Showing papers on "Nonlinear system published in 2011"

Fourier Analysis and Nonlinear Partial Differential Equations

Abstract: Preface.- 1. Basic analysis.- 2. Littlewood-Paley theory.- 3. Transport and transport-diffusion equations.- 4. Quasilinear symmetric systems.- 5. Incompressible Navier-Stokes system.- 6. Anisotropic viscosity.- 7. Euler system for perfect incompressible fluids.- 8. Strichartz estimates and applications to semilinear dispersive equations.- 9. Smoothing effect in quasilinear wave equations.- 10.- The compressible Navier-Stokes system.- References. - List of notations.- Index.

Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation

Abstract: FRACTIONAL ORDER NONLINEAR SYSTEMS MODELING ANALYSIS AND SIMULATION NONLINEAR PHYSICAL SCIENCE PDF Are you looking for fractional order nonlinear systems modeling analysis and simulation nonlinear physical science Books? Now, you will be happy that at this time fractional order nonlinear systems modeling analysis and simulation nonlinear physical science PDF is available at our online library. With our complete resources, you could find fractional order nonlinear systems modeling analysis and simulation nonlinear physical science PDF or just found any kind of Books for your readings everyday.

Robust Adaptive Control of Uncertain Nonlinear Systems in the Presence of Input Saturation and External Disturbance

Abstract: In this technical note, we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance. By using backstepping approaches, two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a Nussbaum function. The Nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation. Unlike some existing control schemes for systems with input saturation, the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance. Besides showing global stability, transient performance is also established and can be adjusted by tuning certain design parameters.

Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms

Abstract: This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations) Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes At the same time, the book opens many directions for possible future research

Solitons in nonlinear lattices

Abstract: This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are also surveyed, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation. The solitons are considered in one, two, and three dimensions. Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions can be drawn. In particular, a novel fundamental property of one-dimensional solitons, which does not occur in the absence of NLs, is a finite threshold value of the soliton norm, necessary for their existence. In multidimensional settings, the stability of solitons supported by the spatial modulation of the nonlinearity is a truly challenging problem, for theoretical and experimental studies alike. In both the one-dimensional and two-dimensional cases, the mechanism that creates solitons in NLs in principle is different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.

On the Convergence of Discrete Approximations to the Navier-Stokes Equations

Abstract: A class of useful difference approximations to the full nonlinear Navier-Stokes equations is analyzed; the convergence of these approximations to the solutions of the corresponding differential equations is established and the rate of convergence is estimated.

The Duffing Equation: Nonlinear Oscillators and their Behaviour

Abstract: List of Contributors. Preface. 1 Background: On Georg Duffing and the Duffing Equation (Ivana Kovacic and Michael J. Brennan). 1.1 Introduction. 1.2 Historical perspective. 1.3 A brief biography of Georg Duffing. 1.4 The work of Georg Duffing. 1.5 Contents of Duffing's book. 1.6 Research inspired by Duffing s work. 1.7 Some other books on nonlinear dynamics. 1.8 Overview of this book. References. 2 Examples of Physical Systems Described by the Duffing Equation (Michael J. Brennan and Ivana Kovacic). 2.1 Introduction. 2.2 Nonlinear stiffness. 2.3 The pendulum. 2.4 Example of geometrical nonlinearity. 2.5 A system consisting of the pendulum and nonlinear stiffness. 2.6 Snap-through mechanism. 2.7 Nonlinear isolator. 2.8 Large deflection of a beam with nonlinear stiffness. 2.9 Beam with nonlinear stiffness due to inplane tension. 2.10 Nonlinear cable vibrations. 2.11 Nonlinear electrical circuit. 2.12 Summary. References. 3 Free Vibration of a Duffing Oscillator with Viscous Damping (Hiroshi Yabuno). 3.1 Introduction. 3.2 Fixed points and their stability. 3.3 Local bifurcation analysis. 3.4 Global analysis for softening nonlinear stiffness ( < 0). 3.5 Global analysis for hardening nonlinear stiffness ( < 0). 3.6 Summary. Acknowledgments. References. 4 Analysis Techniques for the Various Forms of the Duffing Equation (Livija Cveticanin). 4.1 Introduction. 4.2 Exact solution for free oscillations of the Duffing equation with cubic nonlinearity. 4.3 The elliptic harmonic balance method. 4.4 The elliptic Galerkin method. 4.5 The straightforward expansion method. 4.6 The elliptic Lindstedt Poincare method. 4.7 Averaging methods. 4.8 Elliptic homotopy methods. 4.9 Summary. References. Appendix AI: Jacob elliptic function and elliptic integrals. Appendix 4AII: The best L2 norm approximation. 5 Forced Harmonic Vibration of a Duffing Oscillator with Linear Viscous Damping (Tamas Kalmar-Nagy and Balakumar Balachandran). 5.1 Introduction. 5.2 Free and forced responses of the linear oscillator. 5.3 Amplitude and phase responses of the Duffing oscillator. 5.4 Periodic solutions, Poincare sections, and bifurcations. 5.5 Global dynamics. 5.6 Summary. References. 6 Forced Harmonic Vibration of a Duffing Oscillator with Different Damping Mechanisms (Asok Kumar Mallik). 6.1 Introduction. 6.2 Classification of nonlinear characteristics. 6.3 Harmonically excited Duffing oscillator with generalised damping. 6.4 Viscous damping. 6.5 Nonlinear damping in a hardening system. 6.6 Nonlinear damping in a softening system. 6.7 Nonlinear damping in a double-well potential oscillator. 6.8 Summary. Acknowledgments. References. 7 Forced Harmonic Vibration in a Duffing Oscillator with Negative Linear Stiffness and Linear Viscous Damping (Stefano Lenci and Giuseppe Rega). 7.1 Introduction. 7.2 Literature survey. 7.3 Dynamics of conservative and nonconservative systems. 7.4 Nonlinear periodic oscillations. 7.5 Transition to complex response. 7.6 Nonclassical analyses. 7.7 Summary. References. 8 Forced Harmonic Vibration of an Asymmetric Duffing Oscillator (Ivana Kovacic and Michael J. Brennan). 8.1 Introduction. 8.2 Models of the systems under consideration. 8.3 Regular response of the pure cubic oscillator. 8.4 Regular response of the single-well Helmholtz Duffing oscillator. 8.5 Chaotic response of the pure cubic oscillator. 8.6 Chaotic response of the single-well Helmholtz Duffing oscillator. 8.7 Summary. References. Appendix Translation of Sections from Duffing's Original Book (Keith Worden and Heather Worden). Glossary. Index.

The Navier-Stokes Equations: An Elementary Functional Analytic Approach

Abstract: Preface.- I Introduction.- II Preliminary Results.- III The Stationary Navier-Stokes Equations.- IV The Linearized Nonstationary Theory.- V The Full Nonlinear Navier-Stokes Equations.- Bibliography.- Index.ai

Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems

Abstract: This paper investigates fast finite-time control of nonlinear dynamics using terminal sliding-mode (TSM) scheme. Some new norms of fast TSM strategies are proposed, and a faster convergence rate is established in comparison with the conventional fast TSM. A novel concept of nonsingular fast TSM, which is able to avoid the possible singularity during the control phase, is adopted in the robust high-precision control of uncertain nonlinear systems. Numerical simulation on a two-link rigid robot manipulator demonstrates the effectiveness of the proposed algorithm. Copyright © 2010 John Wiley & Sons, Ltd.

Data-Driven Model-Free Adaptive Control for a Class of MIMO Nonlinear Discrete-Time Systems

Abstract: In this paper, a data-driven model-free adaptive control (MFAC) approach is proposed based on a new dynamic linearization technique (DLT) with a novel concept called pseudo-partial derivative for a class of general multiple-input and multiple-output nonlinear discrete-time systems. The DLT includes compact form dynamic linearization, partial form dynamic linearization, and full form dynamic linearization. The main feature of the approach is that the controller design depends only on the measured input/output data of the controlled plant. Analysis and extensive simulations have shown that MFAC guarantees the bounded-input bounded-output stability and the tracking error convergence.

A Novel Data-Driven Control Approach for a Class of Discrete-Time Nonlinear Systems

Abstract: In this work, a novel data-driven control approach, model-free adaptive control, is presented based on a new dynamic linearization technique for a class of discrete-time single-input and single-output nonlinear systems. The main feature of the approach is that the controller design depends merely on the input and the output measurement data of the controlled plant. The theoretical analysis shows that the approach guarantees the bounded input and bounded output stability and tracking error monotonic convergence. The comparison experiments verify the effectiveness of the proposed approach.

Wave Turbulence

Abstract: In this paper we review recent developments in the statistical theory of weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT) We revise WT theory using a generalisation of the random phase approximation (RPA) This generalisation takes into account that not only the phases but also the amplitudes of the wave Fourier modes are random quantities and it is called the ``Random Phase and Amplitude'' approach This approach allows to systematically derive the kinetic equation for the energy spectrum from the the Peierls-Brout-Prigogine (PBP) equation for the multi-mode probability density function (PDF) The PBP equation was originally derived for the three-wave systems and in the present paper we derive a similar equation for the four-wave case Equation for the multi-mode PDF will be used to validate the statistical assumptions about the phase and the amplitude randomness used for WT closures Further, the multi-mode PDF contains a detailed statistical information, beyond spectra, and it finally allows to study non-Gaussianity and intermittency in WT, as it will be described in the present paper In particular, we will show that intermittency of stochastic nonlinear waves is related to a flux of probability in the space of wave amplitudes

Sliding-Mode Robot Control With Exponential Reaching Law

Abstract: In this paper, sliding-mode control is applied on multi-input/multi-output (MIMO) nonlinear systems. A novel approach is proposed, which allows chattering reduction on control input while keeping high tracking performance of the controller in steady-state regime. This approach consists of designing a nonlinear reaching law by using an exponential function that dynamically adapts to the variations of the controlled system. Experimental study was focused on a MIMO modular robot arm. Experimental results are presented to show the effectiveness of the proposed approach, regarding particularly the chattering reduction on control input in steady-state regime.

Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons

Abstract: The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic analysis, perturbation theory, the method of multiple scales, deep and shallow water waves, nonlinear optics including fiber optic communications, mode-locked lasers and dispersion-managed wave phenomena. Most chapters feature exercise sets, making the book suitable for advanced courses or for self-directed learning. Graduate students and researchers will find this an excellent entry to a thriving area at the intersection of applied mathematics, engineering and physical science.

Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior

Abstract: 15 developed a thermal model for the LiCoO2-mesocarbon microbead MCMB pouch cells based on the PP model and obtained good agreement between model predictions and experimental data. A disadvantage common to the P2D model and the PP model is the long simulation time due to the large number of nonlinear equations, so these models become computationally inefficient for simulating conditions such as cycling behavior and series/parallel configuration of stacked cells in battery packs. To improve computational run time without compromising accuracy, the singleparticle model SP modelRef. 3 and 16 was proposed. The SP model ignores the detailed distribution of local concentration and potential in the solution phase and instead accounts for a lumped solution resistance term. Furthermore, the local reaction currents across the porous electrode are assumed to be constant, which allows treatment of a porous electrode as a large number of single particles, all of which are subjected to the same conditions. These assumptions are reasonable for low applied current densities, thin electrodes, and highly conductive electrodes. In such cases the overpotential is primarily affected by the diffusion in the solid state. At high current densities, the concentration gradients in the electrolyte become important. The model presented here does not include these concentration gradients and is consequently limited to low to moderate current densities. These assumptions simplify the model equations significantly. The SP model using a two term polynomial approximation shows good agreement with the detailed PP model for charge/discharge below 1C, where C denotes the cell capacity. 3 In this work, the single-particle model is extended to include thermal effects by adding the energy balance equation to the SP model. Instead of using a two term polynomial approximation, the solid phase diffusion equations are solved by the eigenfunction expansion method, which improved the accuracy of the model. Parameters in this SP thermal model are estimated by fitting the simulated discharge curves up to 1C rate with the experimental data obtained on lithium-ion pouch cells. Also, good agreement between the SP thermal model and the PP thermal model presented in Ref. 15 is obtained.

Observer-Based Adaptive Fuzzy Backstepping Dynamic Surface Control for a Class of MIMO Nonlinear Systems

Abstract: In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of multiple-input-multiple-output nonlinear systems with immeasurable states. Using fuzzy-logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed to estimate the immeasurable states. By combining adaptive-backstepping technique and DSC technique, an adaptive fuzzy output-feedback backstepping-control approach is developed. The proposed control method not only overcomes the problem of “explosion of complexity” inherent in the backstepping-design methods but also overcomes the problem of unavailable state measurements. It is proved that all the signals of the closed-loop adaptive-control system are semiglobally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.

Adaptive Neural Output Feedback Tracking Control for a Class of Uncertain Discrete-Time Nonlinear Systems

Abstract: This brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi-input-multi-output (MIMO) systems in the discrete-time form. The considered MIMO systems are composed of n subsystems with the couplings of inputs and states among subsystems. In order to solve the noncausal problem and decouple the couplings, it needs to transform the systems into a predictor form. The higher order neural networks are utilized to approximate the desired controllers. By using Lyapunov analysis, it is proven that all the signals in the closed-loop system is the semi-globally uniformly ultimately bounded and the output errors converge to a compact set. In contrast to the existing results, the advantage of the scheme is that the number of the adjustable parameters is highly reduced. The effectiveness of the scheme is verified by a simulation example.

Tube-based robust nonlinear model predictive control

Abstract: This paper extends tube-based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube-based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.