Showing papers on "Nonlinear system published in 2004"

Unscented filtering and nonlinear estimation

Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

Active Appearance Models Revisited

Abstract: Active Appearance Models (AAMs) and the closely related concepts of Morphable Models and Active Blobs are generative models of a certain visual phenomenon. Although linear in both shape and appearance, overall, AAMs are nonlinear parametric models in terms of the pixel intensities. Fitting an AAM to an image consists of minimising the error between the input image and the closest model instances i.e. solving a nonlinear optimisation problem. We propose an efficient fitting algorithm for AAMs based on the inverse compositional image alignment algorithm. We show that the effects of appearance variation during fitting can be precomputed (“projected out”) using this algorithm and how it can be extended to include a global shape normalising warp, typically a 2D similarity transformation. We evaluate our algorithm to determine which of its novel aspects improve AAM fitting performance.

Time-Dependent Density Functional Theory

Abstract: Time-dependent density functional theory (TDDFT) can be viewed as an exact reformulation of time-dependent quantum mechanics, where the fundamental variable is no longer the many-body wave function but the density. This time-dependent density is determined by solving an auxiliary set of noninteracting Schrodinger equations, the Kohn-Sham equations. The nontrivial part of the many-body interaction is contained in the so-called exchange-correlation potential, for which reasonably good approximations exist. Within TDDFT two regimes can be distinguished: (a) If the external time-dependent potential is "small," the complete numerical solution of the time-dependent Kohn-Sham equations can be avoided by the use of linear response theory. This is the case, e.g., for the calculation of photoabsorption spectra. (b) For a "strong" external potential, a full solution of the time-dependent Kohn-Sham equations is in order. This situation is encountered, for instance, when matter interacts with intense laser fields. In this review we give an overview of TDDFT from its theoretical foundations to several applications both in the linear and in the nonlinear regime.

Nonlinear Output Regulation: Theory and Applications

Abstract: Preface 1. Linear output regulation 2. Introduction to nonlinear systems 3. Nonlinear output regulation 4. Approximation method for the nonlinear output regulation 5. Nonlinear robust output regulation 6. From output regulation to stabilization 7. Global robust output regulation 8. Output regulation for singular nonlinear systems 9. Output regulation for discrete-time nonlinear systems Notes and references Appendices Bibliography Index.

A study of injection locking and pulling in oscillators

Abstract: Injection locking characteristics of oscillators are derived and a graphical analysis is presented that describes injection pulling in time and frequency domains. An identity obtained from phase and envelope equations is used to express the requisite oscillator nonlinearity and interpret phase noise reduction. The behavior of phase-locked oscillators under injection pulling is also formulated.

Disturbance observer based control for nonlinear systems

Abstract: This work presents a general framework for nonlinear systems subject to disturbances using disturbance observer based control (DOBC) techniques. A two-stage design procedure to improve disturbance attenuation ability of current linear/nonlinear controllers is proposed where the disturbance observer design is separated from the controller design. To facilitate this concept, a nonlinear disturbance observer is developed for disturbances generated by an exogenous system, and global exponential stability is established under certain condition. Furthermore, semiglobal stability condition of the composite controller consisting of a nonlinear controller and the nonlinear disturbance observer is established. The developed method is illustrated by the application to control of a two-link robotic manipulator.

Diffuse-charge dynamics in electrochemical systems.

Abstract: The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon= lambdaD/L, where lambdaD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of lambdaDL/D (not lambdaD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and Faradaic processes.

Arbitrary Lagrangian–Eulerian Methods

Abstract: The aim of the present chapter is to provide an in-depth survey of arbitrary Lagrangian–Eulerian (ALE) methods, including both conceptual aspects of the mixed kinematical description and numerical implementation details. Applications are discussed in fluid dynamics, nonlinear solid mechanics and coupled problems describing fluid–structure interaction. The need for an adequate mesh-update strategy is underlined, and various automatic mesh-displacement prescription algorithms are reviewed. This includes mesh-regularization methods essentially based on geometrical concepts, as well as mesh-adaptation techniques aimed at optimizing the computational mesh according to some error indicator. Emphasis is then placed on particular issues related to the modeling of compressible and incompressible flow and nonlinear solid mechanics problems. This includes the treatment of convective terms in the conservation equations for mass, momentum, and energy, as well as a discussion of stress-update procedures for materials with history-dependent constitutive behavior. Keywords: ALE description; convective transport; finite elements; stabilization techniques; mesh regularization and adaptation; fluid dynamics; nonlinear solid mechanics; stress-update procedures; fluid–structure interaction

An introduction to nonlinear finite element analysis

Abstract: 1. Introduction 2. The Finite Element Method: A Review 3. Heat Transfer and other Field Problems in One Dimension 4. Nonlinear Bending of Straight Beams 5. Heat Transfer and other Field Problems in Two Dimensions 6. Nonlinear Bending of Elastic Plates 7. Flows of Viscous Incompressible Fluids 8. Nonlinear Analysis of Time-Dependent Problems 9. Finite Element Formulations of Solids and Structures 10. Material Nonlinearities and Coupled Problems A1 Solution Procedures for Nonlinear Equations A2 Banded Symmetric and Unsymmetric Solvers

Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction.

Abstract: Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches--unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The authors' new unconstrained approach was easiest to apply. All 4 approaches were relatively unbiased for normally distributed indicators, but the constrained and QML approaches were more biased for nonnormal data; the size and direction of the bias varied with the distribution but not with the sample size. QML had more power, but this advantage was qualified by consistently higher Type I error rates. The authors also compared general strategies for defining product indicators to represent the latent interaction factor.

Bayesian P-Splines

Abstract: P-splines are an attractive approach for modeling nonlinear smooth effects of covariates within the additive and varying coefficient models framework. In this article, we first develop a Bayesian version for P-splines and generalize in a second step the approach in various ways. First, the assumption of constant smoothing parameters can be replaced by allowing the smoothing parameters to be locally adaptive. This is particularly useful in situations with changing curvature of the underlying smooth function or with highly oscillating functions. In a second extension, one-dimensional P-splines are generalized to two-dimensional surface fitting for modeling interactions between metrical covariates. In a last step, the approach is extended to situations with spatially correlated responses allowing the estimation of geoadditive models. Inference is fully Bayesian and uses recent MCMC techniques for drawing random samples from the posterior. In a couple of simulation studies the performance of Bayesian P-spline...

Enhancement of nonlinear effects using photonic crystals.

Abstract: The quest for all-optical signal processing is generally deemed to be impractical because optical nonlinearities are usually weak. The emerging field of nonlinear photonic crystals seems destined to change this view dramatically. Theoretical considerations show that all-optical devices using photonic crystal designs promise to be smaller than the wavelength of light, and to operate with bandwidths that are very difficult to achieve electronically. When created in commonly used materials, these devices could operate at powers of only a few milliwatts. Moreover, if these designs are combined with materials and systems that support electromagnetically induced transparency, operation at single-photon power levels could be feasible.

Adaptive neural control of uncertain MIMO nonlinear systems

Abstract: In this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, with couplings in the forms of unknown nonlinearities and/or parametric uncertainties in the input matrices, as well as in the system interconnections without any bounding restrictions. Using the block-triangular structure properties, the stability analyses of the closed-loop MIMO systems are shown in a nested iterative manner for all the states. By exploiting the special properties of the affine terms of the two classes of MIMO systems, the developed neural control schemes avoid the controller singularity problem completely without using projection algorithms. Semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop of MIMO nonlinear systems is achieved. The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. The proposed schemes offer systematic design procedures for the control of the two classes of uncertain MIMO nonlinear systems. Simulation results are presented to show the effectiveness of the approach.

Initial-boundary value problems and the Navier-Stokes equations

Abstract: Preface to the Classics Edition Introduction 1. The Navier-Stokes equations 2. Constant-coefficient Cauchy problems 3. Linear variable-coefficient Cauchy problems in 1D 4. A nonlinear example: Burgers' equations 5. Nonlinear systems in one space dimension 6. The Cauchy problem for systems in several dimensions 7. Initial-boundary value problems in one space dimension 8. Initial-boundary value problems in several space dimensions 9. The incompressible Navier-Stokes equations: the spatially periodic case 10. The incompressible Navier-Stokes equations under initial and boundary conditions Appendices References Author index Subject index.

Stochastic Numerics for Mathematical Physics

Abstract: 1 Mean-square approximation for stochastic differential equations.- 2 Weak approximation for stochastic differential equations.- 3 Numerical methods for SDEs with small noise.- 4 Stochastic Hamiltonian systems and Langevin-type equations.- 5 Simulation of space and space-time bounded diffusions.- 6 Random walks for linear boundary value problems.- 7 Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations.- 8 Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approach.- 9 Application of stochastic numerics to models with stochastic resonance and to Brownian ratchets.- A Appendix: Practical guidance to implementation of the stochastic numerical methods.- A.1 Mean-square methods.- A.2 Weak methods and the Monte Carlo technique.- A.3 Algorithms for bounded diffusions.- A.4 Random walks for linear boundary value problems.- A.5 Nonlinear PDEs.- A.6 Miscellaneous.- References.

Induced-Charge Electrokinetic Phenomena: Theory and Microfluidic Applications

Abstract: We give a general, physical description of "induced-charge electro-osmosis" (ICEO), the nonlinear electrokinetic slip at a polarizable surface, in the context of some new techniques for microfluidic pumping and mixing. ICEO generalizes "ac electro-osmosis" at microelectrode arrays to various di-electric and conducting structures in weak dc or ac electric fields. The basic effect produces microvortices to enhance mixing in microfluidic devices, while various broken symmetries--controlled potential, irregular shape, nonuniform surface properties, and field gradients--can be exploited to produce streaming flows. Although we emphasize the qualitative picture of ICEO, we also briefly describe the mathematical theory (for thin double layers and weak fields) and apply it to a metal cylinder with a dielectric coating in a suddenly applied dc field.

Iterative Linear Quadratic Regulator Design for Nonlinear Biological Movement Systems

Abstract: This paper presents an Iterative Linear Quadratic Regulator (ILQR) method for locally-optimal feedback control of nonlinear dynamical systems. The method is applied to a musculo-skeletal arm model with 10 state dimensions and 6 controls, and is used to compute energy-optimal reaching movements. Numerical comparisons with three existing methods demonstrate that the new method converges substantially faster and finds slightly better solutions.

A continuous asymptotic tracking control strategy for uncertain nonlinear systems

Abstract: In this note, we present a new continuous control mechanism that compensates for uncertainty in a class of high-order, multiple-input-multiple-output nonlinear systems. The control strategy is based on limited assumptions on the structure of the system nonlinearities. A new Lyapunov-based stability argument is employed to prove semiglobal asymptotic tracking.

Maximum likelihood estimation of cascade point-process neural encoding models

Abstract: Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a known parametric function; the assumption that this function is known speeds the estimation process considerably. We investigate the shape of the likelihood function for this type of model, give a simple condition on the nonlinearity ensuring that no non-global local maxima exist in the likelihood—leading, in turn, to efficient algorithms for the computation of the maximum likelihood estimator—and discuss the implications for the form of the allowed nonlinearities. Finally, we note some interesting connections between the likelihood-based estimators and the classical spike-triggered average estimator, discuss some useful extensions of the basic model structure, and provide two novel applications to physiological data.

Finite Time Stability and Robust Control Synthesis of Uncertain Switched Systems

Abstract: Stability analysis is developed for uncertain nonlinear switched systems. While being asymptotically stable and homogeneous of degree q < 0, these systems are shown to approach the equilibrium point in finite time. Restricted to second order systems, this feature is additionally demonstrated to persist regardless of inhomogeneous perturbations. Based on this fundamental property, switched control algorithms are then developed to globally stabilize uncertain minimum phase systems of uniform m-vector relative degree (2,...,2)T. The controllers constructed do not rely on the generation of sliding motions while providing robustness features similar to those possessed by their sliding mode counterparts. The proposed synthesis procedure is illustrated via application to a friction servo-motor.

A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models

Abstract: A unified framework for design of stabilizing controllers for sampled-data differential inclusions via their approximate discrete-time models is presented. Both fixed and fast sampling are considered. In each case, sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete-time plant models also stabilizes the exact discrete-time plant model for sufficiently small integration and/or sampling periods. Previous results in the literature are extended to cover: 1) continuous-time plants modeled as differential inclusions; 2) general approximate discrete-time plant models; 3) dynamical discontinuous controllers modeled as difference inclusions; and 4) stability with respect to closed arbitrary (not necessarily compact) sets.

Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays

Abstract: This study introduces a guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback and generalized dynamic output feedback approaches are considered. The generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base. It considers both the dynamic part and the output part of T-S fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems. Based on delay-dependent Lyapunov functional approach, some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation (PDC) first. Second, the corresponding conditions are extended into the generalized dynamic output feedback closed-loop system via so-called generalized PDC technique. The upper bound of time-delay can be obtained using convex optimization such that the system can be stabilized for all time-delays whose sizes are not larger than the bound. The minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function. The effectiveness of the proposed method can be shown by the simulation examples.