Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1999"

Adaptive control and synchronization of Lorenz systems

Abstract: This study addresses the adaptive control and synchronization problems of Lorenz systems with unknown system parameters. Based on the Lyapunov stability theory, an adaptive control law with single-state variable feedback is derived such that the trajectory of the Lorenz system is globally stabilized to an equilibrium point of the uncontrolled system. In addition, the adaptive control law is also applied to achieve the state synchronization of two identical Lorenz systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

Stochastic stabilizability and H∞ control for discrete-time jump linear systems with time delay ☆

Abstract: In this paper, the stochastic stabilizability and H∞ disturbance attenuation are studied for discrete-time linear time-delay systems that possess randomly jumping parameters using the linear matrix inequality approach. The transition of the jumping parameters is governed by a finite-state Markov process. A sufficient condition is first established on the stochastic stability using the stochastic Lyapunov functional approach. Then sufficient conditions on the existence of a stochastic stabilizing and γ-suboptimal H∞ state feedback controller are presented. It is shown that the stochastic stabilizing H∞ state feedback controller can be constructed through numerical solution of a set of coupled linear matrix inequalities. The state delay systems are first treated and extension to a class of general delay systems are then considered.

A note on stability of neutral delay-differential systems

Abstract: In this note, asymptotic stability of linear neutral delay-differential systems is investigated. A delay-independent sufficient condition for the stability of the system is derived in terms of the spectral radius. The proposed criterion requires more relaxed assumption than those reported in the literature. The effectiveness of the method is illustrated in numerical examples.

Sequential decision fusion: theory and applications

Abstract: A decision fusion problem is considered in which each one of a set of sensors receives a sequence of observations about the state of the system. The observations are quantized at each time step and sent to the fusion center where a binary decision is to be made at a stopping time. Applications of this problem setting are discussed and techniques for finding optimal solutions are presented.

Optimum quantization for detector fusion: some proofs, examples, and pathology

Abstract: We consider optimal decentralized (or equivalently, quantized) detection for the Neyman– Pearson, Bayes, Ali–Silvey distance, and mutual (Shannon) information criteria. In all cases, it is shown that the optimal sensor decision rules are quantizers that operate on the likelihood ratio of the observations. We further show that randomized fusion rules are suboptimal for the mutual information criterion. We also show that if the processes observed at the sensors are conditionally independent and identically distributed, and the criterion for optimization is either a member of a subclass of the Ali–Silvey distances or local mutual information, then the quantizers used at all of the sensors are identical. We give an example to show that for the Neyman–Pearson and Bayes criteria this is not generally true. We go into some detail with respect to this last, and derive necessary conditions for an assumptions of identical sensor quantizer maps to be reasonable.

The voting as a way to increase the decision reliability

Abstract: The class of weighted voting decision rules are studied. The estimates for probability of erroneous decision are obtained for a number of cases. The “accelerated perceptron” algorithm for weights correction is proposed and studied in learning and self-learning modes. The computer simulation results are provided.

Optimization of circular fins with variable thermal parameters

Abstract: The optimization of rectangular profile circular fins with variable thermal conductivity and convective heat transfer coefficients is discussed. The linear variation of the thermal conductivity is considered to be of the form k = ka(1+β(T−Ta)), and the heat transfer coefficient is assumed to vary according to an exponential function with the distance from the bore of the form h = hb exp (γ(r−rb)\(re−rb)). The nonlinear conducting–convecting–radiating heat transfer equation is solved by the differential transformation method. The effective of convective–radiative heat transfer at the fin tip is considered. It is shown that, considering the thermal conductivity and heat transfer coefficient are both constant, for a given fin volume, the optimum fin length is almost independent of the fin base temperature for pure convection. However, for both convection–radiation and pure radiation, the length of the optimum fins for higher temperatures is shorter than the length of the fins with lower temperatures.

Set-models of information-gap uncertainty: axioms and an inference scheme

Abstract: The sparsity and complexity of information in many technological situations has led to the development of new methods for quantifying uncertain evidence, and new schemes of inference from uncertain data. This paper deals with set-models of information-gap uncertainty which employ geometrical rather than measure-theoretic tools, and which are radically different from both probability and fuzzy-logic possibility models. The first goal of this paper is the construction of an axiomatic basis for info-gap models of uncertainty. The result is completely different from Kolmogorov's axiomatization of probability. Once we establish an axiomatically distinct framework for uncertainty, we arrive at a new possibility for inference and decision from uncertain evidence. The development of an inference scheme from info-gap models of uncertainty is the second goal of this paper. This inference scheme is illustrated with two examples: a logical riddle and a mechanical engineering design decision.

Synthesis of grounded capacitor and grounded resistor oscillators

Abstract: Three novel oscillators that employ grounded capacitors and grounded resistors and using the current conveyor as the active building block are given. The proposed oscillators are based on modification of the well known two-integrator loop oscillator. The proposed oscillators have the advantages of independent oscillation control by varying a single grounded resistor as well as independent frequency control through another grounded resistor. A novel current mode oscillator using two-output current conveyors is generated from one of the proposed oscillators. The oscillators reported in this paper are suitable for very large-scale integration, by using MOS grounded resistors. PSpice simulations to confirm the excellent performance of each of the proposed oscillators are included.

Closed-loop identification of transfer function model for unstable systems

Abstract: A simple method of identifying first order plus time delay transfer function model is proposed for unstable systems. The method is based on a single experiment on a closed-loop system with a step change in the set point of a PI or PID controller. The step response and derived analytical formulae are used to calculate the steady-state gain, time delay and time constant of the unstable system. Simulation results are given for transfer function models and on nonlinear model equation of an unstable bioreactor. The identified model parameters and/or the designed PID controllers settings are compared with those of the exact or the linearized model used.

Preference fusion when the number of alternatives exceeds two: indirect scoring procedures☆

Abstract: We consider the problem of aggregation of incomplete preferences represented by arbitrary binary relations or incomplete paired comparison matrices. For a number of indirect scoring procedures we examine whether or not they satisfy the axiom of self-consistent monotonicity. The class of win-loss combining scoring procedures is introduced which contains a majority of known scoring procedures. Two main results are established. According to the first one, every win-loss combining scoring procedure breaks self-consistent monotonicity. The second result provides a sufficient condition of satisfying self-consistent monotonicity.

Neural network forecast combining with interaction effects

Abstract: In this paper we discuss and expand recent innovations in forecast combining with artificial neural networks (ANNs). In particular, we demonstrate that ANNs can outperform traditional forecast combining procedures, such as least-squares weighting, because ANNs can account for traditionally uncaptured interaction effects between time series forecasts. Data employed in this study are price volatility forecasts for the S & P500 stock index.

Expert SMC-based fuzzy control with genetic algorithms

Abstract: Based on sliding mode control (SMC), an expert fuzzy controller synthesized by a collection of fuzzy linguistic control rules is proposed in this paper. The control strategy of the proposed controller is characterized by the linguistic terms in the fuzzy control rules. The membership functions of consequent part in fuzzy control rules are adjusted according to some adaptive law for tracking objective of a control task. The membership functions of antecedent part are well defined to satisfy the stability requirement of control systems. In this paper, a well behavior of SMC-based fuzzy control system is synthesized through the following stages: first, develop an adaptive law to approximate the equivalent control of sliding mode control for improving its performance; second, append a hitting control term to achieve a stable control system and to translate arbitrary state toward an prespecified sliding surface; third, based on the principles of SMC, the fuzzy control rules are emulated; finally, apply genetic algorithms to learning membership functions for obtaining an optimal fuzzy control. A nonlinear simulation example is applied to confirm the validity of the proposed approach.

Bond graph-based simulation of non-linear inverse systems using physical performance specifications

Abstract: Analysis and simulation of non-linear inverse systems are sometimes necessary in the design of control systems particularly when trying to determine an input control required to achieve some predefined output specifications. But unlike physical systems which are proper, the inverse systems are very often improper leading to numerical problems in simulation as their models sometimes have a high index when written in the form of differential-algebraic equations (DAE). This paper provides an alternative approach whereby performance specifications and the physical system are combined within a single bond graph leading to a greatly simplified simulation problem.

Least-squares identification of a class of multivariable systems with correlated disturbances

Abstract: A valuable new way of taking advantage of signal processing techniques to implement unbiased parameter estimation was reported in Feng and Zheng (IEE Proc.-Control Theory Appl. 138 (1991) 484–492). In this paper, some extensions to the recently developed bias-eliminated least-squares method are made such that the method can be employed to perform unbiased identification of multi-input–single-output systems subject to colored noise. A set of digital prefilters are suitably designed to pre-process the input data sampled from multi-input channels, which gives rise to a system of linear equality constraints with respect to system parameters. Then combined with a bias correction procedure, the colored-noise-induced bias in the least-squares parameter estimators can be removed efficiently. The performance of the developed method is both analyzed theoretically and illustrated by means of simulation results.

A family of Colpitts-like chaotic oscillators

Abstract: A family of chaotic oscillators with qualitative dynamics similar to the chaotic Colpitts oscillator is introduced. The oscillators use a single current feedback op amp, configured as a noninverting voltage-controlled voltage source, as the active building block, and a nonlinear element with an antisymmetrical current—voltage characteristic. A procedure for obtaining the chaotic oscillators by modifying simple harmonic oscillators is demonstrated. These chaos generators are suitable for high-frequency operation; device parasitics have negligible effect. Experimental results, PSpice circuit simulations and numerical simulations of the derived mathematical models are included.

An improved approach for nonlinear system identification using neural networks

Abstract: The ability of a neural network to realize some complex nonlinear function makes them attractive for system identification. In the recent past, neural networks trained with back-propagation learning algorithm have gained attention for the identification of nonlinear dynamic systems. However, the conventional back-propagation algorithm suffers from a slow rate of convergence. In this paper, we present an improvement to the back-propagation algorithm based on the use of an independent, adaptive learning rate parameter for each weight with adaptable nonlinear function. Simulation results show that the learning speed is increased significantly by making the slope of nonlinearity adaptive since it amplifies those directions in weight space that are successfully chosen by gradient descent. The results demonstrate that the suggested method gives better error minimization and faster convergence.

Design of MIMO integral variable structure controllers

Abstract: The MIMO integral variable structure control (MIMOIVSC) scheme is proposed for a class of linear MIMO dynamic systems with nonlinear matched perturbations. This scheme is composed of two types of controllers. One is variable structure controller, which gives robust stability for system in the presence of parameter variations, uncertainties, and/or disturbances. The other is integral controller, which can eliminate steady-state error for step tracking. When the system is in the sliding mode, the dynamic equations of the closed-loop system can be reduced to a linear form and its eigenvalues can be arbitrarily assigned. In addition, an observer can be employed for state estimation, so that the state variables need not be measured. The fulfillment of sliding condition, including the case when estimated states are used, is verified. Two numerical examples are given to demonstrate the applicability of the proposed control scheme.

Memoryless H∞ controller for singular systems with delayed state and control ☆

Abstract: In this paper, the memoryless H∞ controllers for singular systems with delayed state and control are presented. Based on the modified Riccati-equation approach, a memoryless linear time-invariant state feedback control law is developed. The controller, which is a delay-independent stabilizer for the singular delayed system will simultaneously reduce the H∞ norm of the closed-loop transfer function from the disturbance to the controlled output to a prescribed level. An illustrative example is included to demonstrate our proposed approach.

A nonlinear resistor and nonlinear inductor using a nonlinear capacitor

Abstract: Ferroelectric capacitors whose rated voltage is basically defined by the requirement of a fair linearity of the (generally nonlinear) capacitors’ voltage–charge characteristic, not by the breakdown voltage, which can be much higher, are widely used today. It is noted, and considered with some details, that the use of such a capacitor in a simple switched-capacitive circuit which imitates a resistance enables a nonlinear frequency-controllable resistance to be obtained, and that the use of such a capacitor as a load for a gyrator circuit enables a nonlinear inductor to be obtained. The topic is interesting from the basic circuit theory aspect, in view of the fact that ferroelectric ceramic capacitors are widely used today, and because of the need to find ways for integral implementation of different nonlinear elements.

Theoretical performance of genetic pattern classifier

Abstract: An investigation is carried out to formulate some theoretical results regarding the behavior of a genetic-algorithm-based pattern classification methodology, for an infinitely large number of training data points n ,i n anN-dimensional space RN. It is proved that for nPR, and for a suƒciently large number of iterations, the performance of this classifier (when hyperplanes are considered to generate class boundaries) approaches that of the Bayes classifier, which is the optimal classifier when the class distributions and the a priori probabilities are known. It is shown that the optimum number of hyperplanes generated by the proposed classifier is equal to that required to model the Bayes decision boundary when there exists only one partition of the feature space that provides the Bayes error probability. Extensive experimental results on overlapping data sets following triangular and normal distributions with both linear and non-linear class boundaries are provided that conform to these claims. The claims also hold good when circular surfaces are considered as constituting elements/segments of boundaries. It is also shown experimentally that the variation of recognition score with a priori class probability for both the classifiers is similar. ( 1999 The Franklin Institute. Published by Elsevier Science Ltd.

Maximal stability bounds of singularly perturbed systems

Abstract: The maximal stability bound e ∗ of a linear time-invariant singularly perturbed system is derived in an explicit and closed form, such that the stability of the systems is guaranteed for 0⩽e ∗ . Two new approaches including time- and frequency-domain methods are employed to solve this problem. The former leads to a generalized eigenvalue problem of a matrix pair. The latter is based on plotting the eigenvalue loci of a real rational function matrix derived by an LFT description system. The results obtained are coincident. Two illustrative examples are given to show the feasibility of the proposed techniques.

Propagation of thermal waves in transient heat conduction in a thin film

Abstract: Wave nature of heat propagation in a very thin film subjected to an exponentially decaying temperature change on both sides is investigated by solving the hyperbolic heat conduction equation. Analytical expressions are obtained for the temperature and heat flux distributions. Numerical computations are performed in order to determine the behavior of temperature and heat flux distributions before and after the collision of the wave fronts from two sides of the film. It is disclosed that in transient heat conduction a heat pulse is transported as a wave only when the decaying frequency of wall temperature equals the reciprocal of thermal relaxation time of the medium (ω = 1\τ), which is attenuated in the film, and that non-Fourier heat conduction is extremely significant with certain range of film thickness and time. The Fouriers law used in macroscale heat conduction cannot be applied. The results also show that both temperature overshoot and temperature undershoot occur in the films with smaller values of x 0 \τC within a very short period of time, and that the first reverse flow of heat occurs at the same moment β = 0.79 for all films with different values of x 0 \τC considered in this work.

Multiple sensor fusion under unknown distributions

Abstract: The sensor S i , i=1, 2, T 20…, N , of a multiple sensor system outputs Y (i) ∈ R , according to an unknown probability distribution P Y ( i ) ∣ X , in response to input X∈ R . The problem is to design a fusion rule f : R N ↦ R , based on a training sample, such that the expected square error I( f )=E[(X−f (Y)) 2 ] is minimized over a family of functions F . In general, f ∗ ϵ F that minimizes I (.) cannot be computed since the underlying distributions are unknown. We consider sufficient conditions and algorithms to compute an estimator f such that I( f )−I( f ∗ ) with probability 1− δ , for any e >0 and 0 δ F . We then review three recent computational methods based on the feedforward sigmoidal networks, the Nadaraya–Watson estimator, and the finite-dimensional vector spaces.

Robust stabilization for systems with parametric uncertainty and time delay

Abstract: In this paper we use the parameter-dependent Lyapunov function framework developed by Haddad and Bernstein to address the problem of robust stabilization for systems with parametric uncertainty and system delay. The principal result involves the construction of a modified Riccati equation for characterizing a memoryless (delay-independent) feedback controller that guarantees robust stability in the face of parametric uncertainty and time delay.

Robust adaptive regulation of potentially inversely unstable first-order hybrid systems

Abstract: This paper presents a robust adaptive stabilization scheme for a class of hybrid time-invariant linear system involving both continuous and discrete signals. The continuous subsystem and the discrete one are both of first-order. The usual assumptions of inverse stability of the plant and knowledge of the high-frequency gain are not required for this first-order hybrid system. The design philosophy used relies on the separation of the continuous and discrete dynamics by generating two additive terms to build the control action. The estimation scheme is unified in the sense that both continuous and discrete estimated parameters are generated from the same adaptation error. The controllability of the nominally estimated plant model is maintained by using an hysteresis switching function under the controllability of the nominal plant. This allows relaxing the usual assumption of stability of the plant inverse. Also, an adaptation dead zone is used for robust stabilization by using a known overbounding function of the contribution of the unmodelled dynamics.

Design for quality and reliability using expert system and computer spreadsheet

Abstract: For all the products, quality and reliability should be designed in. EASYDFQR, which is a computer package for design for quality and reliability, has been developed. Design engineers can use EASYDFQR to obtain important design guidelines for quality and reliability. EASYDFQR is a PC-based expert system. Its knowledge base contains expertise about quality and reliability, such as reliability models, design approaches, failure modes, effects, and criticality analysis (FMECA), fault tree analysis (FTA), derating technique, Kaizen, etc. It can integrate with computer spreadsheets making possible tabular design calculations of quality and reliability. It supports computer graphics for the explanation of design guidelines. In addition, design engineers can obtain the knowledge they need via the shortest path using EASYDFQR. In simple words, EASYDFQR is very helpful for product design.

Numerical computation of the complex dielectric permittivity using Hilbert transform and FFT techniques

Abstract: A procedure is described to efficiently obtain the complex dielectric permittivity of semiconductor materials with numerical routines available in current software applications. This procedure calculates the real component of the dielectric permittivity from its imaginary component by making use of the Hilbert transform properties of the Kramers–Kronig relations. We show the reliability of this approach by reconstructing the real component from the experimentally known dispersion relations of GaAs and InAs. In addition, we use this procedure for the case when the imaginary component is obtained from analytical expressions as is the case for the Franz–Keldysh effect in the absorption of photons in GaAs. We show how the spectral photoreflection of structures where this effect is present can be easily modeled and simulated by this method.

A small gain theorem for locally input to state stable interconnected systems

Abstract: A small-gain theorem for nonlinear systems is established, which, when applied to interconnections of locally input-to-state stable systems, can ensure the “local input-to-state practical stability” of the interconnection. This concept of stability denotes that the state of the interconnection remains bounded for sufficiently small input and initial conditions, but it does not tend to zero for zero input.

Optimal reduction of linear systems

Abstract: The use of direct search (LJ) optimization procedure in multi-pass manner in the fre-quency domain is shown to be a viable approach for obtaining the optimal reduced model of a linear single-input single-output (SISO) system, for which the optimal solution has eluded previous investigators. The resulting second-order reduced model provides very close time-domain response of the original model to both impulse and step inputs. Establishment of the third-order reduced model is computationally more demanding. Similar behaviour is observed with an eigth-order transfer function, where the second-order reduced model is very easily obtained, but higher order reduced models require a considerably larger number of random points to be used in each iteration.