optical system with direct detection. We show that SSBI contamination can be significantly reduced from the data signal when the carrier-to-signal power ratio is sufficiently low.
INTRODUCTION: Introduction to Nonlinear Dynamics and Chaos Theory
McCauley, Joseph L.
1988-01-01
Chapters 1-3 of these lectures were given at the University of Oslo during my academic free half-year August l985-January 1986 which I spent at the Institute for Energy Technology (IFE). Chapter 4 was given by T Riste during my journeys to other Scandinavian institutions where I held seminars covering much of what is reflected in Chapter 5. That chapter represents a contribution to chaos theory that was carried out in collaboration with J Palmore. In place of the universal properties of unimodal maps, which are well-treated in the books by Cvitanovic and Schuster, I have instead based my elementary introduction to scaling and universality upon the damped driven pendulum and circle maps, which are of current interest to experimenters at IFE and elsewhere, as is reflected in the literature over the past year. Also, the circle map has not been so well-treated pedagogically in available texts. The discussion in Chapter 3 is not advanced, but it should prepare the reader for a better appreciation of the literature in that field. I should say that these lectures for the most part were written for students, for experimenters, and for curious theorists from other fields in physics, but not for the experts in nonlinear dynamics. For example, Chapter 3 ends where the hardest work begins. Tn preparing the lectures, I drew heavily upon the books by Arnol'd, Jorna, Jordan and Smith, Lichtenberg and Lieberman, and Schuster, and upon numerous journal articles. The level of the lectures is that of a second year graduate course at the University of Houston, but beginning with undergraduate-level topics in ordinary differential equations. Throughout, I have emphasized my interest in the connection of nonlinear dynamics to statistical mechanics, as well as my interest in "computer arithmetic". I hope that the reader will also find these subjects to be of interest since they have provided me with a great deal of intellectual enjoyment. My free-half-year at IFE would have been
A nonlinear small-deformation theory for transient droplet electrohydrodynamics
Das, Debasish
2016-01-01
The deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of \\cite{taylor1966}, there have been numerous computational and theoretical studies to predict the deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel small-deformation theor...
An extended nonlinear state predictor for a class of nonlinear time delay systems
Institute of Scientific and Technical Information of China (English)
WANG Dong; ZHOU Donghua; JIN Yihui
2004-01-01
An extended nonlinear state predictor (ENSP) for a class of nonlinear systems with input time delay is proposed. Based on the extended Kalman filter (EKF), the ENSP first estimates the current states according to the previous estimations and estimation errors, next calculates the future state values via the system model, and then adjusts the values based on the current errors. After a state predictive algorithm for a class of linear systems is presented, it is extended to a class of nonlinear time delay systems and the detailed ENSP algorithm is further proposed. Finally, computer simulations with the nonlinear example are presented, which demonstrates that the proposed ENSP can effectively and accurately predict the future states for a class of nonlinear time-delay systems no matter whether the state variables change quickly or slowly.
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Barotropic flow over bottom topography— experiments and nonlinear theory
Pfeffer, Richard L.; Kung, Robin; Ding, Wen; Li, Guo-Qing
1993-10-01
Barotropic flow over finite amplitude two-wave bottom topography is investigated both experimentally and theoretically over a broad parameter range. In the experiments, the fluid is contained in a vertically oriented, rotating circular cylindrical annulus. It is forced into motion relative to the annulus by a differentially rotating, rigid, radially sloping lid in contact with the top surface of the fluid. The radial depth variation associated with the slope of the lid, and an equal and opposite slope of the bottom boundary, simulates the effect of the variation of the Coriolis parameter with latitude (β) in planetary atmospheres and in the ocean. The dimensionless parameters which control the fluid behavior are the Rossby number (ɛ), the Ekman number (E), the β parameter, the aspect ratio (δ), the ratio of the mean radius to the gap width (α) and the ratio of the topographic height to the mean fluid depth (η). The Rossby and Ekman numbers are varied over an order of magnitude by conducting experiments at different rotation rates of the annulus. Velocity measurements using photographs of tracer particles suspended in the fluid reveal the existence of a stationary, topographically forced wave superimposed on an azimuthal mean current. With successively larger rotation rates (i.e. lower ɛ and E) the wave amplitude increases and then levels off, the phase displacement of the wave upstream of the topography increases and the azimuthal mean velocity decreases and then levels off. Linear quasigeostophic theory accounts qualitatively, but not quantitatively, for the phase displacement, predicts the wave amplitude poorly and provides no basis for predicting the zonal mean velocity. Accordingly, we have solved the nonlinear, steady-state, quasigeostrophic barotrophic vorticity equation with both Ekman layer and internal dissipation using a spectral colocation method with Fourier representation in the azimuthal direction and Chebyshev polynomial representation in the
Directory of Open Access Journals (Sweden)
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
2012-01-01
The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the...
Constrained tracking control for nonlinear systems.
Khani, Fatemeh; Haeri, Mohammad
2017-09-01
This paper proposes a tracking control strategy for nonlinear systems without needing a prior knowledge of the reference trajectory. The proposed method consists of a set of local controllers with appropriate overlaps in their stability regions and an on-line switching strategy which implements these controllers and uses some augmented intermediate controllers to ensure steering the system states to the desired set points without needing to redesign the controller for each value of set point changes. The proposed approach provides smooth transient responses despite switching among the local controllers. It should be mentioned that the stability regions of the proposed controllers could be estimated off-line for a range of set-point changes. The efficiencies of the proposed algorithm are illustrated via two example simulations. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Nonlinear system modeling based on experimental data
Energy Technology Data Exchange (ETDEWEB)
PAEZ,THOMAS L.; HUNTER,NORMAN F.
2000-02-02
The canonical variate analysis technique is used in this investigation, along with a data transformation algorithm, to identify a system in a transform space. The transformation algorithm involves the preprocessing of measured excitation/response data with a zero-memory-nonlinear transform, specifically, the Rosenblatt transform. This transform approximately maps the measured excitation and response data from its own space into the space of uncorrelated, standard normal random variates. Following this transform, it is appropriate to model the excitation/response relation as linear since Gaussian inputs excite Gaussian responses in linear structures. The linear model is identified in the transform space using the canonical variate analysis approach, and system responses in the original space are predicted using inverse Rosenblatt transformation. An example is presented.
Nonlinear variable structure excitation and steam valving controllers for power system stability
Institute of Scientific and Technical Information of China (English)
Ben WANG; Zongyuan MAO
2009-01-01
A set of novel nonlinear variable structure excitation and steam-valving controllers are proposed in this paper.On the basis of the classical dynamic equations of a generator,excitation control and steam valving control are si-multaneously considered.Design of these controllers combines the differential geometry theory with the variable structure controlling theory.The mathematical model in the form of "an affine nonlinear system" is set up for the control design of a large-scale power plant.The dynamic performance of the nonlinear variable structure controllers proposed for a single ma-chine connected to an infinite bus power system is simulated.Simulation results show that the nonlinear variable structure excitation and steam-valving controllers give satisfactory dynamic performance and good robustness.
Information theory of molecular systems
Nalewajski, Roman F
2006-01-01
As well as providing a unified outlook on physics, Information Theory (IT) has numerous applications in chemistry and biology owing to its ability to provide a measure of the entropy/information contained within probability distributions and criteria of their information ""distance"" (similarity) and independence. Information Theory of Molecular Systems applies standard IT to classical problems in the theory of electronic structure and chemical reactivity. The book starts by introducing the basic concepts of modern electronic structure/reactivity theory based upon the Density Functional Theory
Design Intelligent Model base Online Tuning Methodology for Nonlinear System
Directory of Open Access Journals (Sweden)
Ali Roshanzamir
2014-04-01
Full Text Available In various dynamic parameters systems that need to be training on-line adaptive control methodology is used. In this paper fuzzy model-base adaptive methodology is used to tune the linear Proportional Integral Derivative (PID controller. The main objectives in any systems are; stability, robust and reliability. However PID controller is used in many applications but it has many challenges to control of continuum robot. To solve these problems nonlinear adaptive methodology based on model base fuzzy logic is used. This research is used to reduce or eliminate the PID controller problems based on model reference fuzzy logic theory to control of flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.
Numerical Analysis of Nonlinear Rotor-bearing-seal System
Institute of Scientific and Technical Information of China (English)
CHENG Mei; MENG Guang; JING Jian-ping
2008-01-01
The system state trajectory, Poincaré maps, largest Lyapunov exponents, frequency spectra and bifurcation diagrams were used to investigate the non-linear dynamic behaviors of a rotor-bearing-seal coupled system and to analyze the influence of the seal and bearing on the nonlinear characteristics of the rotor system. Various nonlinear phenomena in the rotor-bearing-seal system, such as periodic motion, double-periodicmotion, multi-periodic motion and quasi-periodic motion were investigated. The results may contribute to a further understanding of the non-linear dynamics of the rotor-bearing-seal coupled system.
Confluence of general Schlesinger systems and Twistor theory
Kimura, Hironobu; Tseveennamjil, Damiran
2016-01-01
We give a description of confluence for the general Schlesinger systems (GSS) from the view point of twistor theory. GSS is a system of nonlinear di¤erential equations on the Grassmannian manifold $G_{2,N}(\\mathbf{C}$ which is obtained, for any partition $\\lambda$ of $N$, as the integrability condition of a connection $\
Stabilization of a Nonlinear Delay System
Directory of Open Access Journals (Sweden)
Walid Arouri
2012-01-01
Full Text Available Problem statement: The analysis and control of delayed systems are becoming more and more research topics in progress. This is mainly due to the fact that the delay is frequently encountered in technological systems. This can affect their significantly operations. Most control command laws are based on current digital computers and delays are intrinsic to the process or in the control loop caused by the transmission time control sequences, or computing time. The delay may affect one or more states of the considered system. It may also affect the establishment of the command. Several studies have investigated the stability of delay systems under the assumption that the delay is a variable phenomenon; such variation is considered to be bounded or limited to facilitate analysis of the system. In this study we propose a modelling of delayed system by using the multimodels and switched system theory. The analysis of stability is based on the use of second Lyapunov method. The issued stability conditions are expressed as Bilinear Matrix Inequalities impossible to resolve. Thats why we propose the same original relaxations to come over this difficulty, an example of induction machine is given to illustrate over approach. Approach: We propose to use the control theory developed for switched systems to synthesis a control laws for the stabilisation of delays system. Results: We stabilize the induction machine around many operating points despite the non linearities. Conclusion: The developed method is less conservative and less pessimistic than the used classical methods.
Heli Hu; Dan Zhao; Qingling Zhang
2013-01-01
The sliding mode control and optimization are investigated for a class of nonlinear neutral systems with the unmatched nonlinear term. In the framework of Lyapunov stability theory, the existence conditions for the designed sliding surface and the stability bound ${\\alpha }^{\\ast }$ are derived via twice transformations. The further results are to develop an efficient sliding mode control law with tuned parameters to attract the state trajectories onto the sliding surface in finit...
Robust Passivity and Feedback Design for Nonlinear Stochastic Systems with Structural Uncertainty
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper discusses the robust passivity and global stabilization problems for a class of uncertain nonlinear stochastic systems with structural uncertainties. A robust version of stochastic Kalman-Yakubovitch-Popov (KYP lemma is established, which sustains the robust passivity of the system. Moreover, a robust strongly minimum phase system is defined, based on which the uncertain nonlinear stochastic system can be feedback equivalent to a robust passive system. Following with the robust passivity theory, a global stabilizing control is designed, which guarantees that the closed-loop system is globally asymptotically stable in probability (GASP. A numerical example is presented to illustrate the effectiveness of our results.
Energy Technology Data Exchange (ETDEWEB)
Kakad, Amar [Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto 611-0011 (Japan); Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410-218 (India); Omura, Yoshiharu [Research Institute for Sustainable Humanosphere, Kyoto University, Uji, Kyoto 611-0011 (Japan); Kakad, Bharati [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410-218 (India)
2013-06-15
We perform one-dimensional fluid simulation of ion acoustic (IA) solitons propagating parallel to the magnetic field in electron-ion plasmas by assuming a large system length. To model the initial density perturbations (IDP), we employ a KdV soliton type solution. Our simulation demonstrates that the generation mechanism of IA solitons depends on the wavelength of the IDP. The short wavelength IDP evolve into two oppositely propagating identical IA solitons, whereas the long wavelength IDP develop into two indistinguishable chains of multiple IA solitons through a wave breaking process. The wave breaking occurs close to the time when electrostatic energy exceeds half of the kinetic energy of the electron fluid. The wave breaking amplitude and time of its initiation are found to be dependent on characteristics of the IDP. The strength of the IDP controls the number of IA solitons in the solitary chains. The speed, width, and amplitude of IA solitons estimated during their stable propagation in the simulation are in good agreement with the nonlinear fluid theory. This fluid simulation is the first to confirm the validity of the general nonlinear fluid theory, which is widely used in the study of solitary waves in laboratory and space plasmas.
Linearized oscillation theory for a nonlinear delay impulsive equation
Berezansky, Leonid; Braverman, Elena
2003-12-01
For a scalar nonlinear impulsive delay differential equationwith rk(t)≥0,hk(t)≤t, limj-->∞ τj=∞, such an auxiliary linear impulsive delay differential equationis constructed that oscillation (nonoscillation) of the nonlinear equation can be deduced from the corresponding properties of the linear equation. Coefficients rk(t) and delays are not assumed to be continuous. Explicit oscillation and nonoscillation conditions are established for some nonlinear impulsive models of population dynamics, such as the impulsive logistic equation and the impulsive generalized Lasota-Wazewska equation which describes the survival of red blood cells. It is noted that unlike nonimpulsive delay logistic equations a solution of a delay impulsive logistic equation may become negative.
Nonlinear waves in $\\cal PT$-symmetric systems
Konotop, Vladimir V; Zezyulin, Dmitry A
2016-01-01
Recent progress on nonlinear properties of parity-time ($\\cal PT$-) symmetric systems is comprehensively reviewed in this article. $\\cal PT$ symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying $\\cal PT$ symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a $\\cal PT$-symmetric system. The natural inclusion of nonlinearity into these $\\cal PT$ systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above $\\cal PT$-symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear $\\cal PT$-symmetric systems arising from various physical disciplines ...
Robust stabilization of general nonlinear systems with structural uncertainty
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
Analytical Evaluation of the Nonlinear Vibration of Coupled Oscillator Systems
DEFF Research Database (Denmark)
Bayat, M.; Shahidi, M.; Barari, Amin
2011-01-01
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate ap...... accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.......We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate...
A new active absorption system and its performance to linear and non-linear waves
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak;
2016-01-01
Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...
Cao, M.; Shen, T.L.; Song, Y.H.; Mei, S.W.
2002-01-01
The paper proposes a nonlinear robust controller for steam governor control in power systems. Based on dissipation theory, an innovative recursive design method is presented to construct the storage function of single machine infinite bus (SMIB) and multi-machine power systems. Furthermore, the nonl
Institute of Scientific and Technical Information of China (English)
Jia Li-Xin; Dai Hao; Hui Meng
2010-01-01
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems.Based on Lyapunov stability theory and numerical differentiation，a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems.Numerical simulation results are presented to illustrate the effectiveness of this method.
Gunderson, R. W.
1975-01-01
A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.
Bifurcations and Patterns in Nonlinear Dissipative Systems
Energy Technology Data Exchange (ETDEWEB)
Guenter Ahlers
2005-05-27
This project consists of experimental investigations of heat transport, pattern formation, and bifurcation phenomena in non-linear non-equilibrium fluid-mechanical systems. These issues are studies in Rayleigh-B\\'enard convection, using both pure and multicomponent fluids. They are of fundamental scientific interest, but also play an important role in engineering, materials science, ecology, meteorology, geophysics, and astrophysics. For instance, various forms of convection are important in such diverse phenomena as crystal growth from a melt with or without impurities, energy production in solar ponds, flow in the earth's mantle and outer core, geo-thermal stratifications, and various oceanographic and atmospheric phenomena. Our work utilizes computer-enhanced shadowgraph imaging of flow patterns, sophisticated digital image analysis, and high-resolution heat transport measurements.
Stability Analysis for Class of Switched Nonlinear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza; How, Jonathan P.
2010-01-01
Stability analysis for a class of switched nonlinear systems is addressed in this paper. Two linear matrix inequality (LMI) based sufficient conditions for asymptotic stability are proposed for switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which...
A nonlinear theory for elastic plates with application to characterizing paper properties
M. W. Johnson; Thomas J. Urbanik
1984-03-01
A theory of thin plates which is physically as well as kinematically nonlinear is, developed and used to characterize elastic material behavior for arbitrary stretching and bending deformations. It is developed from a few clearly defined assumptions and uses a unique treatment of strain energy. An effective strain concept is introduced to simplify the theory to a...
Data-Driven H∞ Control for Nonlinear Distributed Parameter Systems.
Luo, Biao; Huang, Tingwen; Wu, Huai-Ning; Yang, Xiong
2015-11-01
The data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.
Nonlinear Absorption and Refraction in Multilevel Organic Molecular System
Institute of Scientific and Technical Information of China (English)
LI Chun-Fei; DENG Xiao-Xu; WANG Yu-Xiao
2000-01-01
The nonlinear absorption and refraction in a multilevel organic molecular system is described by using the density matrix theory. The total absorptive coefficient of the system in the low-density case is equal to a linear sum of contributions from each energy level. Similarly, the total refractive index is equal to a linear sum of contributions from each energy level plus the refractive index of the vacuum. The absorption coefficient or refractive index due to each level is proportional to the population of that level, where the constant of proportionality is called the absorption cross-section or the refraction volume, respectively. The relation between the absorption cross-section and the refraction volume for each level is also given.
Nonlinear identification of MDOF systems using Volterra series approximation
Prawin, J.; Rao, A. Rama Mohan
2017-02-01
Most of the practical engineering structures exhibit nonlinearity due to nonlinear dynamic characteristics of structural joints, nonlinear boundary conditions and nonlinear material properties. Meanwhile, the presence of non-linearity in the system can lead to a wide range of structural behavior, for example, jumps, limit cycles, internal resonances, modal coupling, super and sub-harmonic resonances, etc. In this paper, we present a Volterra series approximation approach based on the adaptive filter concept for nonlinear identification of multi-degree of freedom systems, without sacrificing the benefits associated with the traditional Volterra series approach. The effectiveness of the proposed approach is demonstrated using two classical single degrees of freedom systems (breathing crack problem and Duffing Holmes oscillator) and later we extend to multi-degree of freedom systems.
Structure and Asymptotic theory for Nonlinear Models with GARCH Errors
F. Chan (Felix); M.J. McAleer (Michael); M.C. Medeiros (Marcelo)
2011-01-01
textabstractNonlinear time series models, especially those with regime-switching and conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with li
Extension to nonlinear stability theory of the circular Couette flow
Yau, Pun Wong; Wang, Shixiao; Rusak, Zvi
2016-11-01
A nonlinear stability analysis of the viscous circular Couette flow to axisymmetric perturbations under axial periodic boundary conditions is developed. The analysis is based on investigating the properties of a reduced Arnol'd energy-Casimir function Ard of Wang (2009). We show that all the inviscid flow effects as well as all the viscous-dependent terms related to the flow boundaries vanish. The evolution of ΔArd depends solely on the viscous effects of the perturbation's dynamics inside the flow domain. The requirement for the temporal decay of ΔArd leads to novel sufficient conditions for the nonlinear stability of the circular Couette flow in response to axisymmetric perturbations. Comparisons with historical studies show that our results shed light on the experimental measurements of Wendt (1933) and significantly extend the classical nonlinear stability results of Serrin (1959) and Joseph & Hung (1971). When the flow is nonlinearly stable and evolves axisymmetrically for all time, then it always decays asymptotically in time to the circular Couette flow determined uniquely by the setup of the rotating cylinders. This study provides new physical insights into a classical flow problem that was studied for decades.
New theoretical framework for OFDM/CDMA systems with peak-limited nonlinearities
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new theoretical framework for the evaluation of the in-band nonlinear distortion effects on the performance of OFDM systems is presented. In contrast to previous works that approximate the nonlinear noise as a Gaussian additive random process, the new framework is based on the properties of the large deviations of a stationary Gaussian process and shot noise theories, which can evaluate the performance of the OFDM system with high accuracy, especially at realistic scenarios where the Gaussian approximation of the nonlinear noise is no longer valid. The approach can be used to evaluate many communication systems with peak-limited nonlinearities and high PAPR, such as the downlink performance analysis of large capacity DS-CDMA systems.
A Non-Hermitian Approach to Non-Linear Switching Dynamics in Coupled Cavity-Waveguide Systems
DEFF Research Database (Denmark)
Heuck, Mikkel; Kristensen, Philip Trøst; Mørk, Jesper
2012-01-01
We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations.......We present a non-Hermitian perturbation theory employing quasi-normal modes to investigate non-linear all-optical switching dynamics in a photonic crystal coupled cavity-waveguide system and compare with finite-difference-time-domain simulations....
Three positive doubly periodic solutions of a nonlinear telegraph system
Institute of Scientific and Technical Information of China (English)
Fang-lei WANG; Yu-kun AN
2009-01-01
This paper studies existence of at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, by using the Green function and maximum principle, existence of solutions of a nonlinear telegraph system is equivalent to existence of fixed points of an operator. By imposing growth conditions on the nonlinearities, existence of at least three fixed points in cone is obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces. In other words, there exist at least three positive doubly periodic solutions of nonlinear telegraph system.
From Hamiltonian chaos to complex systems a nonlinear physics approach
Leonetti, Marc
2013-01-01
From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach collects contributions on recent developments in non-linear dynamics and statistical physics with an emphasis on complex systems. This book provides a wide range of state-of-the-art research in these fields. The unifying aspect of this book is a demonstration of how similar tools coming from dynamical systems, nonlinear physics, and statistical dynamics can lead to a large panorama of research in various fields of physics and beyond, most notably with the perspective of application in complex systems. This book also: Illustrates the broad research influence of tools coming from dynamical systems, nonlinear physics, and statistical dynamics Adopts a pedagogic approach to facilitate understanding by non-specialists and students Presents applications in complex systems Includes 150 illustrations From Hamiltonian Chaos to Complex Systems: A Nonlinear Physics Approach is an ideal book for graduate students and researchers working in applied...
Jeribi, Aref
2015-01-01
Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices with nonlinear entries in Banach spaces and Banach algebras. The book provides researchers and graduate students with a unified survey of the fundamental principles of fixed point theory in Banach spaces and algebras. The authors present several exten
Stabilization of a class of switched nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) ByrnesIsidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented.Finally, as an application the stability of switched lorenz systems is investigated.
Optimization theory for large systems
Lasdon, Leon S
2011-01-01
Important text examines most significant algorithms for optimizing large systems and clarifying relations between optimization procedures. Much data appear as charts and graphs and will be highly valuable to readers in selecting a method and estimating computer time and cost in problem-solving. Initial chapter on linear and nonlinear programming presents all necessary background for subjects covered in rest of book. Second chapter illustrates how large-scale mathematical programs arise from real-world problems. Appendixes. List of Symbols.
Ergodic theory and dynamical systems
Coudène, Yves
2016-01-01
This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of commen...
General systems theory mathematical foundations
Mesarovic, Mihajlo D
1975-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
A solution to the non-linear equations of D=10 super Yang-Mills theory
Mafra, Carlos R
2015-01-01
In this letter, we present a formal solution to the non-linear field equations of ten-dimensional super Yang--Mills theory. It is assembled from products of linearized superfields which have been introduced as multiparticle superfields in the context of superstring perturbation theory. Their explicit form follows recursively from the conformal field theory description of the gluon multiplet in the pure spinor superstring. Furthermore, superfields of higher mass dimensions are defined and their equations of motion spelled out.
FBFN-based adaptive repetitive control of nonlinearly parameterized systems
Institute of Scientific and Technical Information of China (English)
Wenli Sun; Hong Cai; Fu Zhao
2013-01-01
An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy ba-sis function network (FBFN). The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mecha-nism. Based on the Lyapunov stability theory, an adaptive repeti-tive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the control er singularity problem is solved. The proposed approach does not require an exact structure of the sys-tem dynamics, and the proposed control er is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simula-tion results demonstrate the effectiveness of the proposed method.
Nonlinear system modeling with random matrices: echo state networks revisited.
Zhang, Bai; Miller, David J; Wang, Yue
2012-01-01
Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.
Contribution to stability analysis of nonlinear control systems
Directory of Open Access Journals (Sweden)
varc Ivan
2003-12-01
Full Text Available The Popov criterion for the stability of nonlinear control systems is considered. The Popov criterion gives sufficient conditions for stability of nonlinear systems in the frequency domain. It has a direct graphical interpretation and is convenient for both design and analysis. In the article presented, a table of transfer functions of linear parts of nonlinear systems is constructed. The table includes frequency response functions and offers solutions to the stability of the given systems. The table makes a direct stability analysis of selected nonlinear systems possible. The stability analysis is solved analytically and graphically.Then it is easy to find out if the nonlinear system is or is not stable; the task that usually ranks among the difficult task in engineering practice.
NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS
Institute of Scientific and Technical Information of China (English)
周承倜; 王列东
2001-01-01
Hamilton Principle was uaed to derive the general governing equations of nonlinear dynamic stability for laminated cylindrical shells in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were solved by variational method. Analysis reveals that under the action of dynamic load,laminated cylindrical shells will fall into a state of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed: i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shells. So, in research of dynamic stability for laminated shells, to consider these factors is important.
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
Nonlinear theory of a hot-wire anemometer
Betchov, R
1952-01-01
A theoretical analysis is presented for the hot-wire anemometer to determine the differences in resistance characteristics as given by King's equation for an infinite wire length and those given by the additional considerations of (a) a finite length of wire with heat loss through its ends and (b) heat loss due to a nonlinear function of the temperature difference between the wire and the air.
Theory of plasmonic effects in nonlinear optics: the case of graphene
Rostami, Habib; Polini, Marco
2016-01-01
We develop a microscopic large-$N$ theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory, which reduces to the well-known random phase approximation in the linear-response limit, is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional (2D) gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved by virtue of the finiteness of the quasi-homogeneous second-order nonlinear response of this inversion-symmetric 2D material.
Stabilization and regulation of nonlinear systems a robust and adaptive approach
Chen, Zhiyong
2015-01-01
The core of this textbook is a systematic and self-contained treatment of the nonlinear stabilization and output regulation problems. Its coverage embraces both fundamental concepts and advanced research outcomes and includes many numerical and practical examples. Several classes of important uncertain nonlinear systems are discussed. The state-of-the art solution presented uses robust and adaptive control design ideas in an integrated approach which demonstrates connections between global stabilization and global output regulation allowing both to be treated as stabilization problems. Stabilization and Regulation of Nonlinear Systems takes advantage of rich new results to give students up-to-date instruction in the central design problems of nonlinear control, problems which are a driving force behind the furtherance of modern control theory and its application. The diversity of systems in which stabilization and output regulation become significant concerns in the mathematical formulation of practical contr...
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FUZun-Tao; LIUShi-Da; LIUShi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Applications of Elliptic Equation to Nonlinear Coupled Systems
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear coupled systems. Itis shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wavesolutions, periodic wave solutions and so on, so this method can be taken as a unified method in solving nonlinear coupled systems.
Noninteracting control of nonlinear systems based on relaxed control
Jayawardhana, B.
2010-01-01
In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to
Vibrations of Nonlinear Systems. The Method of Integral Equations,
Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not...parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi...
Exact solutions for some nonlinear systems of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)], E-mail: aramady@yahoo.com
2009-04-30
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear systems of partial differential equations (PDEs) is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDEs) are obtained. Graphs of the solutions are displayed.
ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Zuoxin; HAN Jingqing; ZHAO Suxia; WU Yongxian
2002-01-01
In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by Lyapunov function approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.
Experimental Identification of Concentrated Nonlinearity in Aeroelastic System
Directory of Open Access Journals (Sweden)
Nayfeh Ali H
2012-07-01
Full Text Available Identification of concentrated nonlinearity in the torsional spring of an aeroelastic system is performed. This system consists of a rigid airfoil that is supported by a linear spring in the plunge motion and a nonlinear spring in the pitch motion. Quadratic and cubic nonlinearities in the pitch moment are introduced to model the concentrated nonlinearity. The representation of the aerodynamic loads by the Duhamel formulation yielded accurate values for the flutter speed and frequency. The results show that the use of the Duhamel formulation to represent the aerodynamic loads yields excellent agreement between the experimental data and the numerical predictions.
Nonlinear Time-Domain Strip Theory Formulation for Low-Speed Manoeuvering and Station-Keeping
Directory of Open Access Journals (Sweden)
Thor I. Fossen
2004-10-01
Full Text Available This paper presents a computer effective nonlinear time-domain strip theory formulation for dynamic positioning (DP and low-speed manoeuvring. Strip theory or 2D potential theory, where the ship is divided in 20 to 30 cross sections, can be used to compute the potential coefficients (added mass and potential damping and the exciting wave loads (Froude-Krylov and diffraction forces. Commercially available programs are ShipX (VERES by Marintek (Fathi, 2004 and SEAWAY by Amarcon (Journée & Adegeest, 2003, for instance. The proposed method can easily be extended to utilize other strip theory formulations or 3-D potential programs like WAMIT (2004. The frequency dependent potential damping, which in classic theory results in a convolution integral not suited for real-time simulation, is compactly represented by using the state-space formulation of Kristiansen & Egeland (2003. The separation of the vessel model into a low-frequency model (represented by zerofrequency added mass and damping and a wave-frequency model (represented by motion transfer functions or RAOs, which is commonly used for simulation, is hence made superfluous. Transformations of motions and coefficients between different coordinate systems and origins, i.e. data frame, hydrodynamic frame, body frame, inertial frame etc., are put into the rigid framework of Fossen (1994, 2002. The kinematic equations of motion are formulated in a compact nonlinear vector representation and the classical kinematic assumption that the Euler angles are small is removed. This is important for computation of accurate control forces at higher roll and pitch angles. The hydrodynamic forces in the steadily translating hydrodynamic reference frame (equilibrium axes are, however, assumed tobe linear. Recipes for computation of retardation functions are presented and frequency dependent viscous damping is included. Emphasis is placed on numerical computations and representation of the data from VERES and
A Contextualised General Systems Theory
Kirsty Kitto
2014-01-01
A system is something that can be separated from its surrounds, but this definition leaves much scope for refinement. Starting with the notion of measurement, we explore increasingly contextual system behaviour and identify three major forms of contextuality that might be exhibited by a system: (1) between components; (2) between system and experimental method; and (3) between a system and its environment. Quantum theory is shown to provide a highly useful formalism from which all three forms...
Optimal Transmission Power in a Nonlinear VLC System
Institute of Scientific and Technical Information of China (English)
ZHAO Shuang; CAI Sunzeng; KANG Kai; QIAN Hua
2016-01-01
In a visible light communication (VLC) system, the light emitting diode (LED) is nonlinear for large signals, which limits the trans⁃mission power or equivalently the coverage of the VLC system. When the input signal amplitude is large, the nonlinear distortion creates harmonic and intermodulation distortion, which degrades the transmission error vector magnitude (EVM). To evaluate the impact of nonlinearity on system performance, the signal to noise and distortion ratio (SNDR) is applied, defined as the linear sig⁃nal power over the thermal noise plus the front end nonlinear distortion. At a given noise level, the optimal system performance can be achieved by maximizing the SNDR, which results in high transmission rate or long transmission range for the VLC system. In this paper, we provide theoretical analysis on the optimization of SNDR with a nonlinear Hammerstein model of LED. Simula⁃tion results and lab experiments validate the theoretical analysis.
Model reduction of nonlinear systems subject to input disturbances
Ndoye, Ibrahima
2017-07-10
The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.
Nonlinear phase noise in coherent optical OFDM transmission systems.
Zhu, Xianming; Kumar, Shiva
2010-03-29
We derive an analytical formula to estimate the variance of nonlinear phase noise caused by the interaction of amplified spontaneous emission (ASE) noise with fiber nonlinearity such as self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in coherent orthogonal frequency division multiplexing (OFDM) systems. The analytical results agree very well with numerical simulations, enabling the study of the nonlinear penalties in long-haul coherent OFDM systems without extensive numerical simulation. Our results show that the nonlinear phase noise induced by FWM is significantly larger than that induced by SPM and XPM, which is in contrast to traditional WDM systems where ASE-FWM interaction is negligible in quasi-linear systems. We also found that fiber chromatic dispersion can reduce the nonlinear phase noise. The variance of the total phase noise increases linearly with the bit rate, and does not depend significantly on the number of subcarriers for systems with moderate fiber chromatic dispersion.
Linear systems theory revisited
Willigenburg, van L.G.; Koning, de W.L.
2008-01-01
This paper investigates and clarifies how different definitions of reachability, observability, controllability, reconstructability and minimality that appear in the control literature, may be equivalent or different, depending on the type of linear system. The differences are caused by (1) whether
Three-dimensional nonlinear theory of travelling wave tubes and simulation
Institute of Scientific and Technical Information of China (English)
李斌; 杨中海
2003-01-01
A three-dimensional (3D) nonlinear theory of travelling wave tubes (TWTs) is developed, which includes a fundamental radio frequency (RF) and harmonics. When the instantaneous bandwidth exceeds an octave, the harmonic is generated and the mutual coupling between the harmonic and the fundamental RF can be observed in TWTs due to nonlinear interaction between the electron beam and the RF. At low frequencies the harmonic has an obvious effect.Based upon Tien's disc model, a plastic 3D super-particle model is proposed to improve the nonlinear analysis of TWTs.Numerical results employing a periodic magnetic focusing field are presented.
Gorbach, Andrey V
2016-01-01
We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\\hbar\\omega=(2/3)E_F$.
Nonlinear Dynamics, Chaotic and Complex Systems
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Energy Technology Data Exchange (ETDEWEB)
Kok Yan Chan, G.; Sclavounos, P. D.; Jonkman, J.; Hayman, G.
2015-04-02
A hydrodynamics computer module was developed for the evaluation of the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The recently developed formulation allows the computation of linear and nonlinear loads on floating bodies in the time domain and avoids the computationally intensive evaluation of temporal and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loads is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory
Newhall, Katherine A.; Vanden-Eijnden, Eric
2017-06-01
This paper is concerned with the longtime dynamics of the nonlinear wave equation in one-space dimension, u_{tt} - κ ^2 u_{xx} +V'(u) =0 \\quad x\\in [0,1] where κ >0 is a parameter and V( u) is a potential bounded from below and growing at least like u^2 as |u|→ ∞. Infinite energy solutions of this equation preserve a natural Gibbsian invariant measure, and when the potential is double-welled, for example when V(u) = 1/4 (1-u^2)^2, there is a regime such that two small disjoint sets in the system's phase-space concentrate most of the mass of this measure. This suggests that the solutions to the nonlinear wave equation can be metastable over these sets, in the sense that they spend long periods of time in these sets and only rarely transition between them. Here, we quantify this phenomenon by calculating exactly via transition state theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. We also investigate numerically how the mean TST frequency compares to the rate at which a typical solution crosses this dividing surface. These numerical results suggest that the dynamics of the nonlinear wave equation is ergodic and rapidly mixing with respect to the Gibbs invariant measure when the parameter κ in small enough. In this case, successive transitions between the two regions are roughly uncorrelated and their dynamics can be coarse-grained to jumps in a two-state Markov chain whose rate can be deduced from the mean TST frequency. This is a regime in which the dynamics of the nonlinear wave equation displays a metastable behavior that is not fundamentally different from that observed in its stochastic counterpart in which random noise and damping terms are added to the equation. For larger κ , however, the dynamics either stops being ergodic, or its mixing time becomes larger than the inverse of the TST frequency
Metastability of the Nonlinear Wave Equation: Insights from Transition State Theory
Newhall, Katherine A.; Vanden-Eijnden, Eric
2017-01-01
This paper is concerned with the longtime dynamics of the nonlinear wave equation in one-space dimension, u_{tt} - κ^2 u_{xx} +V'(u) =0 quad xin [0,1] where κ >0 is a parameter and V(u) is a potential bounded from below and growing at least like u^2 as |u|→ ∞. Infinite energy solutions of this equation preserve a natural Gibbsian invariant measure, and when the potential is double-welled, for example when V(u) = 1/4 (1-u^2)^2 , there is a regime such that two small disjoint sets in the system's phase-space concentrate most of the mass of this measure. This suggests that the solutions to the nonlinear wave equation can be metastable over these sets, in the sense that they spend long periods of time in these sets and only rarely transition between them. Here, we quantify this phenomenon by calculating exactly via transition state theory (TST) the mean frequency at which the solutions of the nonlinear wave equation with initial conditions drawn from its invariant measure cross a dividing surface lying in between the metastable sets. We also investigate numerically how the mean TST frequency compares to the rate at which a typical solution crosses this dividing surface. These numerical results suggest that the dynamics of the nonlinear wave equation is ergodic and rapidly mixing with respect to the Gibbs invariant measure when the parameter κ in small enough. In this case, successive transitions between the two regions are roughly uncorrelated and their dynamics can be coarse-grained to jumps in a two-state Markov chain whose rate can be deduced from the mean TST frequency. This is a regime in which the dynamics of the nonlinear wave equation displays a metastable behavior that is not fundamentally different from that observed in its stochastic counterpart in which random noise and damping terms are added to the equation. For larger κ, however, the dynamics either stops being ergodic, or its mixing time becomes larger than the inverse of the TST frequency
Robust Control Design for Uncertain Nonlinear Dynamic Systems
Kenny, Sean P.; Crespo, Luis G.; Andrews, Lindsey; Giesy, Daniel P.
2012-01-01
Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.
Identification of the nonlinear vibration system of power transformers
Jing, Zheng; Hai, Huang; Pan, Jie; Yanni, Zhang
2017-01-01
This paper focuses on the identification of the nonlinear vibration system of power transformers. A Hammerstein model is used to identify the system with electrical inputs and the vibration of the transformer tank as the output. The nonlinear property of the system is modelled using a Fourier neural network consisting of a nonlinear element and a linear dynamic block. The order and weights of the network are determined based on the Lipschitz criterion and the back-propagation algorithm. This system identification method is tested on several power transformers. Promising results for predicting the transformer vibration and extracting system parameters are presented and discussed.
Durning, Steven J; Lubarsky, Stuart; Torre, Dario; Dory, Valérie; Holmboe, Eric
2015-01-01
The purpose of this article is to propose new approaches to assessment that are grounded in educational theory and the concept of "nonlinearity." The new approaches take into account related phenomena such as "uncertainty," "ambiguity," and "chaos." To illustrate these approaches, we will use the example of assessment of clinical reasoning, although the principles we outline may apply equally well to assessment of other constructs in medical education. Theoretical perspectives include a discussion of script theory, assimilation theory, self-regulated learning theory, and situated cognition. Assessment examples to include script concordance testing, concept maps, self-regulated learning microanalytic technique, and work-based assessment, which parallel the above-stated theories, respectively, are also highlighted. We conclude with some practical suggestions for approaching nonlinearity.
Parameter Identification of Weakly Nonlinear Vibration System in Frequency Domain
Directory of Open Access Journals (Sweden)
Jiehua Peng
2004-01-01
Full Text Available A new method of identifying parameters of nonlinearly vibrating system in frequency domain is presented in this paper. The problems of parameter identification of the nonlinear dynamic system with nonlinear elastic force or nonlinear damping force are discussed. In the method, the mathematic model of parameter identification is frequency response function. Firstly, by means of perturbation method the frequency response function of weakly nonlinear vibration system is derived. Next, a parameter transformation is made and the frequency response function becomes a linear function of the new parameters. Then, based on this function and with the least square method, physical parameters of the system are identified. Finally, the applicability of the proposed technique is confirmed by numerical simulation.
Robust nonlinear variable selective control for networked systems
Rahmani, Behrooz
2016-10-01
This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.
Berry phase in a generalized nonlinear two-level system
Institute of Scientific and Technical Information of China (English)
Liu Ji-Bing; Li Jia-Hua; Song Pei-Jun; Li Wei-Bin
2008-01-01
In this paper,we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field.Both the field nonlinearity and the atom-field coupling nonlinearity are considered.We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case.In addition,we also find that the geometric phase may be easily observed when the field nonlinearity is not considered.The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered.We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.
Adaptive Control of Nonlinear Systems With Applications to the Control of Flexible Robot Arms
1991-10-28
parameters in order to review non. output regulation problem is reviewed and the robust- linear regulator theory in the absence of uncertainty. ness of...system is then rameter uncertainty in the nonlinear output regulation problem ., Recent work by Isidori and Byrnes [1) has z = f(z,9’)+g(z,9)u+p(:,9)w
THE NONLINEAR BOUNDARY VALUE PROBLEM FOR A CLASS OF INTEGRO-DIFFERENTIAL SYSTEM
Institute of Scientific and Technical Information of China (English)
Rongrong Tang
2006-01-01
In this paper, using the theory of differential inequalities, we study the nonlinear boundary value problem for a class of integro-differential system. Under appropriate assumptions, the existence of solution is proved and the uniformly valid asymptotic expansions for arbitrary n-th order approximation and the estimation of remainder term are obtained simply and conveniently.
Prykarpatsky, Anatoliy K; Golenia, Jolanta; Taneri, Ufuk
2009-01-01
Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered.
Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System
Institute of Scientific and Technical Information of China (English)
Amjad Hussain; Syed Tauseef Mohyud-Din; Ahmet Yildirim
2012-01-01
MacMillan's equations are extended to Poincaré's formalism,and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré parameters.The equivalence of the results obtained here with other forms of equations of motion is demonstrated.An illustrative example of the theory is provided as well.
Nonlinear stochastic systems with incomplete information filtering and control
Shen, Bo; Shu, Huisheng
2013-01-01
Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: · a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; · new concepts such as random sensor and signal saturations for more realistic modeling; and · demonstration of the use of techniques such...
Design of nonlinear adaptive steam valve controllers for a turbo-generator system
Energy Technology Data Exchange (ETDEWEB)
Bekiaris-Liberis, N.K.; Paraskevopoulos, P.N. [National Technical Univ. of Athens Zographou, Athens (Greece); Boglou, A.K. [Technology Education Inst. of Kavala Agios Loukas, Kavala (Greece); Arvanitis, K.G.; Pasgianos, G.D. [Agricultural Univ. of Athens, Athens (Greece)
2008-07-01
This paper reported on a study that investigated the control of power systems consisting of interconnected networks of transmission lines linking generators and loads. Improving both small and large perturbation stability and dynamic performance is important because power systems have become less stable in the past 15 years due to the use of controllers that have been designed on the basis of linearized synchronous generators and turbine models. The high nonlinear nature of power system models and the resulting disturbances render conventional linear controller design techniques obsolete for use in power systems control. Power system engineers are becoming aware of the role of turbine steam valves in improving the dynamic stability of power systems and damping low frequency oscillations. Advanced nonlinear control strategies are needed since the conventional steam valve control theory cannot guarantee transient stability in cases where operational conditions and parameters vary considerably. A design approach to a nonlinear adaptive control system with unknown parameters was developed and applied to the turbine main steam valve control of a power system. A fourth order machine model was used along with an adaptive backstepping method to construct the Lyapunov function in order to obtain a nonlinear adaptive controller to solve the turbine fast valving nonlinear control problem. The newly designed nonlinear adaptive controller can make the resulting adaptive system asymptotically stable. The proposed controller is accompanied by a dynamic estimator of parameters and includes nonlinear damping terms, which guarantee input-output stability even without the use of the adaptive law. Simulation results showed that the proposed nonlinear adaptive controller performs better than other turbine main steam valve control techniques. It can face large parametric uncertainty and results in a closed-loop system that is able to face large and smaller disturbances, providing a
Selection principles and pattern formation in fluid mechanics and nonlinear shell theory
Sather, Duane P.
1987-01-01
Research accomplishments are summarized and publications generated under the contract are listed. The general purpose of the research was to investigate various symmetry breaking problems in fluid mechanics by the use of structure parameters and selection principles. Although all of the nonlinear problems studied involved systems of partial differential equations, many of these problems led to the study of a single nonlinear operator equation of the form F(w, lambda, gamma) = 0, (w is an element of H), (lambda is an element of R1), (gamma is an element of R1). Instead of varying only the load parameter lambda, as is often done in the study of such equations, one of the main ideas used was to vary the structure parameter gamma in such a way that stable solutions were obtained. In this way one determines detailed stability results by making use of the structure of the model equations and the known physical parameters of the problem. The approach was carried out successfully for Benard-type convection problems, Taylor-like problems for short cylinders, rotating Couette-Poiseuille channel flows, and plane Couette flows. The main focus of the research was on wave theory of vortex breakdown in a tube. A number of preliminary results for inviscid axisymmetric flows were obtained.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
H {sub {infinity}} analysis of nonlinear stochastic time-delay systems
Energy Technology Data Exchange (ETDEWEB)
Shu Huisheng [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)] e-mail: hsshu@dhu.edu.cn; Wei Guoliang [Department of Applied Mathematics, Dong Hua University, Shanghai 200051 (China)
2005-10-01
In this paper, the H {sub {infinity}} analysis problem is studied for a general class of nonlinear stochastic systems with time-delay. The stochastic systems are described in terms of stochastic functional differential equations. The Razumikhin-type lemma is employed to establish sufficient conditions for the time-delay stochastic systems to be internally stable, and the H {sub {infinity}} analysis problem is studied in order to quantify the disturbance rejection attenuation level of the nonlinear stochastic time-delay system. In particular, the paper obtains the general conditions under which the L {sub 2} gain of the system is less than or equal to a given constant. Some easy-to-test criteria are also given so as to determine whether the nonlinear stochastic time-delay system under investigation is internally stable and whether it achieves certain H {sub {infinity}} performance index. Finally, illustrative examples are provided to show the usefulness of the proposed theory.
Rinkevicius, Zilvinas; Li, Xin; Sandberg, Jaime A R; Ågren, Hans
2014-05-21
We generalize a density functional theory/molecular mechanics approach for heterogeneous environments with an implementation of quadratic response theory. The updated methodology allows us to address a variety of non-linear optical, magnetic and mixed properties of molecular species in complex environments, such as combined metallic, solvent and confined organic environments. Illustrating calculations of para-nitroaniline on gold surfaces and in solution reveals a number of aspects that come into play when analyzing second harmonic generation of such systems--such as surface charge flow, coupled surface-solvent dynamics and induced geometric and electronic structure effects of the adsorbate. Some ramifications of the methodology for applied studies are discussed.
Nonlinear Dynamic Theory of Acute Cell Injuries and Brain Ischemia
Taha, Doaa; Anggraini, Fika; Degracia, Donald; Huang, Zhi-Feng
2015-03-01
Cerebral ischemia in the form of stroke and cardiac arrest brain damage affect over 1 million people per year in the USA alone. In spite of close to 200 clinical trials and decades of research, there are no treatments to stop post-ischemic neuron death. We have argued that a major weakness of current brain ischemia research is lack of a deductive theoretical framework of acute cell injury to guide empirical studies. A previously published autonomous model based on the concept of nonlinear dynamic network was shown to capture important facets of cell injury, linking the concept of therapeutic to bistable dynamics. Here we present an improved, non-autonomous formulation of the nonlinear dynamic model of cell injury that allows multiple acute injuries over time, thereby allowing simulations of both therapeutic treatment and preconditioning. Our results are connected to the experimental data of gene expression and proteomics of neuron cells. Importantly, this new model may be construed as a novel approach to pharmacodynamics of acute cell injury. The model makes explicit that any pro-survival therapy is always a form of sub-lethal injury. This insight is expected to widely influence treatment of acute injury conditions that have defied successful treatment to date. This work is supported by NIH NINDS (NS081347) and Wayne State University President's Research Enhancement Award.
Directory of Open Access Journals (Sweden)
Chaojiao Sun
2016-01-01
Full Text Available An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.
ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jiaqi MO; Wantao LIN
2008-01-01
A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.
On Restructurable Control System Theory
Athans, M.
1983-01-01
The state of stochastic system and control theory as it impacts restructurable control issues is addressed. The multivariable characteristics of the control problem are addressed. The failure detection/identification problem is discussed as a multi-hypothesis testing problem. Control strategy reconfiguration, static multivariable controls, static failure hypothesis testing, dynamic multivariable controls, fault-tolerant control theory, dynamic hypothesis testing, generalized likelihood ratio (GLR) methods, and adaptive control are discussed.
Directory of Open Access Journals (Sweden)
Šutová Zuzana
2014-12-01
Full Text Available The article deals with the active control of oscillation patterns in nonlinear dynamical systems and its possible use. The purpose of the research is to prove the possibility of oscillations frequency control based on a change of value of singular perturbation parameter placed into a mathematical model of a nonlinear dynamical system at the highest derivative. This parameter is in singular perturbation theory often called small parameter, as ε → 0+. Oscillation frequency change caused by a different value of the parameter is verified by modelling the system in MATLAB.
Anticipation and the Non-linear Dynamics of Meaning-Processing in Social Systems
Leydesdorff, Loet
2009-01-01
Social order does not exist as a stable phenomenon, but can be considered as "an order of reproduced expectations." When anticipations operate upon one another, they can generate a non-linear dynamics which processes meaning. Although specific meanings can be stabilized, for example in social institutions, all meaning arises from a global horizon of possible meanings. Using Luhmann's (1984) social systems theory and Rosen's (1985) theory of anticipatory systems, I submit algorithms for modeling the non-linear dynamics of meaning in social systems. First, a self-referential system can use a model of itself for the anticipation. Under the condition of functional differentiation, the social system can be expected to entertain a set of models; each model can also contain a model of the other models. Two anticipatory mechanisms are then possible: a transversal one between the models, and a longitudinal one providing the system with a variety of meanings. A system containing two anticipatory mechanisms can become h...
Identification of systems containing nonlinear stiffnesses using backbone curves
Londoño, Julián M.; Cooper, Jonathan E.; Neild, Simon A.
2017-02-01
This paper presents a method for the dynamic identification of structures containing discrete nonlinear stiffnesses. The approach requires the structure to be excited at a single resonant frequency, enabling measurements to be made in regimes of large displacements where nonlinearities are more likely to be significant. Measured resonant decay data is used to estimate the system backbone curves. Linear natural frequencies and nonlinear parameters are identified using these backbone curves assuming a form for the nonlinear behaviour. Numerical and experimental examples, inspired by an aerospace industry test case study, are considered to illustrate how the method can be applied. Results from these models demonstrate that the method can successfully deliver nonlinear models able to predict the response of the test structure nonlinear dynamics.
Phonon mechanisms of nonlinear decay and dephasing of mesoscopic vibrational systems
Atalaya, Juan; Kenny, Thomas W.; Dykman, Mark I.
2015-03-01
The frequencies and the decay rates of mesoscopic oscillators depend on vibration amplitudes. Nonlinear decay has been seen recently in various nano- and micro-mechanical systems. Here we consider a microscopic mechanism of nonlinear decay, the nonlinear coupling of the vibrational mode of interest, for example, a flexural mode, to other vibrations. Typically, the modes of interest have low eigenfrequencies ω0. Their decay comes from the coupling to acoustic-phonon type vibrations with much higher frequency and density of states. Thus, nonlinear decay requires quartic anharmonic coupling or cubic anharmonicity in the higher order. We find the decay rate for the inverse lifetime of the involved phonons, which is determined by the internal nonlinearity and the boundary scattering, being either much larger or smaller than ω0. The results extend the thermo-elastic, Akhiezer, and Landau-Rumer decay theory to nonlinear decay of mesoscopic modes and make specific predictions on the temperature and frequency dependence of the decay rate for different types of systems. We show that nonlinear decay is invariably accompanied by dephasing. We also show that in nano-electro-mechanical systems the decay rate can be electrostatically controlled.
Theory and Simulations of Solar System Plasmas
Goldstein, Melvyn L.
2011-01-01
"Theory and simulations of solar system plasmas" aims to highlight results from microscopic to global scales, achieved by theoretical investigations and numerical simulations of the plasma dynamics in the solar system. The theoretical approach must allow evidencing the universality of the phenomena being considered, whatever the region is where their role is studied; at the Sun, in the solar corona, in the interplanetary space or in planetary magnetospheres. All possible theoretical issues concerning plasma dynamics are welcome, especially those using numerical models and simulations, since these tools are mandatory whenever analytical treatments fail, in particular when complex nonlinear phenomena are at work. Comparative studies for ongoing missions like Cassini, Cluster, Demeter, Stereo, Wind, SDO, Hinode, as well as those preparing future missions and proposals, like, e.g., MMS and Solar Orbiter, are especially encouraged.
A Contextualised General Systems Theory
Directory of Open Access Journals (Sweden)
Kirsty Kitto
2014-10-01
Full Text Available A system is something that can be separated from its surrounds, but this definition leaves much scope for refinement. Starting with the notion of measurement, we explore increasingly contextual system behaviour and identify three major forms of contextuality that might be exhibited by a system: (1 between components; (2 between system and experimental method; and (3 between a system and its environment. Quantum theory is shown to provide a highly useful formalism from which all three forms of contextuality can be analysed, offering numerous tests for contextual behaviour, as well as modelling possibilities for systems that do indeed display it. I conclude with the introduction of a contextualised general systems theory based on an extension of this formalism
Institute of Scientific and Technical Information of China (English)
王庆林; 陈悦
1999-01-01
Aim To present a simple and effective method for the design of nonlinear and time-varying control system. Methods A new concept of dynamic equilibrium of a system and its stability were presented first. It was pointed out that what is controlled directly by the input of a control system is the system's dynamic equilibrium rather than the states. Based on it, a new feedback linearization method for nonlinear system based on the Lyapunov direct method was given. Simulation studies were also carried out. Results The example and simulation show that by use of the method, the controller design becomes very simple and the control effect is quite satisfying. Conclusion The new method unifies the stabilizing problem(regulating problem) with the tracking problem. It is a very simple and effective method for the design of nonlinear and time-varying control system.%目的给出一种简单有效的非线性时变控制系统设计方法.方法提出了动平衡态及其稳定性的概念.指出控制系统输入直接控制的是系统的动平衡态而不是系统的状态.在此基础上,给出了一种基于李雅普诺夫直接方法的非线性时变系统反馈线性方法并进行了仿真研究.结果实例和仿真表明采用这一方法不仅使控制系统的设计变得简单,同时其控制效果也是令人满意的.结论新方法将控制系统设计的调节问题与跟踪问题统一起来,是一种简单和有效的非线性时变控制系统设计方法.
Energy Technology Data Exchange (ETDEWEB)
Cloutier, J.R.; D`Souza, C.N.; Mracek, C.P. [Air Force Armament Directorate, Eglin, FL (United States)
1994-12-31
A little known technique for systematically designing nonlinear regulators is analyzed. The technique consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation (SDRE) is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = -R{sup -1}(x)B{sup T}(x)P(x)x, where P(x) is the solution of the SDRE. In the case of scalar x, it is shown that the SDRE approach yields a control solution which satisfies all of the necessary conditions for optimality even when the state and control weightings are functions of the state. It is also shown that the solution is globally asymptotically stable. In the multivariable case, the optimality, suboptimality and stability properties of the SDRE method are investigated. Under various mild assumptions of controllability and observability, the following is shown: (a) concerning the necessary conditions for optimality, where H is the Hamiltonian of the system, H{sub u} = 0 is always satisfied and, under stability, {lambda} = -H{sub x} is asymptotically satisfied at a quadratic rate as the states are driven toward the origin, (b) if it exists, a parameter-dependent SDC parameterization can be computed such that the multivariable SDRE closed loop solution satisfies all of the necessary conditions for optimality for a given initial condition, and (c) the method is locally asymptotically stable. A general nonlinear minimum-energy (nonlinear H{sub {infinity}}) problem is then posed. For this problem, the SDRF, method involves the solution of two coupled state-dependent Riccati equations at each point x along the trajectory. In the case of full state information, again under mild assumptions of controllability and observability, it is shown that the SDRE non-linear H{sub {infinity}} controller is internally locally asymptotically stable.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
A new, challenging benchmark for nonlinear system identification
Tiso, Paolo; Noël, Jean-Philippe
2017-02-01
The progress accomplished during the past decade in nonlinear system identification in structural dynamics is considerable. The objective of the present paper is to consolidate this progress by challenging the community through a new benchmark structure exhibiting complex nonlinear dynamics. The proposed structure consists of two offset cantilevered beams connected by a highly flexible element. For increasing forcing amplitudes, the system sequentially features linear behaviour, localised nonlinearity associated with the buckling of the connecting element, and distributed nonlinearity resulting from large elastic deformations across the structure. A finite element-based code with time integration capabilities is made available at https://sem.org/nonlinear-systems-imac-focus-group/. This code permits the numerical simulation of the benchmark dynamics in response to arbitrary excitation signals.
On absolute stability of nonlinear systems with small delays
Directory of Open Access Journals (Sweden)
M. I. Gil
1998-01-01
Full Text Available Nonlinear nonautonomous retarded systems with separated autonomous linear parts and continuous nonlinear ones are considered. It is assumed that deviations of the argument are sufficiently small. Absolute stability conditions are derived. They are formulated in terms of eigenvalues of auxiliary matrices.
XXIII International Conference on Nonlinear Dynamics of Electronic Systems
Stoop, Ruedi; Stramaglia, Sebastiano
2017-01-01
This book collects contributions to the XXIII international conference “Nonlinear dynamics of electronic systems”. Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.
Reconfigurable Control of Input Affine Nonlinear Systems under Actuator Fault
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Galeazzi, Roberto
2015-01-01
This paper proposes a fault tolerant control method for input-affine nonlinear systems using a nonlinear reconfiguration block (RB). The basic idea of the method is to insert the RB between the plant and the nominal controller such that fault tolerance is achieved without re-designing the nominal...
Analysis and Design Methods for Nonlinear Control Systems
1990-03-01
entitled "Design of Nonlinear PID Controllers ." In this paper it is demonstrated that the extended linearization approach can be applied to standard...Sciences and Systems, Baltimore, Maryland, pp. 675-680, 1987. [3] WJ. Rugh, "Design of Nonlinear PID Controllers ," AIChE Journa Vol. 33, No. 10, pp. 1738
Breather compactons in nonlinear Klein-Gordon systems.
Dinda, P T; Remoissenet, M
1999-11-01
We demonstrate the existence of a localized breathing mode with a compact support, i.e., a stationary breather compacton, in a nonlinear Klein-Gordon system. This breather compacton results from a delicate balance between the harmonicity of the substrate potential and the total nonlinearity induced by the substrate potential and the coupling forces between adjacent lattice sites.
General Systems Theory and Instructional Systems Design.
Salisbury, David F.
1990-01-01
Describes basic concepts in the field of general systems theory (GST) and identifies commonalities that exist between GST and instructional systems design (ISD). Models and diagrams that depict system elements in ISD are presented, and two matrices that show how GST has been used in ISD literature are included. (11 references) (LRW)
Cosmology emerging as the gauge structure of a nonlinear quantum system
Kam, Chon-Fai
2016-01-01
Berry phases and gauge structures in parameter spaces of quantum systems are the foundation of a broad range of quantum effects such as quantum Hall effects and topological insulators. The gauge structures of interacting many-body systems, which often present exotic features, are particularly interesting. While quantum systems are intrinsically linear due to the superposition principle, nonlinear quantum mechanics can arise as an effective theory for interacting systems (such as condensates of interacting bosons). Here we show that gauge structures similar to curved spacetime can arise in nonlinear quantum systems where the superposition principle breaks down. In the canonical formalism of the nonlinear quantum mechanics, the geometric phases of quantum evolutions can be formulated as the classical geometric phases of a harmonic oscillator that represents the Bogoliubov excitations. We find that the classical geometric phase can be described by a de Sitter universe. The fundamental frequency of the harmonic o...
Nonlinear stability of cylindrical shells subjected to axial flow: Theory and experiments
Karagiozis, K. N.; Païdoussis, M. P.; Amabili, M.; Misra, A. K.
2008-01-01
This paper, is concerned with the nonlinear dynamics and stability of thin circular cylindrical shells clamped at both ends and subjected to axial fluid flow. In particular, it describes the development of a nonlinear theoretical model and presents theoretical results displaying the nonlinear behaviour of the clamped shell subjected to flowing fluid. The theoretical model employs the Donnell nonlinear shallow shell equations to describe the geometrically nonlinear structure. The clamped beam eigenfunctions are used to describe the axial variations of the shell deformation, automatically satisfying the boundary conditions and the circumferential continuity condition exactly. The fluid is assumed to be incompressible and inviscid, and the fluid-structure interaction is described by linear potential flow theory. The partial differential equation of motion is discretized using the Galerkin method and the final set of ordinary differential equations are integrated numerically using a pseudo-arclength continuation and collocation techniques and the Gear backward differentiation formula. A theoretical model for shells with simply supported ends is presented as well. Experiments are also described for (i) elastomer shells subjected to annular (external) air-flow and (ii) aluminium and plastic shells with internal water flow. The experimental results along with the theoretical ones indicate loss of stability by divergence with a subcritical nonlinear behaviour. Finally, theory and experiments are compared, showing good qualitative and reasonable quantitative agreement.
Characterization of nonlinear dynamic systems using artificial neural networks
Energy Technology Data Exchange (ETDEWEB)
Urbina, A. [Univ. of Texas, El Paso, TX (United States); Hunter, N.F. [Los Alamos National Lab., NM (United States). Engineering Science and Analysis Div.; Paez, T.L. [Sandia National Labs., Albuquerque, NM (United States). Experimental Structural Dynamics Dept.
1998-12-01
The efficient characterization of nonlinear systems is an important goal of vibration and model testing. The authors build a nonlinear system model based on the acceleration time series response of a single input, multiple output system. A series of local linear models are used as a template to train artificial neutral networks (ANNs). The trained ANNs map measured time series responses into states of a nonlinear system. Another NN propagates response states in time, and a third ANN inverts the original map, transforming states into acceleration predictions in the measurement domain. The technique is illustrated using a nonlinear oscillator, in which quadratic and cubic stiffness terms play a major part in the system`s response. Reasonable maps are obtained for the states, and accurate, long-term response predictions are made for data outside the training data set.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
LINEAR AND NONLINEAR AERODYNAMIC THEORY OF INTERACTION BETWEEN FLEXIBLE LONG STRUCTURE AND WIND
Institute of Scientific and Technical Information of China (English)
徐旭; 曹志远
2001-01-01
In light of the characteristics of the interactions between flexible structure and wind in three directions, and based on the rational mechanical section-model of structure, a new aerodynamic force model is accepted, i. e. the coefficients of three component forces are the functions of the instantaneous attack angle and rotational speed Ci = Ci(β(t),θ),(i = D, L, M). So, a new method to formulate the linear and nonlinear aerodynamic items of wind and structure interacting has been put forward in accordance with "strip theory"and modified "quasi-static theory ", and then the linear and nonlinear coupled theory of super-slender structure for civil engineering analyzing are converged in one model. For the linear aerodynamic-force parts, the semi-analytical expressions of the items so-called "flutter derivatives" corresponding to the one in the classic equations have been given here,and so have the nonlinear parts. The study of the stability of nonlinear aerodynamic-coupled torsional vibration of the old Tacoma bridge shows that the form and results of the nonlinear control equation in rotational direction are in agreement with that of V. F. Bohm's.
Analysis and design of robust decentralized controllers for nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Schoenwald, D.A.
1993-07-01
Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.
Nonlinear system identification and control based on modular neural networks.
Puscasu, Gheorghe; Codres, Bogdan
2011-08-01
A new approach for nonlinear system identification and control based on modular neural networks (MNN) is proposed in this paper. The computational complexity of neural identification can be greatly reduced if the whole system is decomposed into several subsystems. This is obtained using a partitioning algorithm. Each local nonlinear model is associated with a nonlinear controller. These are also implemented by neural networks. The switching between the neural controllers is done by a dynamical switcher, also implemented by neural networks, that tracks the different operating points. The proposed multiple modelling and control strategy has been successfully tested on simulated laboratory scale liquid-level system.
Impulsive control of nonlinear systems with time-varying delays
Institute of Scientific and Technical Information of China (English)
Yu Yong-Bin; Bao Jing-Fu; Zhang Hong-Bin; Zhong Qi-Shui; Liao Xiao-Feng; Yu Jue-Sang
2008-01-01
A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.
Control design approaches for nonlinear systems using multiple models
Institute of Scientific and Technical Information of China (English)
Junyong ZHAI; Shumin FEI; Feipeng DA
2007-01-01
It is difficult to realize control for some complex nonlinear systems operated in different operating regions.Based on developing local models for different operating regions of the process, a novel algorithm using multiple models is proposed. It utilizes dynamic model bank to establish multiple local models, and their membership functions are defined according to respective regions. Then the nonlinear system is approximated to a weighted combination of the local models.The stability of the nonlinear system is proven. Finally, simulations are given to demonstrate the validity of the proposed method.
W-Stability of Multistable Nonlinear Discrete-Time Systems
Directory of Open Access Journals (Sweden)
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
Robust Fault Diagnosis Algorithm for a Class of Nonlinear Systems
Directory of Open Access Journals (Sweden)
Hai-gang Xu
2015-01-01
Full Text Available A kind of robust fault diagnosis algorithm to Lipschitz nonlinear system is proposed. The novel disturbances constraint condition of the nonlinear system is derived by group algebra method, and the novel constraint condition can meet the system stability performance. Besides, the defined robust performance index of fault diagnosis observer guarantees the robust. Finally, the effectiveness of the algorithm proposed is proved in the simulations.
Dynamic Analysis of Vibrating Systems with Nonlinearities
M. Kalami, Yazdi; Ahmadian, H.; Mirzabeigy, A.; Yildirim, A.
2012-02-01
The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
A Phase Field Model of Deformation Twinning: Nonlinear Theory and Numerical Simulations
2011-03-01
anisotropic elastic constants. The present phase field method does not enable resolution of atomic details of defect structures afforded by quantum or...multiple twins, following the theory in Appendix B. 6. Conclusions A nonlinear theory has been developed to address mechani - cal twinning. The general...Mag. A 63 (1991) 1001–1012. [25] A. Paxton, P. Gumbsch, M. Methfessel, A quantum mechanical calculation of the theoretical strength of metals, Phil. Mag
Modal theory of slow light enhanced third-order nonlinear effects in photonic crystal waveguides.
Chen, Tao; Sun, Junqiang; Li, Linsen
2012-08-27
In this paper, we derive the couple-mode equations for third-order nonlinear effects in photonic crystal waveguides by employing the modal theory. These nonlinear interactions include self-phase modulation, cross-phase modulation and degenerate four-wave mixing. The equations similar to that in nonlinear fiber optics could be expanded and applied for third-order nonlinear processes in other periodic waveguides. Based on the equations, we systematically analyze the group-velocity dispersion, optical propagation loss, effective interaction area, slow light enhanced factor and phase mismatch for a slow light engineered silicon photonic crystal waveguide. Considering the two-photon and free-carrier absorptions, the wavelength conversion efficiencies in two low-dispersion regions are numerically simulated by utilizing finite difference method. Finally, we investigate the influence of slow light enhanced multiple four-wave-mixing process on the conversion efficiency.
Nonlinear Large Deformation Theory of Composite Arches Using Truncated Rotations
1993-12-01
presented and solution techniques tend to be problem specific, making this theory difficult to extend to general structures. Recently, Minguet and Dugundji ...frame via Euler angles. Minguet and Dugundji have conducted numerous tests on cantilevered conmposite beams in an effort to evaluate bending of...from AS4-3501-6 graphite epoxy in various orientations. This problem is of particular interest as Minguet and Dugundji [22] present actual test data
Music from chaos: nonlinear dynamical systems as generators of musical materials
Bidlack, Rick Aaron
1990-01-01
A body of scientific/mathematical theory arising from a description of the behavior of complex dynamical systems is explored in terms of its pertinence to and utility in musical schemes for the generation of melodic lines and textures. Such systems are known to model significant behavioral features of real-world phenomena, including turbulent or chaotic behavior. Many of the features of nonlinear dynamical systems that are intriguing from a mathematical point of view, especially the propertie...
Bab, Saeed; Khadem, S. E.; Shahgholi, Majid; Abbasi, Amirhassan
2017-02-01
The current paper investigates the effects of a number of smooth nonlinear energy sinks (NESs) located on the disk and bearings on the vibration attenuation of a rotor-blisk-journal bearing system under excitation of a mass eccentricity force. The blade and rotor are modeled using the Euler-Bernoulli beam theory. The nonlinear energy sinks on the bearing have a linear damping and an essentially nonlinear stiffness. The nonlinear energy sinks on the disk have a linear damping, linear stiffness, and an essentially nonlinear stiffness. It can be seen that the linear stiffness of the NESs on the disk is eliminated by the negative stiffness induced by the centrifugal force, and the collection of the NESs can be tuned to a required rotational speed of the rotor by varying the linear stiffness of the NESs. Furthermore, the remained stiffness of the NESs on the disk after elimination of their linear stiffness, would be essentially a nonlinear (nonlinearizable) one. Two nonlinear energy sinks in the vertical axes are positioned on the bearing housing and nnd NESs are located on the perimeter of the disk. The equations of motion are extracted using the extended Hamilton principle. The modal coordinates and complex transformations are employed to decrease the number of equations of motion. A genetic algorithm is used to optimize the parameters of the nonlinear energy sinks and its objective function is considered as minimizing the vibration of the rotating system within an operating speed range. In order to examine the periodic and non-periodic solutions of the system, time history, bifurcation diagram, Poincaré map, phase portrait, Lyapunov exponent, and power spectra analyses are performed. System shows periodic and quasi-periodic motions for different values of the system parameters. It is shown that the NESs on the disk and bearings have almost local effects on vibration reduction of rotating system. In addition, the optimum NESs remove the instability region from the
Advanced nonlinear engine speed control systems
DEFF Research Database (Denmark)
Vesterholm, Thomas; Hendricks, Elbert
1994-01-01
: accurately tracking of a desired engine speed in the presence of model uncertainties and severe load disturbances. This is accomplished by using advanced nonlinear control techniques such as input/output-linearization and sliding mode control. These techniques take advantage of a nonlinear model......Several subsidiary control problems have turned out to be important for improving driveability and fuel consumption in modern spark ignition (SI) engine cars. Among these are idle speed control and cruise control. In this paper the idle speed and cruise control problems will be treated as one...
Dimensional reduction of nonlinear time delay systems
Directory of Open Access Journals (Sweden)
M. S. Fofana
2005-01-01
infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions of the Duffing and van der Pol equations. For both nonlinear delay equations, transcendental characteristic equations of linearized stability are examined through Hopf bifurcation. The infinite-dimensional nonlinear solutions of the delay equations are decomposed into stable and centre subspaces, whose respective dimensions are determined by the linearized stability of the transcendental equations. Linear semigroups, infinitesimal generators, and their adjoint forms with bilinear pairings are the additional candidates for the infinite-dimensional reduction.
Leech Lattice Extension of the Non-linear Schrodinger Equation Theory of Einstein spaces
Chapline, George
2015-01-01
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations fo...
Imaging theory of nonlinear second harmonic and third harmonic generations in confocal microscopy
Institute of Scientific and Technical Information of China (English)
TANG; Zhilie; XING; Da; LIU; Songhao
2004-01-01
The imaging theory of nonlinear second harmonic generation (SHG) and third harmonic generation (THG) in confocal microscopy is presented in this paper. The nonlinear effect of SHG and THG on the imaging properties of confocal microscopy has been analyzed in detail by the imaging theory. It is proved that the imaging process of SHG and THG in confocal microscopy, which is different from conventional coherent imaging or incoherent imaging, can be divided into two different processes of coherent imaging. The three-dimensional point spread functions (3D-PSF) of SHG and THG confocal microscopy are derived based on the nonlinear principles of SHG and THG. The imaging properties of SHG and THG confocal microscopy are discussed in detail according to its 3D-PSF. It is shown that the resolution of SHG and THG confocal microscopy is higher than that of single-and two-photon confocal microscopy.
Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
Xiao-Yuan Luo; Zhi-Hao Zhu; Xin-Ping Guan
2009-01-01
In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of "explosion of complexity" in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globaily uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller (SMC). Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.
Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input
Institute of Scientific and Technical Information of China (English)
张克勤; 庄开宇; 苏宏业; 褚健; 高红
2002-01-01
This paper presents a sliding mode (SM) based identifier to deal wit h the parameter identification problem for a class of parameter uncertain nonlin ear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonline ar system; an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.
Systems Theory and Systems Approach to Leadership
Directory of Open Access Journals (Sweden)
Dr.Sc. Berim Ramosaj
2014-06-01
Full Text Available Systems theory is product of the efforts of many researchers to create an intermediate field of coexistence of all sciences. If not for anything else, because of the magnitude that the use of systemic thinking and systemic approach has taken, it has become undisputed among the theories. Systems theory not only provides a glossary of terms with which researchers from different fields can be understood, but provides a framework for the presentation and interpretation of phenomena and realities. This paper addresses a systematic approach to leadership, as an attempt to dredge leadership and systems theory literature to find the meeting point. Systems approach is not an approach to leadership in terms of a manner of leader’s work, but it’s the leader's determination to factorize in his leadership the external environment and relationships with and among elements. Leader without followers is unable to exercise his leadership and to ensure their conviction he should provide a system, a structure, a purpose, despite the alternative chaos. Systems approach clarifies the thought on the complexity and dynamism of the environment and provides a framework for building ideas. If the general system theory is the skeleton of science (Boulding: 1956, this article aims to replenish it with leadership muscles by prominent authors who have written on systems theory and leadership, as well as through original ideas. In this work analytical methods were used (by analyzing approaches individually as well as synthetic methods (by assaying individual approaches in context of entirety. The work is a critical review of literature as well as a deductive analysis mingled with models proposed by authors through inductive analysis. Meta-analysis has been used to dissect the interaction and interdependence between leadership approaches.
Adaptive Third-Order Leader-Following Consensus of Nonlinear Multi-agent Systems with Perturbations
Institute of Scientific and Technical Information of China (English)
SUN Mei; CHEN Ying; CAO Long; WANG Xiao-Fang
2012-01-01
We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies. Based on graph theory and Lyapunov stability theory, the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations. Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.%We investigate the third-order leader-following consensus problem of nonlinear multi-agent systems in undirected network topologies.Based on graph theory and Lyapunov stability theory,the adaptive control method is employed to achieve leader-following consensus in an undirected network of agents with nonlinear third-order dynamics against the perturbations.Simulation examples validate the correctness of the results and show that the control gains have a great influence on the convergence performance of errors for a short time.
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1994-01-01
In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the st