Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1997"
TL;DR: An analytical study of the asymptotic differences between different members of the family proposed in goodness of fit, together with an examination of closer approximations to the exact distribution of these statistics than the commonly used chi-squared distribution.
Abstract: In this paper we investigate the Jensen-Shannon parametric divergence for testing goodness-of-fit for point estimation. Most of the work presented is an analytical study of the asymptotic differences between different members of the family proposed in goodness of fit, together with an examination of closer approximations to the exact distribution of these statistics than the commonly used chi-squared distribution. Finally the minimum Jensen-Shannon divergence estimates are introduced and compared with other well-known estimators by computer simulation.
130 citations
TL;DR: In this paper, the potentials of neural networks-based control techniques are explored by applying a nonlinear generalized minimum variance control methodology to a simulated application example, in particular, reference is made to the control problem of regulating the output temperature of a liquid-satured steam heat exchanger by acting on the liquid flow-rate.
Abstract: In this paper the potentials of neural networks-based control techniques are explored by applying a nonlinear generalized minimum variance control methodology to a simulated application example. In particular, reference is made to the control problem of regulating the output temperature of a liquid-satured steam heat exchanger by acting on the liquid flow-rate. Due to the non-minimum phase characteristic of the dynamics of the process, a simple inverting minimum variance controller is unsuitable. On the other hand, an effective solution is provided by a detuned model reference approach, which introduces a penalization factor in the control variable. A steady-state off-set error problem, caused by the neural network approximations, is tackled by means of an hybrid control structure, which combines a nonlinear integral action block with a neural controller. A comparison analysis is made to show the effectiveness of the proposed neural control schemes with respect to classical linear controllers.
87 citations
TL;DR: Novel nanoelectronic architecture paradigms based on cells composed of coupled quantum dots, and possible realizations of these structures in a variety of semiconductor systems (including GaAs/AlGaAs, Si/SiGe, and Si SiO 2 ), rings of metallic tunnel-junctions, and candidates for molecular implementations.
Abstract: We discuss novel nanoelectronic architecture paradigms based on cells composed of coupled quantum dots. Boolean logic functions may be implemented in specific arrays of cells representing binary information, the so-called Quantum-Dot Cellular Automata (QCA). Cells may also be viewed as carrying analog information, and we outline a network-theoretic description of such Quantum-Dot Nonlinear Networks (Q-CNN). In addition, we discuss possible realizations of these structures in a variety of semiconductor systems (including GaAs/AlGaAs, Si/SiGe, and Si SiO 2 ), rings of metallic tunnel-junctions, and candidates for molecular implementations.
82 citations
TL;DR: In this paper, the effects of free convection currents with one relaxation time on the flow of a viscoelastic conduction fluid through a porous medium, which is bounded by a vertical plane surface, have been studied.
Abstract: Effects of free convection currents with one relaxation time on the flow of a viscoelastic conduction fluid through a porous medium, which is bounded by a vertical plane surface, have been studied. The state space approach developed in Ezzat (Can. J. Phys, Vol. 72, p. 311, 1994; J. Appl. Math. Comput., Vol. 64, p. 1, 1994) is adopted for the solution of one-dimensional problems in magnetohydrodynamic free convection flow with thermal relaxation time. The resulting formulation together with the Laplace transform technique is applied to a variety of problems. The solutions to a problem of an electrically conducting visocelastic fluid in the presence of hydromagnetic free convection flow and to a problem of the flow between two parallel fixed plates are obtained. A discussion of the effects of cooling and heating on a viscoelastic conducting fluid is given. Numerical results are illustrated graphically for both problems considered.
69 citations
TL;DR: In this article, an extension of the general structured observer (GSO) is developed to estimate both the system state and the unknown input simultaneously, and the existence conditions of a stable UIO are the same as those of the stable left inverse system.
Abstract: Using the framework of the general structured (GS) observer, we present a straightforward procedure for designing an unknown input observer (UIO) for a linear system subject to unknown inputs or uncertain disturbances. The set of all GS observers insensitive to unknown inputs is derived in this paper. Moreover, an extension of the UIO, called the extended UIO, is developed to estimate both the system state and the unknown input simultaneously. We show the existence conditions of a stable UIO are the same as those of a stable left inverse system. In addition, well-conditioned designs for both the state and unknown input estimations are also explored. Conditions of transmission zeros reveal that to achieve a stable UIO, the uncertain system should be minimum-phase. To overcome this restriction, we adopt a two-delay output stabilized method to design the stabilized UIO without implementing extra sensors. Experimental results for a DC servo motor system demonstrate the applicability of the proposed methodologies.
52 citations
TL;DR: Three alternative algorithms, representing modifications of earlier works and based on the decision-theoretic approach, are presented and appear to offer the best performance over a large number of modulation types.
Abstract: In this paper, a review of the more recent papers published in the area of modulation recognition is introduced. Three alternative algorithms, representing modifications of earlier works and based on the decision-theoretic approach, are presented. These appear to offer the best performance over a large number of modulation types. For example, the average analogue modulations recognition success rate is ≈99% at 10 dB SNR, the average digital modulations recognition success rate is ≈99% at the SNR of 10 dB, and the average analogue and digital modulations recognition success rate is ≈93% at 15 dB SNR.
48 citations
TL;DR: In this paper, the authors present a systematic formulation for the dynamic analysis and synthesis of control of mechanical systems in partly specified motion, where motion specifications are modelled as program constraints on a controlled system, and the control that ensure their realization is determined.
Abstract: The paper presents a systematic formulation for the dynamic analysis and synthesis of control of mechanical systems in partly specified motion. The motion specifications are modelled as program constraints on a controlled system, and the control that ensure their realization is determined. It is shown that program constraints may be realized by tangent control reactions with respect to the program constraint manifold, and this yields a very specific structure of the governing equations of the problem. The equations arise as DAEs, and the index of the DAEs may considerably exceed three. Index five and index 2n + 1 DAEs that describe control problems in mechanics are reported as illustrations. A method for analyzing the system motion consistent with the constraints and, based on the solution, synthesizing the program control is developed and applied to solve the mentioned case studies.
47 citations
TL;DR: In this article, an analytical approach for the quantitative prediction of stability and bifurcations of approximate periodic solutions of the generalized Duffing oscillator x + δ x + α 1 x+ α 2 x 3 = L 0 cos Ωt is presented.
Abstract: An analytical approach for the quantitative prediction of stability and bifurcations of approximate periodic solutions of the generalized Duffing oscillator x + δ x + α 1 x + α 2 x 3 = L 0 cos Ωt is presented. This approach is based on an improved harmonic balance method. Four types of Duffing oscillator are considered. Various stability and bifurcation conditions are derived. To verify the procedure, a comparison of the analytical results with numerical solutions is presented. Good agreement is observed. Numerical simulations using the analytically computed stability conditions are employed to expedite the numerical experimentations. Phase portraits for all four kinds of Duffing oscillator are shown. The number of stable and unstable solutions agree exactly with the analytical predictions.
40 citations
TL;DR: In this article, it was shown that a bond graph can explain the form of multibody system equations and can also suggest practical explicit differential equation formulations closely related to the descriptor differential algebraic equations of multi-body formulations.
Abstract: The dynamics of complex interconnected mechanical systems can be described using a number of formalized procedures in the field of multibody dynamics but it is not always easy to understand the significance of the quantities introduced as part of these various procedures. Bond graphs can also be used to describe mechanical systems and often provide intuitive and physically motivated means for enforcing constraints among interacting bodies. Using the example of a multilink inverted pendulum which has been often studied, we show that a bond graph can explain the form of multibody system equations. The bond graph can also suggest practical explicit differential equation formulations closely related to the descriptor differential algebraic equations of multibody formulations. Some subtleties associated with the interpretation of Lagrange multipliers will also be discussed and related to different ways in which constraint equations can be formulated.
38 citations
TL;DR: In this author's opinion, synergetics will find important applications in medicine, for instance in the analysis of MEG and EEG patterns, and in the development of devices with brain-like functions.
Abstract: Synergetics is an interdisciplinary field of research. It deals with open systems that are composed of many individual parts which interacts with each other and can form spatial, temporal, or functional structures by self-organization. The research goal of synergetics is three-fold: (1) are there general principles of self-organization? (2) are there analogies in the behavior of self-organizing systems? (3) can new devices be constructed because of the results (1) and (2)? From a mathematical point of view, synergetics deals with nonlinear partial stochastic differential equations and studies their solutions close to those points where the solutions change their behavior qualitatively. As will be shown in this article, synergetics in its present form is based on the concepts of stability and instability, control parameters, order parameters and the slaving principle. The slaving principle allows one to compress the information that is necessary to describe complex systems into a few order parameters. This is possible if systems are close to their instability points, but it appears that the order parameter concept is also applicable to situations away from such instabilities. At the level of the order parameter equations, profound analogies between otherwise quite different systems become visible. This allows one to realize the same process (for instance, dealing with information) on quite different material substrates. The order parameter concept and the slaving principle are explained and their extension to discrete noisy maps and to delay equations are mentioned. These results can be applied to pattern formation in fluids, lasers, semiconductors, plasmas and other fields. A section is devoted to the analysis of spatio-temporal patterns in terms of order parameters and the slaving principle. It is shown how the concepts of synergetics can be utilized to devise a new type of computer for pattern recognition. In connection with preprocessing, it can recognize patterns that are shifted, scaled or rotated in space and that are deformed. It can recognize scenes and also facial expressions as well as movement patterns. The learning procedure is briefly outlined. Because of the analogy principle of synergetics, this computer allows for hardware realizations by means of semiconductors and lasers. Decision making by humans or machines is interpreted by means of an analogy with pattern recognition. Further sections are devoted to recognition of dynamic processes and learning by machines. In this author's opinion, synergetics will find important applications in medicine, for instance in the analysis of MEG and EEG patterns, and in the development of devices with brain-like functions. Future tasks for synergetics will be the application of the order parameter concept and the slaving principle to the integration of specialized computers or computer algorithms, for instance for the recognition of faces, movement patterns and so on, into a computer network for scene analysis and decision making. This will hold also for complicated production processes, and so on. Generally speaking, the potentialities of synergetics are based on its self-organization principles.
27 citations
TL;DR: Different from traditional techniques, the tuning procedure of the proposed method is described in terms of fuzzy rules, in which the input variables are the error signal and its derivative, and the output variable are the PID parameters.
Abstract: A method is proposed to optimal-tune the parameters of PID controllers. Different from traditional techniques, the tuning procedure of the proposed method is described in terms of fuzzy rules, in which the input variables are the error signal and its derivative, and the output variables are the PID parameters. A genetic algorithm (GA) is then used to search for the optimal PID parameters that will minimize the integral of the squared error. In the simulation examples, comparison between the proposed method and other tuning techniques is made. In addition, simulation is also carried out on a ball and beam system to show the application of the proposed method to nonlinear systems.
TL;DR: In this paper, a decentralized output feedback control algorithm is employed to control the inherently unstable magnetic suspension rotor system, and the experimental results indicate that the controlled rotor performs well at rotor speeds up to 12,000 rpm.
Abstract: This study proposes design procedures for the permanent-magnet-biased magnetic bearings (PEMBs) in rotor systems. Many aspects of designing magnetic bearings are discussed, e.g. the selection of a permanent magnet material, dimensions of electromagnets and permanent magnets, gap length, load capacity and maximum Ampere-turns. Linearization and DC current driver are the two constraints for determining feasible designs. According to an analytical model with a rigid body assumption for the rotor-bearing system, a decentralized output feedback control algorithm is employed to control this inherently unstable magnetic suspension rotor system. Experimental results indicate that the controlled rotor performs well at rotor speeds up to 12,000 rpm.
TL;DR: A novel switch definition which is at the same time simple and more general is given and a formulation giving state and output equations is presented by using the bond graph model of switch-containing systems.
Abstract: This study gives a novel switch definition which is at the same time simple and more general. In addition, a formulation giving state and output equations is presented by using the bond graph model of switch-containing systems. The use of a computer program called BONDSO is described and examples of the application are given.
TL;DR: In this article, the authors present a history of nonlinear dynamics, including the Poincare and Lyapunov results, and discuss the development and contributions of the theory, characterized by the Birkhoff-Andronov school and the Krylov-Bogoliubov school.
Abstract: This paper does not pretend to present a comprehensive history of nonlinear dynamics. Its purpose is more modest and limited to some historical aspects of this topic. The first part of this paper deals with the early foundations of nonlinear dynamics (essentially the Poincare and Lyapunov results). The succeeding sections cover the period 1910–1970 and describe the development and contributions of the theory, characterized by the Birkhoff-Andronov school, and the Krylov-Bogoliubov school. After 1970 , the development of new results in nonlinear dynamics has become ‘explosive’. A part of these results is presented in a summarized form. The last section suggests some possible trends for future research.
TL;DR: In this article, a model of singular perturbation for discrete-time non-linear systems is proposed and sufficient conditions for both asymptotic and exponential stability are obtained.
Abstract: Recently we have introduced a model of singular perturbation for discrete-time non-linear systems. This paper is aimed at validating the proposed model. In fact, a discrete version of the well-known Tikhonov's theorem on singular perturbation of continuous-time systems is established. The second aim is to study stability problems of such systems. Sufficient conditions for both asymptotic and exponential stability are obtained. As a result, significant order reduction of stability problems is achieved. This is achieved by allowing a small parameter whose upper bound is estimated. Finally a simple example is given to illustrate the applications of the results.
TL;DR: In this article, the theory of nonlinear systems, especially that of strange attractors, and its perspectives are reviewed, with special attention given to the recent results concerning hyperbolic attractors and features of high-dimensional systems in the Newhouse regions.
Abstract: We review the theory of nonlinear systems, especially that of strange attractors, and give its perspectives. Special attention is given to the recent results concerning hyperbolic attractors and features of high-dimensional systems in the Newhouse regions. We present an example of a ‘wild’ strange attractor of the topological dimension three.
TL;DR: In this article, a frequency domain methodology for the design of practical, low order controllers for processes involving relatively large dead time is presented, which consists of determining the optimum structure and parameters of the controller so that the closed loop disturbance response matches the response of a pre-specified reference model.
Abstract: A frequency domain methodology for the design of practical, low order controllers for processes involving relatively large dead time is presented. The methodology consists of determining the optimum structure and parameters of the controller so that the closed loop disturbance response matches the response of a pre-specified reference model. This approach allows the designer to directly incorporate acceptable disturbance rejection characteristics for the closed loop system in the early stages of design. The most important task in the methodology is the selection of an appropriate reference model. It is shown that the reference model must meet certain mathematical conditions to guarantee physical realizability of the controller and the internal stability of the system. A reference specification procedure is developed to provide a large margin of robustness for the design while assuring a fast decay of the disturbance response. The power of the methodology is demonstrated by several non-trivial design examples pertaining to stable, unstable and non-minimum-phase process models with significant dead time. The tradeoff between robustness and response speed is discussed and illustrated.
TL;DR: A self-learning Neural-net-based Fuzzy logic System is designed to determine the gains of a PID controller, which uses knowledge of plant input/output behavior to update parameters of the NFS.
Abstract: A self-learning Neural-net-based Fuzzy logic System (NFS) is designed to determine the gains of a PID controller. The controller operates in a closed-loop system. The NFS receives the error, error integral and error derivative signals, and by fuzzy inference it adjusts the controller gains. As a result, these gains vary with time to achieve good performance compared to a conventional PID controller. A modified random optimization learning algorithm is given to train the NFS. The learning algorithm does not require a model of the plant being controlled. Instead, it uses knowledge of plant input/output behavior to update parameters of the NFS.
TL;DR: New two-sided matrix bounds of the solution for the continuous and discrete algebraic matrix Lyapunov equations are proposed and can give a supplement to those results reported in the literature.
Abstract: This paper proposes new two-sided matrix bounds of the solution for the continuous and discrete algebraic matrix Lyapunov equations. The coefficient matrix of the Lyapunov equation is assumed to be diagonalizable. The present matrix bounds can give a supplement to those results reported in the literature.
TL;DR: In this article, the authors describe a procedure for stabilizing a desirable chaotic orbit embedded in a chaotic attractor of dissipative dynamical systems by using small feedback control, based on the observation that certain chaotic orbits may correspond to a desirable system performance.
Abstract: This review describes a procedure for stabilizing a desirable chaotic orbit embedded in a chaotic attractor of dissipative dynamical systems by using small feedback control. The key observation is that certain chaotic orbits may correspond to a desirable system performance. By carefully selecting such an orbit, and then applying small feedback control to stabilize a trajectory from a random initial condition around the target chaotic orbit, desirable system performance can be achieved. As applications, three examples are considered: (1) synchronization of chaotic systems; (2) conversion of transient chaos into sustained chaos; and (3) controlling symbolic dynamics for communication. The first and third problems are potentially relevant to communication in engineering, and the solution of the second problem can be applied to electrical power systems to avoid catastrophic event such as the voltage collapse.
TL;DR: By integrating the conjugate gradient technique into the neural networks, the convergent rate of the solution is significantly improved and the developed networks are also able to track any frequency variation in signal sources.
Abstract: We present a new approach to the problem of sinusoidal frequency estimation using neural networks. The developed neural networks can simultaneously estimate frequencies, amplitudes and phases of a sinusoidal signal from noisy measurements. Furthermore, by integrating the conjugate gradient technique into the neural networks, the convergent rate of the solution is significantly improved. The developed networks are also able to track any frequency variation in signal sources. Due to the neural networks' massive parallelism and high processing speed, this new method is superior to the existing techniques in that the estimation can be carried out in real time. The results are illustrated by stimulation examples.
TL;DR: Examples of intracellular, cellular, tissue, organ and integrative physiology of an individual are outlined within the theory of synchronous concurrent algorithms, and possible directions in population dynamics and applications to ecosystem management are outlined.
Abstract: Nonlinear science has primarily developed from applications of mathematics to physics. The biological sciences are emerging as the dominant growth points of science and technology, and biological systems are characterised by being information dense, spatially extended, organised in interacting hierarchies, and rich in diversity. These characteristics, linked with an increase in available computing power and accessible memory, may lead to a nonlinear science of complicated interacting systems that will link different types of mathematical object within a framework of many-sorted algebras. Examples, drawn from current work on intracellular, cellular, tissue, organ and integrative physiology of an individual, are outlined within the theory of synchronous concurrent algorithms. Possible directions in population dynamics and applications to ecosystem management are outlined.
TL;DR: Using the integral representation for the wideband noise, optimal filter, smoother and predictor for wide-band noise driven linear systems are synthesized in this article, where the optimal filter and smoother are used.
Abstract: Using the integral representation for the wide-band noise, optimal filter, smoother and predictor for the wide-band noise driven linear systems are synthesized.
TL;DR: In this article, it is shown that instability as well as the thermodynamic limit lead to a new formulation of laws of nature in terms of probabilities (instead of trajectories or wave functions).
Abstract: Simple examples such as the Bernouilli shift and the anharmonic lattice are studied. It is shown that instability as well as the thermodynamic limit lead to a new formulation of laws of nature in terms of probabilities (instead of trajectories or wave functions).
TL;DR: In this article, a linear graph representation of a multibody system can be used to automatically derive the complete set of equations of motion in either absolute or joint coordinates, depending upon the elements selected into the spanning tree of the linear graph.
Abstract: The objective of this paper is to show how a single linear graph representation of a multibody system can be used to automatically derive the complete set of equations of motion in either absolute or joint coordinates, depending upon the elements selected into the spanning tree of the linear graph. Criteria for selecting a tree that produces the desired set of equations are given and the systematic nature of this graph-theoretical procedure is demonstrated by means of two planar examples. The first is an open-loop compound pendulum, and the second is a closed-loop four-bar mechanism driven by a time-varying torque.
TL;DR: It is shown that a general purpose computer algebra system like MATHEMATICA is well suited to solve structural design problems involving composite materials.
Abstract: The best layup for a hybrid laminated cylindrical shell subject to a buckling load constraint is determined. The objective of the optimisation is the minimum weight design of these structures. The ply angle is taken as the design variable. Various configurations of graphite and boron epoxy layers are considered in order to determine an optimal stacking sequence. The symbolic computational software package MATHEMATICA is used in the implementation and solution of the problem. This approach simplifies the computational procedure as well as the implementation of the analysis/optimisation routine. Results are given illustrating the dependence of the optimal layup on the cylinder length and radius. It is shown that a general purpose computer algebra system like MATHEMATICA is well suited to solve structural design problems involving composite materials.
TL;DR: In this article, meansquare consistent estimators for both the two-dimensional spectrum and the Fourier transform of its coherent collapse are obtained for non-stationary white noise, and the diagonal smoothing used to estimate the twodimensional spectrum for periodically correlated random processes is shown to extend to non-stochastic white noise.
Abstract: The diagonal smoothing used to estimate the two-dimensional spectrum for periodically correlated random processes is shown to extend to non-stationary white noise. Specifically, meansquare consistent estimators for both the two-dimensional spectrum and the Fourier transform of its coherent collapse are obtained for non-stationary white noise.
TL;DR: Chua's circuit is now playing an equivalent role for the generation and understanding of complex dynamics as discussed by the authors, where simple electronic oscillators were at the origin of many studies related to the qualitative theory of dynamical systems.
Abstract: Simple electronic oscillators were at the origin of many studies related to the qualitative theory of dynamical systems. Chua's circuit is now playing an equivalent role for the generation and understanding of complex dynamics.
TL;DR: In this paper, the stability testing problem for discrete large-scale uncertain systems with time delays in the interconnections is investigated based on the Lyapunov stability theorem associated with norm inequality techniques.
Abstract: Based on the Lyapunov stability theorem associated with norm inequality techniques, the stability testing problem for discrete large-scale uncertain systems with time delays in the interconnections is investigated. Three classes of uncertainties are treated: nonlinear, linear unstructured and linear highly structured uncertainties. Several new delay-independent sufficient conditions, expressed by inequalities, are presented to preserve the asymptotic stability of the discrete large-scale uncertain time-delay systems. Although the Lyapunov stability theorem is utilized, it is not necessary to solve any Lyapunov equation. Two demonstrative examples are given to show the effectiveness of these quantitative results.
TL;DR: In this paper, the authors give an account of the historical development, the current state and possible future developments of experimental nonlinear physics, with emphasis on acoustics, hydrodynamics and optics.
Abstract: This review gives an account of the historical development, the current state and possible future developments of experimental nonlinear physics, with emphasis on acoustics, hydrodynamics and optics. The concepts of nonlinear time-series analysis which are the basis of the analysis of experimental outcomes from nonlinear systems are explained and recent developments pertaining to such different fields as modeling, prediction, nonlinear noise reduction, detecting determinism, synchronization, and spatio-temporal time series are surveyed. An overview is given of experiments on acoustic cavitation, a field rich in nonlinear phenomena such as nonlinear oscillations, chaotic dynamics and structure formation, and one of the first physical systems to exhibit period-doubling and chaos in experiment.