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Showing papers on "Nonlinear system published in 1987"


Book
01 Jan 1987
TL;DR: In this article, the authors introduce the theory of DAE's and the index Linear constant coefficient, linear time varying, and nonlinear index systems, as well as a general linear multistep method.
Abstract: Preface 1. Introduction: why DAE's? Basic types of DAE's applications Overview 2. Theory of DAE's Iintroduction solvability and the index Linear constant coefficient DAE's Linear time varying DAE's Nonlinear systems 3. Multistep methods Introduction DBF convergence BDF methods, DAE's and stiff problems General linear multistep methods 4. One-step methods Introduction Linear constant coefficient systems Nonlinear index one systems Semi-Explicit Nonlinear Index Two systems Order reduction and stiffness Extrapolation Methods 5. Software and DAE's Introduction Algorithms and Strategies in Dassl Obtaining numerical solutions Solving higher index systems 6. Applications. Introduction Systems of rigid bodies Trajectory prescribed path control Electrical networks DAE's arising from the method of lines Bibliography 7. The DAE home page Introduction theoretical advances Numerical analysis advancements DAE software DASSL Supplementary bibliography Index.

2,677 citations


Book
01 Jan 1987
TL;DR: This chapter discusses Trust-Region Mewthods for General Constained Optimization and Systems of Nonlinear Equations and Nonlinear Fitting, and some of the methods used in this chapter dealt with these systems.
Abstract: Preface 1. Introduction Part I. Preliminaries: 2. Basic Concepts 3. Basic Analysis and Optimality Conditions 4. Basic Linear Algebra 5. Krylov Subspace Methods Part II. Trust-Region Methods for Unconstrained Optimization: 6. Global Convergence of the Basic Algorithm 7.The Trust-Region Subproblem 8. Further Convergence Theory Issues 9. Conditional Models 10. Algorithmic Extensions 11. Nonsmooth Problems Part III. Trust-Region Methods for Constrained Optimization with Convex Constraints: 12. Projection Methods for Convex Constraints 13. Barrier Methods for Inequality Constraints Part IV. Trust-Region Mewthods for General Constained Optimization and Systems of Nonlinear Equations: 14. Penalty-Function Methods 15. Sequential Quadratic Programming Methods 16. Nonlinear Equations and Nonlinear Fitting Part V. Final Considerations: Practicalities Afterword Appendix: A Summary of Assumptions Annotated Bibliography Subject and Notation Index Author Index.

2,384 citations


Journal ArticleDOI
TL;DR: An error estimate is presented for this forecasting technique for chaotic data, and its effectiveness is demonstrated by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.
Abstract: We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ``learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.

1,836 citations


Book
01 Jan 1987
TL;DR: The second edition of the Navier-Stokes Equations as mentioned in this paper provides an overview of its application in a variety of problems, including the existence, uniqueness, and regularity of solutions.
Abstract: Preface to the second edition Introduction Part I. Questions Related to the Existence, Uniqueness and Regularity of Solutions: 1. Representation of a Flow: the Navier-Stokes Equations 2. Functional Setting of the Equations 3. Existence and Uniqueness Theorems (Mostly Classical Results) 4. New a priori Estimates and Applications 5. Regularity and Fractional Dimension 6. Successive Regularity and Compatibility Conditions at t=0 (Bounded Case) 7. Analyticity in Time 8. Lagrangian Representation of the Flow Part II. Questions Related to Stationary Solutions and Functional Invariant Sets (Attractors): 9. The Couette-Taylor Experiment 10. Stationary Solutions of the Navier-Stokes Equations 11. The Squeezing Property 12. Hausdorff Dimension of an Attractor Part III. Questions Related to the Numerical Approximation: 13. Finite Time Approximation 14. Long Time Approximation of the Navier-Stokes Equations Appendix. Inertial Manifolds and Navier-Stokes Equations Comments and Bibliography Comments and Bibliography Update for the Second Edition References.

1,342 citations


Book
01 Jan 1987
TL;DR: In this article, a Unified Asymptotic Theory for Nonlinear Regression with Regression Structure (UATRS) is proposed. But it is not a unified theory for dynamic nonlinear models.
Abstract: Univariate Nonlinear Regression. Univariate Nonlinear Regression: Special Situations. A Unified Asymptotic Theory for Nonlinear Models with Regression Structure. Univariate Nonlinear Regression: Asymptotic Theory. Multivariate Nonlinear Regression. Nonlinear Simultaneous Equations Models. A Unified Asymptotic Theory for Dynamic Nonlinear Models. References. Index.

1,187 citations


Journal ArticleDOI
TL;DR: In this article, the authors derived the nonlinear wave equation for an envelope of an electromagnetic wave in a monomode dielectric waveguide and derived the coefficients of the Schrodinger equation with higher-order dispersion and dissipation (both linear and nonlinear) in terms of properties of the eigenfunction of the guided wave as well as of the material nonlinearity and dispersion.
Abstract: We derive the nonlinear wave equation for an envelope of an electromagnetic wave in a monomode dielectric waveguide. Concrete examples are given for a single-mode optical fiber where the coefficients of resultant nonlinear Schrodinger equation with higher-order dispersion and dissipation (both linear and nonlinear) are given in terms of properties of the eigenfunction of the guided wave as well as of the material nonlinearity and dispersion. Using a newly-developed perturbation method, we show that the higher-order dispersions (linear and nonlinear) perserve the profile of a single soliton but to split up a bound N soliton ( N \geq 2 ) into individual solitons with different heights which propagate at different velocities. We also show that the higher-order nonlinear dissipation due to the induced Raman effect downshifts the carrier frequency of a single soliton in proportion to the distance of propagation and to the fourth power of the soliton amplitude.

782 citations


Book
01 Jan 1987
TL;DR: In this article, the Boltzmann Equation Near the Equilibrium was used to prove the existence of the Vlasov-Maxwell system, which is the basis for the present paper.
Abstract: Preface 1. Properties of the Collision Operator. Kinetic Theory, Derivation of the Equations, The Form of the Collision Operator, The Hard Sphere Case, Conservation Laws and the Entropy, Relevance of the Maxwellian, The Jacobian Determinant, The Structure of Collision Invariants, Relationship of the Boltzmann Equation to the Equations of Fluids, References 2. The Boltzmann Equation Near the Vacuum. Invariance of $|x-tv|^2+|x-tu|^2$, Sequences of Approximate Solutions, Satisfaction of the Beginning Condition, Proof that $u=\ell$, Remarks and Related Questions, References 3. The Boltzmann Equation Near the Equilibrium. The Perturbation from Equilibrium, Computation of the Integral Operator, Estimates on the Integral Operator, Properties of $L$, Compactness of $K$, Solution Spaces, An Orthonormal Basis for $N(L)$, Estimates on the Nonlinear Term, Equations for 13 Moments, Computation of the Coefficient Matrices, Compensating Functions, Time Decay Estimates, Time Decay in Other Norms, The Major Theorem, The Relativistic Boltzmann Equation, References 4. The Vlasov--Poisson System. Introduction, Preliminaries and A Priori Estimates, Sketch of the Existence Proof, The Good, the Bad and the Ugly, The Bound on the Velocity Support, Blow-up in the Gravitational Case, References 5. The Vlasov--Maxwell System. Collisionless Plasmas, Control of Large Velocities, Representation of the Fields, Representation of the Derivatives of the Fields, Estimates on the Particle Density, Bounds on the Field, Bounds on the Gradient of the Field, Proof of Existence, References 6. Dilute Collisionless Plasmas. The Small--data Theorem, Outline of the Proof, Characteristics, The Particle Densities, Estimates on the Fields, Estimates on Derivatives of the Fields, References 7. Velocity Averages: Weak Solutions to the Vlasov--Maxwell System. Sketch of the Problem, The Velocity Averaging Smoothing Effect, Convergence of the Current Density, Completion of the Proof, References 8. Convergence of a Particle Method for the Vlasov--Maxwell System. Introduction, The Particle Simulation, The Field Errors, The Particle Errors, Summing the Errors, References Index.

687 citations


Book
01 Jun 1987
TL;DR: The best ebooks about Oscillation Theory of Differential Equations With Deviating Arguments with varying arguments can be downloaded for free here by download this ebook and save to your desktop as mentioned in this paper.
Abstract: The best ebooks about Oscillation Theory Of Differential Equations With Deviating Arguments that you can get for free here by download this Oscillation Theory Of Differential Equations With Deviating Arguments and save to your desktop. This ebooks is under topic such as oscillation theory of first order functional differential oscillation criteria for first order differential oscillation of second order nonlinear impulsive di erential equations with several deviating arguments first-order di erential equations with several deviating oscillation criteria for neutral half-linear differential oscillation in nonautonomous scalar differential equations oscillation of neutral differential equations with damped second order linear differential equation with oscillation behavior of higher order functional characterization of oscillation of fourth order functional a survey on the oscillation of solutions of first order oscillation of second order nonlinear impulsive oscillation criteria for a certain second-order nonlinear oscillatory and nonoscillatory properties of first order oscillation and property b for third-order differential oscillation of neutral nonlinear impulsive parabolic oscillation criteria for damping quasi-linear neutral forced oscillation of neutral impulsive parabolic partial research article oscillation properties for systems of research article some properties of third-order on proper oscillatory and vanishing at infinity solutions oscillation theory for second order dynamic equations survey of oscillation criteria for first order delay oscillation properties of third order neutral delay oscillation theory for second order linear, half-linear oscillations of first order delay and advanced difference oscillation of higher-order nonlinear delay dià ̄¬€erential oscillation criteria for delay and advanced difference oscillation of solutions of impulsive nonlinear parabolic oscillation criteria for damped functional differential oscillation of solutions of à ̄¥rst-order neutral di¤erential on the oscillation of differential equations with periodic nonoscillation and oscillation: theory for functional oscillation criteria of second-order half-linear neutral undergraduate research in mathematics and its applications boundary value problems for delay dià ̄¬€erential equations oscillation and nonoscillation of third order functional oscillations of first order linear delay differential nonoscillation and oscillation: theory for functional on the oscillation of solutions of some ordinary international journal of pure and applied mathematics interval oscillation theorems for second order nonlinear

646 citations


Journal ArticleDOI
TL;DR: In this paper, a nonlinear K-l and K-e model is proposed to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model, and the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts.
Abstract: The commonly used linear K-l and K-e models of turbulence are shown to be incapable of accurately predicting turbulent flows where the normal Reynolds stresses play an important role. By means of an asymptotic expansion, nonlinear K-l and K-e models are obtained which, unlike all such previous nonlinear models, satisfy both realizability and the necessary invariance requirements. Calculations are presented which demonstrate that this nonlinear model is able to predict the normal Reynolds stresses in turbulent channel flow much more accurately than the linear model. Furthermore, the nonlinear model is shown to be capable of predicting turbulent secondary flows in non-circular ducts - a phenomenon which the linear models are fundamentally unable to describe. An additional application of this model to the improved prediction of separated flows is discussed briefly along with other possible avenues of future research.

644 citations


Book
01 Aug 1987
TL;DR: This paper presents a meta-modelling of Time-Delay (TD) Systems using the Generalized Riccati Method and a new approach called Nondelay Conversion Approach, which addresses the problem of suboptimal control of Nonlinear TD Systems.
Abstract: Modeling. Mathematical Description of Time-Delay (TD) Systems: Modeling. State-Space Representation. Frequency-Domain Representation. Linearization of Nonlinear TD Systems. Large-Scale TD Systems. Analysis. Analysis of TD Systems: Homogeneous State Equation - Fundamental Matrix. Forced State Equation - Complete Solution. Adjoint State Equations. Stability of TD Systems: Time Domain. Frequency Domain. Controllability and Observability of Linear TD Systems: Definitions. Criteria. Optimization. Optimization of TD Systems: The Maximum Principle. Generalized Riccati Method. Dynamic Programming Method. Time-Optimal Control. Suboptimal Control of TD Systems: Sensitivity Approach. Nondelay Conversion Approach. Suboptimal Control of Nonlinear TD Systems. Singular Perturbation Method. Sensitivity to Parameter Variations. Near-Optimum Design of Large-Scale TD Systems: Near-Optimum Control of Coupled TD Systems. Hierarchical Control. Applications. Some Applications of TD Systems: Cold Rolling Mills. Traffic Control. Water Resources Systems. A Hydraulic Level System. Control of TD Systems via Smith Predictor. Appendices: Review of Linear Algebra. Review of Laplace, z and Modified z Transforms.

641 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed a robust numerical method for modeling nonlinear gravity waves which is based on the Zakharov equation/mode-coupling idea but is generalized to include interactions up to an arbitrary order M in wave steepness.
Abstract: We develop a robust numerical method for modelling nonlinear gravity waves which is based on the Zakharov equation/mode-coupling idea but is generalized to include interactions up to an arbitrary order M in wave steepness. A large number ( N = O (1000)) of free wave modes are typically used whose amplitude evolutions are determined through a pseudospectral treatment of the nonlinear free-surface conditions. The computational effort is directly proportional to N and M , and the convergence with N and M is exponentially fast for waves up to approximately 80% of Stokes limiting steepness ( ka ∼ 0.35). The efficiency and accuracy of the method is demonstrated by comparisons to fully nonlinear semi-Lagrangian computations (Vinje & Brevig 1981); calculations of long-time evolution of wavetrains using the modified (fourth-order) Zakharov equations (Stiassnie & Shemer 1987); and experimental measurements of a travelling wave packet (Su 1982). As a final example of the usefulness of the method, we consider the nonlinear interactions between two colliding wave envelopes of different carrier frequencies.

01 Jun 1987
TL;DR: It is demonstrated that the backpropagation learning algorithm for neural networks may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method.
Abstract: The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing Simulations are presented that document the additional performance achieved by using nonlinear neural networks First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series Furthermore, the neural net more » seems to be extremely parsimonious in its requirements for data points from the time series We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps 24 refs, 13 figs « less

Journal ArticleDOI
TL;DR: In this paper, the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizacker equation is investigated.
Abstract: This paper deals with the existence of multiple solutions of Hartree-Fock equations for Coulomb systems and related equations such as the Thomas-Fermi-Dirac-Von Weizacker equation.

Journal ArticleDOI
B. Walcott1, S.H. Zak1
TL;DR: In this paper, the authors propose new types of observers for nonlinear dynamical systems subjected to bounded nonlinearities or uncertainties, and a measure for the rate at which the estimates converge to the actual states is derived.
Abstract: This note proposes new types of observers for nonlinear dynamical systems subjected to bounded nonlinearities or uncertainties. The design of these observers utilizes techniques related to variable structure systems theory. A measure for the rate at which the estimates converge to the actual states is derived.

Book
01 Jan 1987
TL;DR: A survey of systems with Chaotic Vibrations can be found in this paper, where the authors present a glossary of terms in Chaotic and nonlinear vibrational theory.
Abstract: 1. Introduction: A New Age of Dynamics. 1.1 What Is Chaotic Dynamics? 1.2 Classical Nonlinear Vibration Theory: A Brief Review. 1.3 Maps and Flows. 2. How to Identify Chaotic Vibrations. 3. A Survey of Systems with Chaotic Vibrations. 3.1 New Paradigms in Dynamics. 3.2 Mathematical Models of Chaotic Physical Systems. 3.3 Physical Experiments in Chaotic Systems. 4. Experimental Methods in Chaotic Vibrations. 4.1 Introduction: Experimental Goals. 4.2 Nonlinear Elements in Dynamical Systems. 4.3 Experimental Controls. 4.4 Phase Space Measurements. 4.5 Bifurcation Diagrams. 4.6 Experimental Poincare Maps. 4.7 Quantitative Measures of Chaotic Vibrations. 5. Criteria for Chaotic Vibrations. 5.1 Introduction. 5.2 Introduction Empirical Criteria for Chaos. 5.3 Theoretical Predictive Criteria. 5.4 Lyapunov Exponents. 6. Fractal Concepts in Nonlinear Dynamics. 6.1 Introduction. 6.2 Measures of Fractal Dimension. 6.3 Fractal Dimension of Strange Attractors. 6.4 Optical Measurement of Fractal Dimension. 6.5 Fractal Basin Boundaries. 6.6 complex Maps and the Mandelbrot Set. Appendix A. Glossary of Terms in Chaotic and Nonlinear Vibrations. Appendix B. Appendix C. Numerical Experiments in Chaos. Appendix C. Chaotic Toys. References. Author Index. Subject Index.

Journal ArticleDOI
TL;DR: In this article, a state feedback control algorithm was proposed to compensate for all the nonlinearities and decouples the effect of stator phase currents in the torque production for a single-link manipulator with SRM.
Abstract: Motivated by technological advances in power electronics and signal processing, and by the interest in using direct drives for robot manipulators, we investigate the control problem of high-performance drives for switched reluctance motors (SRM's). SRM's are quite simple, low cost, and reliable motors as compared to the widely used dc motors. However, the SRM presents a coupled nonlinear multivariable control structure which calls for complex nonlinear control design in order to achieve high dynamic performances. We first develop a detailed nonlinear model which matches experimental data and establish an electronic commutation strategy. Then, on the basis of recent nonlinear control techniques, we design a state feedback control algorithm which compensates for all the nonlinearities and decouples the effect of stator phase currents in the torque production. The position dependent logic of the electronic commutator assigns control authority to one phase, which controls the motion, while the remaining phase currents are forced to decay to zero. Simulations for a direct drive, single link manipulator with the SRM are reported, which show the control performance of the algorithm we propose in nominal conditions and test its robustness versus the most critical parameter uncertainties of payload mass and stator resistance.

Journal ArticleDOI
TL;DR: In this article, a one-parameter family of explicit and implicit total variation diminishing (TVD) schemes is developed which permits incorporation of an expanded group of slope and flux limiters.

Journal ArticleDOI
TL;DR: In this paper, the stability and instability properties of solitary-wave solutions of a general class of equations arise as mathematical models for the unidirectional propagation of weakly nonlinear, dispersive long waves.
Abstract: Considered herein are the stability and instability properties of solitary-wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear, dispersive long waves. Special cases for which our analysis is decisive include equations of the Korteweg-de Vries and Benjamin-Ono type. Necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable.

Journal ArticleDOI
01 Aug 1987
TL;DR: The control problem for robot manipulators with flexible joints is considered and it is shown how to approximate the feedback linearizing control to any order in µ, an approximate feedback linearization which linearizes the system for all practical purposes.
Abstract: The control problem for robot manipulators with flexible joints is considered. The results are based on a recently developed singular perturbation formulation of the manipulator equations of motion where the singular perturbation parameter µ is the inverse of the joint stiffness. For this class of systems it is known that the reduced-order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear static-state feedback, but that the full-order flexible system is not, in general, linearizable in this manner. The concept of integral manifold is utilized to represent the dynamics of the slow subsystem. The slow subsystem reduces to the rigid model as the perturbation parameter µ tends to zero. It is shown that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around µ = 0, it is shown how to approximate the feedback linearizing control to any order in µ. The result is then an approximate feedback linearization which, assuming stability of the fast variables, linearizes the system for all practical purposes.

Journal ArticleDOI
TL;DR: In this paper, a displacement-pressure (up) finite element formulation for the geometrically and materially nonlinear analysis of compressible and almost incompressible solids is proposed.

Journal ArticleDOI
TL;DR: This work presents a simple algebraic procedure, based on the Routh-Hurwitz criterion, for determining the character of the eigenvalues without the need for evaluating the eigens explicitly, for a system of nonlinear ordinary differential equations.
Abstract: In stability analysis of nonlinear systems, the character of the eigenvalues of the Jacobian matrix (i.e., whether the real part is positive, negative, or zero) is needed, while the actual value of the eigenvalue is not required. We present a simple algebraic procedure, based on the Routh-Hurwitz criterion, for determining the character of the eigenvalues without the need for evaluating the eigenvalues explicitly. This procedure is illustrated for a system of nonlinear ordinary differential equations we have studied previously. This procedure is simple enough to be used in computer code, and, more importantly, makes the analysis possible even for those cases where the secular equation cannot be solved.

Journal ArticleDOI
TL;DR: In this paper, a method for finding exact solutions of the nonlinear Schroedinger equations is proposed, in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time.
Abstract: A method is proposed for finding exact solutions of the nonlinear Schroedinger equations. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine solutions of the nonlinear Schroedinger equation. The obtained solutions form a three-parameter family that can be expressed in terms of elliptic Jacobi functions and the incomplete elliptic integral of the third kind. In the general case, the obtained solutions are periodic with respect to the spatial variable and doubly periodic with respect to the time. Special cases for which the solutions can be expressed in terms of elliptic Jacobi functions and elementary functions are considered in detail. Possible fields of practical applications of the solutions are mentioned.

Journal ArticleDOI
TL;DR: In this article, the authors derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems, using an appropriate scalar product in the space of homogeneous vector polynomials, and show that the resonant terms commute with the group generated by the original critical linear operator.

Journal ArticleDOI
TL;DR: In this article, a method based on finite-element collocation is presented, which converts differential equations to algebraic residual equations with unknown coefficients, and then a nonlinear program is formulated, with residuals incorporated as equality constraints and coefficients as decision variables.
Abstract: Many chemical engineering problems require the optimization of systems of differential and algebraic equations. Here a method is presented based on finite-element collocation, which converts differential equations to algebraic residual equations with unknown coefficients. A nonlinear program is then formulated, with residuals incorporated as equality constraints and coefficients as decision variables. Also, adaptive knot placement is used to minimize the approximation error, with necessary and sufficient conditions for optimal knot placement incorporated as additional equality constraints in the nonlinear program. All equality constraints are then solved simultaneously with the optimization problem, thus requiring only a single solution of the approximated model. Finally, problems with discontinuous control profiles can be treated by introducing an extra level of elements (superelements) as decisions in the optimization problem. This approach is demonstrated on a simple optimal control problem as well as a reactor optimization problem with steep temperature profiles and state variable constraints.


Journal ArticleDOI
TL;DR: The extended Luenberger observer as discussed by the authors is a nonlinear observer design for nonlinear single-input single-output (SISO) systems, which is based on the extended Kalman filter (EKF) algorithm.

Journal ArticleDOI
TL;DR: HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix.
Abstract: There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK provides three qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow, and augmented Jacobian matrix. Separate routines are also provided for dense and sparse Jacobian matrices. A high-level driver is included for the special case of polynomial systems.

Journal ArticleDOI
TL;DR: In this article, the authors calculate the electric field dependence of the linear and the third-order nonlinear intersubband optical absorption coefficients of a semiconductor quantum well in the infrared regime.
Abstract: Analytic forms of the linear and the third-order nonlinear optical intersubband absorption coefficients are obtained for general asymmetric quantum well systems using the density matrix formalism, taking into account the intrasubband relaxation. Based on this model, we calculate the electric field dependence of the linear and the third-order nonlinear intersubband optical absorption coefficients of a semiconductor quantum well. The energy of the peak optical intersubband absorption is around 100 meV (wavelength is 12.4 μm). Thus, electrooptical modulators and photodetectors in the infrared regime can be built based on the physical mechanisms discussed here. The contributors to the nonlinear absorption coefficient due to the electric field include 1) the matrix element variation and 2) the energy shifts. Numerical results are illustrated.

Proceedings ArticleDOI
01 Mar 1987
TL;DR: In this paper, the authors proposed a decentralized joint control method based on the disturbance observer where the dynamical equation is not directly solved, and as a result, the joints are able to be decoupled and controlled independently each other by using even 16 bit microprocessors.
Abstract: The dynamics of the multi-degrees of freedom manipulator is highly nonlinear and the compensationagainst this nonlinearity should be indispensable. This paper proposes the decentralizedjoint control method based on the disturbance observer where the dynamical equation is not directly solved. By using the information of the acceleration, the nonlinear term in the dynamical equation is estimated without the mathematically complicated process, and as a result, the joints are able to be decoupled and controlled independently each other by using even 16 bit microprocessors. The simulated and experimented results are shown in the paper to confirm the industrial viability of this method.

Journal ArticleDOI
TL;DR: In this article, the design of feedback controllers for trajectory tracking in single-input/single-output nonlinear systems is studied, and a nonlinear transformation of the form v = k (x) + λ(x) u that transforms this nonlinear input/output system into a linear system is first constructed.
Abstract: This paper studies the design of feedback controllers for trajectory tracking in single-input/ single-output nonlinear systems x = f(x) + g(x) u, y = h(x). A nonlinear transformation of the form v = k(x) + λ(x) u that transforms this nonlinear input/output system into a linear system is first constructed. On the basis of this transformation, an approach for designing control laws for trajectory tracking is presented. The control law is robust in the sense that small changes in it do not produce large steady state errors or loss of stability. The theory provides a unified framework for treating control problems arising in nonlinear chemical processes; this is illustrated by a batch reactor control example.