Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 1988"
TL;DR: In this paper, the mutual information between the state and the observation is defined as an entropy difference between a prior and a posteriori processes, which is then used as a criterion to determine the degree of observability.
Abstract: For the deterministic system observability, two conditions, connectedness and univalence, are introduced and used. Depending on how the conditions are satisfied, observability is classified in three categories: observability in the strict sense, observability in the wide sense and the unobservable case. An underwater acoustical localization tracking example, the bearing-only information problem described in three different coordinates, and an array SONAR problem described in terms of a small number of sensors and various measurement policies are analyzed. For stochastic process observability, an information theoretic approach is introduced. Computed here, is the mutual information between the state and the observation. Since this quantity is expressed as an entropy difference between a prior and a posteriori processes, two densities are required for computation. Due to the difficulty in solving the density equation, an estimated second-moment approximation is considered. Then, mutual information is used as a criterion to determine the “degree of observability”. Sensitivity with respect to various coordinate systems for an array SONAR, a combination of relative delay and Doppler measurements for up to three sensors are compared. Due to complexity of the computations, the tracking results, presented here, rely heavily on simulation.
39 citations
TL;DR: In this article, the impulse-transient-steady-mixed solution properties of fractionalized Maxwell-Kelvin-Voigt type viscoelastic system responses are investigated.
Abstract: Based on the Riemann-Liouville differential formulation, this paper investigates the impulse-transient-steady-mixed solution properties of fractionalized Maxwell-Kelvin- Voigt type viscoelastic system responses. Included in the development are the definition of eigenvalue characteristics, arbitrary operator order, mixed order formulations as well as associated asymptotic characteristics.
39 citations
TL;DR: In this paper, the dominant poles of a linear multivariable system are retained, followed by matching the steady state parts of the unit step responses of the original and reduced systems.
Abstract: The method of reducing the order of a linear multivariable system is discussed. The dominant poles of the original system are retained, followed by matching the steady state parts of the unit step responses of the original and reduced systems. Each element of the transfer function matrix of the original system is considered separately. E coefficients of the numerator polynomials of the elements of the reduced order system transfer function matrix are then determined by minimizing the Integral Square Error (ISE) between the transient parts of the unit step reponses. An example illustrates the method and the result is compared to another method.
36 citations
TL;DR: In this article, a wave-scatter approach is used to represent the physical system interaction through power interchange, represented here using a signal duplex over the connecting bonds and through the element ports.
Abstract: System description requires specification of two things: the elements and their interconnections. In the customary circuit approach these attributes are treated distinctly, but in the wave-scatter approach they are treated uniformly. This permits direct representation of elements such as transformers and gyrators. All physical system interaction occurs through power interchange, represented here using a signal duplex over the connecting bonds and through the element ports. Causality is thus intrinsic and conservation is imposed via unitarity and orthogonality of the element scattering matrices. This representation is suitable for linear and nonlinear systems.
34 citations
TL;DR: A direct method for solving variational problems using Taylor series is discussed in this article, where properties of Taylor series are briefly presented and an operational matrix is utilized to solve the variational problem by means of a direct method.
Abstract: A direct method for solving variational problems using Taylor series is discussed. Properties of Taylor series are briefly presented and an operational matrix is utilized to solve the variational problems by means of a direct method. An illustrative example is given.
22 citations
TL;DR: In this article, a class of optimal control problems for a damped distributed parameter system governed by a system of partial differential equations with side contraints (equality and/or inequality) is considered.
Abstract: A class of optimal control problems for a damped distributed parameter system governed by a system of partial differential equations with side contraints(equality and/or inequality) is considered. Optimal control problems in structural mechanics are often formulated in this framework. A maximum principle is shown to be a necessary condition for the control to be optimal. Under additional convexity assumptions on state variables, the maximum principle is shown to be sufficient for optimality.
20 citations
TL;DR: Petri net reduction techniques are applied to test the inconsistency of a set of clauses in propositional logic, which can be represented as a place|transition net and the inconsistency is tested through the net reductions.
Abstract: Petri net reduction techniques are applied to test the inconsistency of a set of clauses. A set of clauses in propositional logic can be represented as a place|transition net and the inconsistency is tested through the net reductions. In a more general case, a set of clauses in first-order predicate logic can be represented as a resolution Petri net, which is a modified predicate\s|transition net. The resolution-based proof procedure using resolution Petri nets is discussed.
17 citations
TL;DR: In this paper, the nonlinear differential equations governing the elastica configuration of a long and flexible straight bar are solved, when the bar is subjected to compression and bending developed by end forces and coupled together with a uniformly distributed transverse load.
Abstract: The nonlinear differential equations governing the elastica configuration of a long and flexible straight bar are solved, when the bar is subjected to compression and bending developed by end forces and coupled together with a uniformly distributed transverse load. For achieving a straightforward analytic solution of this complicated mode of loading, several convenient functional transformations are introduced. A quantitative analysis of the governing equations is found to be in agreement with the physical problem.
14 citations
TL;DR: In this article, a necessary and sufficient condition for a 3D separable-denominator recursive model to be separately locally controllable and separately locally observable is derived for a state-space model for causal three-dimensional (3D) recursive digital filters.
Abstract: In respect to a state-space model for causal three-dimensional (3-D) recursive digital filters, a necessary and sufficient condition is derived for a 3-D separable-denominator recursive model to be separately locally controllable and separately locally observable. To approximate a given 3-D digital filter by a 3-D separable-denominator recursive model, a technique is developed via singular value decomposition of three finite Hankel matrices. The resulting 3-D separable-denominator recursive model is advantageous to the computational speed and implementation cost in addition to the ease of stability testing. A roundoff noise analysis and a scaling on state variables are discussed for 3-D separable-denominator recursive models. A technique is then presented for the synthesis of an optimal 3-D separable-denominator recursive model which minimizes the output noise due to roundoff subject to a scaling condition on the state variables. Finally, two examples are given to illustrate the utility of the proposed techniques.
9 citations
TL;DR: In this paper, various representations for an incomplete Lipschitz-Hankel integral of K 0 and related integrals are given in terms of elementary, cylindrical, and Kampe de Feriet functions.
Abstract: Various representations for an incomplete Lipschitz-Hankel integral of K 0 and related integrals are given in terms of elementary, cylindrical, and Kampe de Feriet functions. In addition, some properties of the Kampe de Feriet functions associated with these integrals are derived.
9 citations
TL;DR: The results show that the membership function of gray levels has the form of an asymmetric S-function.
Abstract: We have previously established a relationship between fuzzy information and Shannon's information based on the information equivalence between gray-tone images and half-tone images. Using this, the fuzzy membership function for gray level images is determined experimentally. These results show that the membership function of gray levels has the form of an asymmetric S-function.
TL;DR: In this article, an exact numerical solution is given to the eigenvalue problem of stability of Couette flow in a wide-gap region bounded by two concentric cylinders in the presence of constant heat flux at the inner cylinder.
Abstract: An exact numerical solution is given to the eigenvalue problem of stability of Couette flow in a wide-gap region bounded by two concentric cylinders in the presence of constant heat flux at the inner cylinder. Numerical values of ac (the critical wave number) and Tc (the critical Taylor) are calculated for different values of ±μ(=Ω2/Ω1) and η (=R1/R2) where Ω1, Ω2 are the angular velocities of the inner and outer cylinders of radii R1, R2 respectively. It is observed that the presence of radial temperature gradient enhances the stability of the flow, and with a decrease in the gap-width, the flow becomes less stable. In the presence of counter-rotating flow, the flow becomes more stable due to the presence of a radial temperature gradient.
TL;DR: The behavior of the electromagnetic field generated by a small insulated current-carrying loop, placed at an arbitrary angle near the interface of two conducting media, is investigated in this article, using a triple spatial Fourier transform.
Abstract: The behavior of the electromagnetic field generated by a small insulated current-carrying loop, placed at an arbitrary angle near the interface of two conducting media, is investigated. The space where the loop is buried is conducting, the other medium can be conducting, ferromagnetic, or even have the electromagnetic properties of vacuum. The exciting frequencies are such (ULF and VLF) that the magneto-quasi-static approximation can be used. The problem is tackled by the use of a triple spatial Fourier transform. Expressions are derived for the m.v.p. and magnetic field components in both media.
TL;DR: This paper shows that the DFT of a sequence with prime length, P, can be computed efficiently, for selected P's, using number theoretic transforms, using FFT/NTT.
Abstract: Many fast algorithms have been proposed for computing the discrete Fourier transformation. Most of them are based on factorization with the goal of reducing the number of multiplications. They use floating point arithmetic to avoid repetitious scaling and a sizeable wordlength to minimize quantization errors. This paper shows that the DFT of a sequence with prime length, P, can be computed efficiently, for selected P's, using number theoretic transforms. The proposed technique, denoted as FFT/NTT, is illustrated for p = 2M + 1. Advantages include availability of fast algorithms for a set of prime lengths, residue arithmetic with benefit in speed and hardware costs, parallel implementation with short wordlengths through the use of the Chinese remainder theorem, and exact computation except for scaling and round off for the input array and the trigonometric sequences.
TL;DR: In this article, a nonlinear matrix equation is introduced and it is shown that a particular solution of the considered equation contains for SISO systems the same type of information carried in closed-loop characteristic values.
Abstract: A nonlinear matrix equation is introduced and it is shown that a particular solution of the considered equation contains for SISO systems the same type of information carried in closed-loop characteristic values. In addition, it contains equivalent information on the so-defined closed-loop system “signature” where its importance in model reduction problems is outlined. An illustrative example is presented, and results are compared to those of other methods by using the proposed approximated model in a closed-loop scheme.
TL;DR: In this article, the Lur'e problem in linear multivariable time-varying systems is discussed and a differential Riccati equation is used to establish admissible domains of absolute stability for nonlinear controllers.
Abstract: The Lur'e problem in linear multivariable time-varying systems is discussed. It is shown how to obtain and use a differential Riccati equation in order to establish admissible domains of absolute stability for nonlinear controllers.
TL;DR: A simple geometrical proof of the classical Routh test is presented, based on the application of the root locus technique to suitable additive polynomial decompositions, to give a common framework to many stability tests for both continuous- and discrete-time systems.
Abstract: A simple geometrical proof of the classical Routh test is presented. It is based on the application of the root locus technique to suitable additive polynomial decompositions. The procedure allows us to gain a new insight into the problem of polynomial zero clustering and to give a common framework to many stability tests for both continuous- and discrete-time systems.
TL;DR: In this paper, a necessary and sufficient condition to be separately locally controllable and separately locally observable, controllability and observability Gramians are introduced for a three-dimensional (3-D) separable-denominator stat-space model.
Abstract: After showing a necessary and sufficient condition to be separately locally controllable and separately locally observable, controllability and observability Gramians are introduced for a three-dimensional (3-D) separable-denominator stat-space model. A technique is then developed for realizing a 3-D minimal state-space model in balanced form from a given 3-D rational transfer function with separable denominator. This technique is applicable to the model reduction of 3-D separable-denominator digital filters.
TL;DR: In this article, a model reduction method based on matching the energies of the impulse response and of a suitable number of its derivatives is presented, which ensures the stability of the reduced model of a stable system and is computationally simple.
Abstract: A model reduction method based on matching the energies of the impulse response and of a suitable number of its derivatives is presented. In particular, the denominator parameters of the reduced-order transfer function are determined with reference to the impulse response of the system without zeros; then, the numerator parameters are computed by taking into account the contribution of the zeros. The method ensures the stability of the reduced model of a stable system and is computationally simple. The practicality of the method is illustrated by an example. The results obtained show that the time response of the reduced model satisfactorily fits the original system response.
TL;DR: In this paper, a new method based on the combination of the Volterra series and Fourier series to identify the system of abrupt nonlinearity has been developed and the results are more accurate and easier to compute than those of existing methods.
Abstract: A new method based on the combination of the Volterra series and Fourier series to identify the system of abrupt nonlinearity has been developed and the results are more accurate and easier to compute than those of existing methods. Equations are derived for the N th and K th orders of the truncated Volterra—Fourier repeated series. Additional accuracy can be obtained by using Fejer's method to eliminate the Gibbs phenomenon at discontinuity. Convergence of the repeated series of the double series is established and the radius of acceptable convergence is derived by the d'Alembert criterion. An example for the nonlinear element of dead zone plus jump is given to illustrate this method. Two additional examples, an on—off clipper and a full-wave rectifier is presented and compared with the Hermite polynomial series approximation. It is found that the Volterra—Fourier method gives a far more accurate approximation near the point of expansion and also within a relatively large part of period of the Fourier series. It also admits a wider class of nonlinear functions, including abruptly nonlinear ones.
TL;DR: In this paper, the authors consider linear time-invariant singular systems, which can be decoupled via a Proportional-derivative (PD) feedback of special form.
Abstract: We consider linear time-invariant singular systems, which can be decoupled via a Proportional-derivative ( PD ) feedback of special form. A method based on a transfer function duality property is proposed for simultaneous decoupling and pole placement by using an augmented system designed for this purpose. A method is also presented for decoupling and pole placement of singular systems via output feedback.
TL;DR: In this article, the separation criterion of axially symmetric incompressible laminar flow in close agreement on the separation point of the sphere with experimental data is presented by correlating to two-dimensional flow by the successive solution of a boundary layer equation.
Abstract: The separation criterion of axially symmetric incompressible laminar flow in close agreement on the separation point of the sphere with experimental data is presented by correlating to two-dimensional flow by the successive solution of a boundary layer equation. Applying the presented criterion and analysis, the location and laminar separation boundary layer characteristics of incompressible axisymmetric as well as two-dimensional flow can be accurately predicted using external inviscid velocity distribution only and not by referring to boundary layer flow.
TL;DR: The relationship of the matching polynomial is formalized, and used to derive some known results on rook polynomials and also to demonstrate a different approach to classical problems involving rooks.
Abstract: It is well known that the matching polynomial is related to the rook polynomial. Mention has been made of this in several articles (e.g. E.J. Farrell, Proc. 4th Yugoslav, Seminar in Graph Theory, Nov. Sad., pp. 137–150, 1983 and C.D. Godsil and I. Gutman, J. Graph Theory, Vol. 5, pp. 137–144, 1981). In this expository article, the relationship is formalized, and used to derive some known results on rook polynomials and also to demonstrate a different approach to classical problems involving rooks.
TL;DR: In this article, a simple approach to the treatment of the behaviour of the coupling and the relative simplicity of the models of oscillators participating in the system enables an analytical solution to be found for many of the details of system dynamics without a need to resort to complicated approximate methods.
Abstract: The phenomenon of coupling of several sinusoidal oscillators is discussed The oscillators are arranged in a chain, and each oscillator affects its next neighbour in the chain and is affected by it The coupling is, therefore, bilateral and its main effect is due to variations in phase differences between neighbouring oscillators The simple approach to the treatment of the behaviour of the coupling and the relative simplicity of the models of oscillators participating in the system enables an analytical solution to be found for many of the details of system dynamics without a need to resort to complicated approximate methods The results are supported by computer simulation The present work follows a previous successful treatment of simpler systems (a system of two coupled oscillators and a system of oscillators coupled in a ring) The paper concludes by considering the possible application of the present results for analyzing some technological and natural systems
TL;DR: In this article, a practical method for the analysis of limit cycles in multivariable feedback control systems having separable nonlinear elements is presented, where the limit cycles are found by using a criterion generated by the stability-equation method.
Abstract: A practical method is presented for the analysis of limit cycles in multivariable feedback control systems having separable nonlinear elements. The limit cycles are found by use of a criterion generated by the stability-equation method. Numerical examples are given and compared to other methods in the current literature.
TL;DR: In this article, a systematic procedure for the design of multivariable feedback control systems is proposed, where the desirable overall compensator is decomposed into N cascaded sub-compensators to be determined in each step.
Abstract: A systematic procedure is proposed for the design of multivariable feedback control systems. For an N x N multivariable control system, the desirable overall compensator is decomposed into N cascaded sub-compensators to be determined in each step. The stability-equation method is used to find the desirable sub-compensators. After step N, the overall closed-loop system can be designed diagonal dominant and have a desirable performance closely related to the characteristic roots of each subsystem. A 4 x 4 boiler furnace system is chosen as an example, and comparisons are made with methods in the current literature.
TL;DR: The method has the distinct advantage that it reduces the two-point boundary-value difference equations into a set of algebraic equations which involves specified boundary conditions and is particularly amenable to computer programming and parallel processing.
Abstract: A method of finite series expansion using discrete Legendre orthogonal polynomials (DLOP's) is proposed for the finite-time optimal control of time-varying discrete systems with a quadratic performance index Computational algorithms are derived for solving two-point boundary-value canonical state equations The method has the distinct advantage that it reduces the two-point boundary-value difference equations into a set of algebraic equations which involves specified boundary conditions Hence, the method is particularly amenable to computer programming and parallel processing
TL;DR: In this article, the application of Edgeworth series expansions to approximate the distribution of a test statistic is considered for relative efficiency studies, and the relative efficiency of the sign detector compared to the linear detector is computed for the detection of a constant signal in generalized Gaussian noise.
Abstract: The application of Edgeworth series expansions to approximate the distribution of a test statistic is considered for relative efficiency studies. To illustrate the utility of this approach, the relative efficiency of the sign detector compared to the linear detector is computed for the detection of a constant signal in generalized Gaussian noise. Relative efficiency results computed using exact analysis, Gaussian approximations, and the ARE are presented for comparison. It is demonstrated numerically that the Edgeworth approach to relative efficiency analysis gives close agreement with results derived through exact analysis.
TL;DR: In this paper, the authors address the problem of DC ion flow field problems, such as those of overhead HVDC transmission lines, electrostatic precipitators and DC power equipment with gaseous insulation.
Abstract: Some theoretical and practical (computational) questions are addressed related to the solution of DC ion flow field problems, such as those of overhead HVDC transmission lines, electrostatic precipitators and DC power equipment with gaseous insulation. Ions are produced by corona activities at energized parts. These ions lead to formation of space charge which fills the surrounding space and influences the electric field distribution. The arrangement of the space charge itself is, at the same time, governed by the electric field in space. The problem is therefore nonlinear, and iterative approaches are normally employed to compute the field quantities. The question of uniqueness of solution is addressed first. Then, conditions needed for convergence of iterative algorithms are studied. A new and very successful algorithm is presented. An important feature of the proposed algorithm is the use of the Charge Simulation Method for solution of Poisson fields. Numerical examples are given to illustrate the presented concepts.
TL;DR: In this article, the authors used symbolic algebraic computation with the MACSYMA package to derive the expressions for the coordinate surfaces of the disk-cyclide coordinate system, which is based on a conformal transformation using the Jacobian elliptic function.
Abstract: Disk-cyclide coordinate systems are orthogonal and curvilinear, and are based on a conformal transformation using the Jacobian elliptic function cn. The expressions for the coordinate surfaces of this system have been presented previously (P. Moon and D.E. Spencer, “Field Theory Handbook”, Springer, Berlin, 1961, 1971). However, they are found to be incorrect. Rederivation of the expressions involved a relatively tedious variable-elimination process which we therefore carried out using symbolic algebraic computation with the MACSYMA package.