Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2006"

Adaptive feedback cancellation in hearing aids

Abstract: In general feedback cancellation setups, standard adaptive filtering techniques fail to provide a reliable feedback path estimate if the desired signal is spectrally colored because of the presence of a closed signal loop. In this paper, several approaches for improving the estimation accuracy of the adaptive feedback canceller in hearing aids will be reviewed, including constrained adaptation and bandlimited adaptation of the feedback canceller as well as adaptation with the prediction-error method (PEM) using a fixed or adaptive model of the desired signal. Partitioned-block frequency-domain implementations of these algorithms will be compared for acoustic feedback paths measured in two commercial behind-the-ear hearing aids. In addition, it is shown that the tracking performance of the PEM-based feedback canceller with adaptive signal model can be improved by the so-called shadow filter approach known from echo cancellation.

The Cauchy–Schwarz divergence and Parzen windowing: Connections to graph theory and Mercer kernels

Abstract: This paper contributes a tutorial level discussion of some interesting properties of the recent Cauchy–Schwarz (CS) divergence measure between probability density functions. This measure brings together elements from several different machine learning fields, namely information theory, graph theory and Mercer kernel and spectral theory. These connections are revealed when estimating the CS divergence non-parametrically using the Parzen window technique for density estimation. An important consequence of these connections is that they enhance our understanding of the different machine learning schemes relative to each other.

A new set of orthogonal functions and its application to the analysis of dynamic systems

Abstract: The present work proposes a complementary pair of orthogonal triangular function (TF) sets derived from the well-known block pulse function (BPF) set. The operational matrices for integration in TF domain have been computed and their relation with the BPF domain integral operational matrix is shown. It has been established with illustration that the TF domain technique is more accurate than the BPF domain technique as far as integration is concerned, and it provides with a piecewise linear solution. As a further study, the newly proposed sets have been applied to the analysis of dynamic systems to prove the fact that it introduces less mean integral squared error (MISE) than the staircase solution obtained from BPF domain analysis, without any extra computational burden. Finally, a detailed study of the representational error has been made to estimate the upper bound of the MISE for the TF approximation of a function f ( t ) of Lebesgue measure.

The linear Legendre mother wavelets operational matrix of integration and its application

Abstract: The linear Legendre mother wavelets operational matrix of integration P is derived. A general procedure of forming this matrix P is given. This matrix P can be used to solve problems such as calculus of variations, differential equations, optimal control and integral equations. Illustrative examples are included to demonstrate the validity and applicability of matrix P.

Unified modeling and analysis of a proportional valve

Abstract: Developments in nonlinear control theory have made it possible to design controllers for systems having non-smooth nonlinearities in their dynamics. Hydraulic systems that use inexpensive proportional valves are examples of such systems, where nonlinearities arise due to valve geometry and spool imperfections. Without a proper valve model, however, nonlinear analysis and control of these hydraulic systems is not possible. We have developed nonlinear equations for a generic proportional valve model and have used them to obtain simplified flow rate expressions under generally accepted assumptions. These equations relate a set of geometric spool properties and physical model parameters to the flow rate through the valve ports. The development focuses on obtaining a single set of flow rate equations applicable to critical center, overlapped, and underlapped proportional valves. These unified model equations are useful for simulation and nonlinear controller design. We have also demonstrated that the errors incurred when using the unified valve model are dependent on the damping coefficient alone and are less than 10% in the frequency range within which most valves are used.

Backstepping design for controlling electrohydraulic servos

Abstract: The backstepping technique is one of the tools which provides control Lyapunov functions (CLFs) and, therefore, control laws for automatic systems. In this paper, the backstepping design for position and force nonlinear electrohydraulic servos is investigated. Three control laws ensuring the asymptotic stability of references tracking are obtained by constructing CLFs on the errors concerning the state variables and theirs desired values. The possibility of converting a position servo into a force servo, with only minimal hard modification, is proved. An approach based on partitioning the state system into two subsystems—a first one stable, and a second one taken as framework of control synthesis by backstepping technique—was developed and used. Using as reference point a flight controls hydromechanical servo, numerical simulations were reported from viewpoint of servo time constant performance. Certain conjectures, concerning the behaviour of systems mathematical models, in connection with mathematical methodologies of control synthesis operating on them, are finally stressed.

Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms

Abstract: In this paper, the global exponential robust stability is investigated for Cohen–Grossberg neural network with time-varying delays and reaction–diffusion terms, this neural network contains time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. Neither the boundedness and differentiability on the activation functions nor the differentiability on the time-varying delays are assumed. By using general Halanay inequality and M-matrix theory, several new sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of equilibrium point for Cohen–Grossberg neural network with time-varying delays and reaction–diffusion terms. Several previous results are improved and generalized, and three examples are given to show the effectiveness of the obtained results.

A new continuous action-set learning automaton for function optimization

Abstract: In this paper, we study an adaptive random search method based on continuous action-set learning automaton for solving stochastic optimization problems in which only the noise-corrupted value of function at any chosen point in the parameter space is available. We first introduce a new continuous action-set learning automaton (CALA) and study its convergence properties. Then we give an algorithm for optimizing an unknown function.

Face recognition under pose variations

Abstract: In recent years, face recognition has attracted significant attention from the research and commercial communities. Because of the wide variation in face images, face recognition for real applications remains a very challenging problem. A large number of face recognition algorithms, along with their modifications, have been proposed over the past three decades. This paper presents a review of the typical algorithms that aim to overcome one of the main obstacles in the face recognition task, the variations in face pose. These algorithms are categorized and briefly described. Future research challenges in pose-invariant face recognition are also identified.

Practical stability of descriptor systems with time delays in terms of two measurements

Abstract: This paper introduces the concepts of practical stability for descriptor systems with time delays in terms of two measurements. Some results of practical stability parallel to Lyapunov stability theorems are given. Based on Lyapunov functions and the comparison principle, a criterion, by which the problem of a descriptor system with time delay is reduced to that of a standard state-space system without time delays, is derived. Finally, the application of the results obtained is demonstrated through an analysis of a class of linear time-invariant descriptor systems with time delay.

A novel controller design and evaluation for networked control systems with time-variant delays

Abstract: A new delayed state-variable model for networked control systems is presented, upon which a linear quadratic regulator (LQR) is designed. A method of delays-estimation online is also given. A fuzzy logic with LQR controller is addressed for the difficulty on implementation of LQR in networked control systems (NCSs) with time-variant delays. Simulation results prove that the novel controller can make the system stable and robustly preserve the performance in terms of time-variant delays.

Approximations to the solution of linear Fredholm integrodifferential–difference equation of high order

Abstract: There are few techniques available to numerically solve linear Fredholm integrodifferential-difference equation of high-order. In this paper we show that the Taylor matrix method is a very effective tool in numerically solving such problems. This method transforms the equation and the given conditions into the matrix equations. By merging these results, a new matrix equation which corresponds to a system of linear algebraic equation is obtained. The solution of this system yields the Taylor coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the differential, difference, differential–difference and Fredholm integral equations. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method.

An enhanced psychoacoustic model based on the discrete wavelet packet transform

Abstract: The perception of acoustic information by humans is based on the detailed temporal and spectral analysis provided by the auditory processing of the received signal. The incorporation of this process in psychoacoustical computational models has contributed significantly both in the development of highly efficient audio compression schemes as well as in effective audio watermarking methods. In this paper, we present an approach based on the discrete wavelet packet transform, which closely mimics the multi-resolution properties of the human ear and also includes simultaneous and temporal auditory masking. Experimental results show that the proposed technique offers better masking capabilities and it reduces the signal-to-masking ratio when compared to related approaches, without introducing audible distortion. Those results have implications that are important both for audio compression by permitting further bit rate reduction, and for watermarking by providing greater signal space for information hiding.

Signal constellations in the hyperbolic plane: A proposal for new communication systems

Abstract: Signal constellations in the hyperbolic plane are provided as an alternative to traditional signal constellations in the Euclidean plane, since channels may actually exist for which the latter signal constellations are not as suitable as the former. A hyperbolic gaussian probability density function, based solely on geometrical considerations, is derived to determine the performance of the hyperbolic signal constellations. Benefits result from an approach conceived in terms of reduced signal-to-noise ratio, needed to achieve a prescribed error rate and equivalent optimum receiver complexity.

The T-class of time–frequency distributions: Time-only kernels with amplitude estimation

Abstract: This paper presents a class of time-frequency distributions (TFDs) characterized by time-lag kernels which are functions of time only. If the parameters of the time-only kernels are properly chosen, their corresponding TFDs, the T-distributions, are more efficient than their two-dimensional counterparts in terms of cross-terms suppression while keeping a high-energy concentration (resolution) around the IF law of non-stationary signals. The proposed class is a subclass of Cohen's Class of quadratic TFDs. We have shown that separable time-lag kernels should be lag-independent (or time-only) for best resolution. In addition, non-parametric amplitude estimation is possible directly from the T-distributions in case of FM signals, a property that is not verified by other TFDs. Two examples of the T-distributions are given and their performance is compared to other TFDs with numerical examples using synthetic and real-life signals.

Optimal strictly positive real controllers using direct optimization

Abstract: In this paper, we consider the H 2 -optimal control problem subject to the constraint that the resulting controller be strictly positive real. A direct numerical optimization approach is adopted in conjunction with a controller parametrization that is linear in the unknown parameters. The SPR constraint is easily expressed at each frequency in the form of a linear inequality. The method is applied to a numerical example from the literature and good results are achieved. In particular, the proposed method is particularly adept at determining low order controllers.

Parameter estimation of an unstable system with a PID controller in a closed loop configuration

Abstract: An essential part of the auto-tuning control involves parameter estimation of a suitable low order model. Since a common way to control an unstable system is via a PID controller, there is a growing interest in the application of new PID-based algorithms for the identification task. In this light the relative advantages of two recently published methods are investigated. The first method is based on typical data of the reaction curve and the time delay is measured directly from the initial portion of the curve. The second method utilizes a least-squares algorithm to get an equivalent time delay together with the values of the other parameters. Thus, the obtained time delay approximates not only the true delay but also part of the nonlinear and the higher order dynamics. This is an advantage when a PID auto-tuning is sought. Two examples are provided to demonstrate and compare between the results of the methods.

LQG optimal control of discrete stochastic systems under parametric and noise uncertainties

Abstract: In this paper, the linear-quadratic-Gaussian (LQG) optimal control problem is considered and a robust minimax controller composed of the Kalman filter and the optimal regulator is synthesized to guarantee the asymptotic stability of the discrete time-delay systems under both parametric uncertainties and uncertain noise covariances. Designed procedures are finally elaborated with an illustrative example.

A flow and routing control policy for communication networks with multiple competitive users

Abstract: This paper is concerned with deriving an optimal flow and routing control policy for two-node parallel link communication networks with multiple competing users. The model assumes that each user has a flow demand which needs to be optimally selected and routed on the network links. The flow and routing control policy for each user seeks to maximize the user's total throughput and minimize its expected delay. To derive such a policy, we consider a utility function for each user that combines these two objectives in an additive fashion with preference constants that can be adjusted to reflect the user's own preferences between maximizing throughput and minimizing delay. Additionally, we provide each user with the ability to make these preferences link-dependent to reflect the user's preferences for certain links over others in the network. A condition that depends on the link capacities and preference constants is derived to guarantee the existence and uniqueness of a non-symmetric flow and routing control policy solution which satisfies the Nash equilibrium of non-cooperative game theory. The Nash equilibrium is a desirable solution for such networks because it insures that no user can improve its utility by unilaterally deviating from its Nash control policy. We discuss in detail several interesting properties of this equilibrium and in particular, its relationship to the users’ preference constants. Two illustrative examples are also presented.

Periodic solutions for a kind of Rayleigh equation with two deviating arguments

Abstract: In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Rayleigh equation with two deviating arguments of the form x″+f(x′(t))+g1(t,x(t-τ1(t)))+g2(t,x(t-τ2(t)))=p(t).

Improved closed loop identification of transfer function model for unstable systems

Abstract: The method of identifying first order plus time delay transfer function model proposed for unstable systems by Ananth and Chidambaram [Closed loop identification to transfer function model for unstable systems, J. Franklin Inst. 336 (1999) 1055–1061] is modified to avoid the stability problems [Cheres, Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication] of the method. Two modifications are proposed. In the first modification of the method, the under-determined algebraic equations problem is converted into an optimization problem for calculation of the three parameters of the first order plus time delay (FOPTD) model. A simple method is given for the initial guess values of the model parameters. In the second approach, from the definition of Laplace transform of the output response, a third equation is formulated. The resulted three equations, in terms of the three parameters of the transfer function model, are then numerically solved. Simulation results are given for the second order plus time delay transfer function considered by Cheres 2005 [Parameter estimation of an unstable system with a PID controller in a closed loop configuration, J. Franklin Inst., 2005, accepted for publication]. The responses of the identified models with the same PID controllers are compared with that of the actual system. PID controllers are designed based on the identified models. The closed loop responses of the controllers on the original system are evaluated and compared. The present methods give better control performances.

Multi-layer self-organizing polynomial neural networks and their development with the use of genetic algorithms

Abstract: In this paper, we introduce a new architecture of genetic algorithms (GA)-based self-organizing polynomial neural networks (SOPNN) and discuss a comprehensive design methodology. Let us recall that the design of the “conventional” PNNs uses an extended group method of data handling (GMDH) and exploits polynomials (such as linear, quadratic, and modified quadratic functions) as well as considers a fixed number of input nodes (as being selected in advance by a network designer) at polynomial neurons (or nodes) located in each layer. The proposed GA-based SOPNN gives rise to a structurally optimized structure and comes with a substantial level of flexibility in comparison to the one we encounter in conventional PNNs. The design procedure applied in the construction of each layer of a PNN deals with its structural optimization involving the selection of preferred nodes (or PNs) with specific local characteristics (such as the number of input variables, the order of the polynomial, and a collection of the specific subset of input variables) and addresses specific aspects of parametric optimization. An aggregate performance index with a weighting factor is proposed in order to achieve a sound balance between approximation and generalization (predictive) abilities of the network. To evaluate the performance of the GA-based SOPNN, the model is experimented with using chaotic time series data. A comparative analysis reveals that the proposed GA-based SOPNN exhibits higher accuracy and superb predictive capability in comparison to some previous models available in the literature.

Confidence and Reliability Measures in Speaker Verification

Abstract: Speaker verification is a biometric identity verification technique whose performance can be severely degraded by the presence of noise Using a coherent notation, we reformulate and review several methods which have been proposed to quantify the uncertainty in verification results, some with a view to coping with the effects of mismatched training-testing environments We also include a recently proposed method, which is firmly rooted in a probabilistic approach and interpretation, and explicitly measures signal quality before assigning a reliability value to the speaker verification classifier's decision We evaluate the performance of the confidence and reliability measures over a noisy 251-users database, showing that taking into account signal-domain quality can lead to better accuracy in prediction of classifier errors We discuss possible strategies for using the measures in a speaker verification system, balancing acquisition duration and verification error rate

A matrix method for solving high-order linear difference equations with mixed argument using hybrid legendre and taylor polynomials

Abstract: A numerical method for solving the higher order linear difference equations with variable coefficients and mixed argument under the mixed conditions is presented. The method is based on the hybrid Legendre and Taylor polynomials. The solution is obtained in terms of Legendre polynomials. IIIustrative examples are included to demonstrate the validity and applicability of the technique.

Spectral efficiency of a single-cell multi-carrier DS-CDMA system in Rayleigh fading

Abstract: The spectral efficiency of a multi-carrier direct-sequence code-division multiple-access (MC/DS-CDMA) system operating in a Rayleigh fading environment is investigated and evaluated in terms of the theoretically achievable channel capacity (in the Shannon sense) per user, estimated in an average sense. This short paper covers operation of the considered system over broadcast communication randomly time-varying channels as applicable to wireless radio networks and single-cell indoor mobile systems and leads to the derivation of a closed-form expression for the achieved spectral efficiency. Furthermore, the relation between the number of the employed sub-carriers and the achieved spectral efficiency is revealed.

Invariant ellipsoids for single-input system with actuator saturation by employing output feedback

Abstract: In this paper, the invariant ellipsoids theorem is introduced into a class of common saturated single-input system by employing output feedback with state-delay, and as a result, a sufficient condition is presented for stability analysis. The result is given in forms of linear matrix inequalities (LMI).

A note on the coherence-based signal-to-noise ratio estimation in systems with periodic inputs

Abstract: Coherence plays a very important role in linear systems analysis, since, in addition to quantify the similarity between signals, it is related to other quantities of interest, such as the signal-to-noise ratio (SNR). The sampling distribution of coherence estimates between Gaussian signals is well established, and hence, in this particular case, the statistics of SNR can be readily found if it is calculated from coherence estimates. However, in some applications, one of the signals is periodic, leading to a different coherence sampling distribution, which has been recently investigated. This work aims at developing analytical expressions for bias, variance and the probability density function of coherence-based SNR estimates under this particular assumption. Routines for obtaining this latter as well as critical values of the estimates are also provided.

A new nonautonomous version of Chua's circuit: Experimental observations

Abstract: In this study, a novel nonautonomous version of autonomous Chua's circuit is presented. The proposed nonautonomous version of Chua's circuit was designed by placing a sinusoidal source to the inner structure of the nonlinear resistor, namely, Chua's diode. The circuit's chaotic dynamics have been investigated by PSpice simulations and laboratory experiments.

A further note on stability criterion of linear neutral delay-differential systems

Abstract: This paper is a further note which corrects an error of the paper by Park and Won. A new stability criteria which is less conservative than those in the literature is presented.

Analyses and designs of a nonlinear mechanical scanning control system

Abstract: In this literature, a scanning system with special mechanical structure and electronic control circuit is analyzed and designed. The scanning control system enlarges the field of view (FOV) and saves more 48% power consumption than conversional scanning systems with scanning motor. The considered system is characterized and analyzed by an equivalent nonlinear feedback control system. All analyzed results are verified by digital simulating and real system testing datum.