Showing papers in "International Journal of Systems Science in 1974"
TL;DR: In this paper, the problem of making the transfer function between disturbances and controlled outputs identically zero by using state feedback, feedforward control and dynamic compensation in linear timo invariant system is treated and a constructive solve ability condition is presented.
Abstract: The problem of making the transfer function between disturbances and controlled outputs identically zero by using state feedback, feedforward control and dynamic compensation in u linear timo invariant system is treated and a constructive solve ability condition is presented.
61 citations
TL;DR: In this paper, simple matricial methods are used to develop a basis for the design of multivariable continuous-time tracking systems which are generalized versions of classical single-input single-output servomechanisms.
Abstract: In this paper, simple matricial methods are used to develop a basis for the design of multivariable continuous-time tracking systems which are generalized versions of classical single-input single-output servomechanisms.
58 citations
TL;DR: A hierarchical system theory approach to the discrete-time system identification problem is considered for stochastic large-scale system applications and is conducted in a two level hierarchical structure with two principles of coordination.
Abstract: Hierarchical decomposition is considered to be one of the most powerful and offective tools to deal with complexity. Hierarchical system theory, which deals with system decomposition and coordination, can be used to decentralize and reduce the computational efforts requirements for many large-scale problems. This is achieved by decomposing the original system problem into several lower order easier to handle sub-problems, which are then coordinated such that the overall system objectives are met. In this work a hierarchical system theory approach to the discrete-time system identification problem is considered for stochastic large-scale system applications. A set of sequential discrete-time hierarchical identification algorithms, suitable for known and unknown system noise moments, are first obtained using a maximum a posteriori (MAP) approach with covariance matching and maximum likelihood (ML) methods. This is conducted in a two level hierarchical structure with two principles of coordination. ...
32 citations
29 citations
TL;DR: In this paper, the Smith normal form and the greatest common right divisor of polynomial matrices are calculated using transformation matrices and matrix multipliers, respectively, without explicit calculation of the Greate3t common divisors of poynomials.
Abstract: Polynomial matrices play an important part in linear system calculations. New computational procedures are given for calculation of the Smith normal form and the greatest common right divisor of polynomial matrices. It is shown how suitable transformation matrices can be determined for the calculation of the Smith normal form, and how a set of polynomial matrix multipliers can be calculated for the greatest common right divisor problem. Neither of these algorithms relies on explicit calculation of the greate3t common divisor of polynomials. Limited numerical experience has shown that the3e algorithms are both fast and accurate.
17 citations
TL;DR: Information-theoretic concepts are developed and employed to obtain conditions for a minimax error entropy stochastic approximation algorithm to estimate the state of a non-linear discrete time system on noisy linear measurements of the state.
Abstract: Information-theoretic concepts are developed and employed to obtain conditions for a minimax error entropy stochastic approximation algorithm to estimate the state of a non-linear discrete time system baaed on noisy linear measurements of the state. Two recursive suboptimal error entropy estimation procedures are presented along with an upper bound formula for the resulting error entropy. A simple example is utilized to compare the optimal and suboptimal error entropy estimators and the minimum mean Square error linear estimator.
16 citations
TL;DR: In this article, a three-area interconnected power system model is used to demonstrate the decomposition of the original system based on its particular characteristics and the implementation of hierarchical algorithms for system identification.
Abstract: This paper presents an application of hierarchical identification procedures of the previous paper to the identification of interconnected power system states and parameters from input—output observed data. A three-area interconnected power system model is used to demonstrate the decomposition of the original system based on its particular characteristics and the implementation of hierarchical algorithms for system identification. The adaptivity of these procedures to structural changes are also illustrated. Numerical results are obtained by conducting a digital simulation of the three-area system and using the hierarchical identification and coordination algorithms to estimate the states and unknown system parameters. Computational aspects of the hierarchical system identification solutions are discussed.
16 citations
TL;DR: In this article, the authors presented a method of obtaining an analytical expression for the transfer function of a system in the form of a ratio of two polynomials of the complex variable, 8, from the frequency response-data.
Abstract: This article presents a method of obtaining an analytical expression for the transfer function of a system in the form of a ratio of two polynomials of the complex variable, 8, from the frequency response- data. The method alleviates the deficiencies of some of the other methods previously reported in the literature. First, it guarantees that the denominator polynomial, when factorized, would not have right-half plane poles and, second, there is no need to know the degrees of the numerator and denominator polynomials, a priori. By systematically examining the time response of the synthesized transfer function, say to a unit step function, the method guarantees that the form and the coefficient values of the transfer function which is finally arrived at do give the best fit to the frequency response data. The minimum mean square error criterion is used to judge the goodness of fit.
16 citations
TL;DR: Even though formalized approaches to modelling (such as the systems approach) exists ; modelling, as well as the use of models, remains very much an art rather than a science.
Abstract: This paper discusses the basic concepts of models and modelling. The difference in information contents between a model and the real or imagined situation it is intended to represent is pointed out, and the fact that a model should not be divorced from its intended purpose is strongly emphasized. The act of modelling is defined and discussed. It is concluded that even though formalized approaches to modelling (such as the systems approach) exists ; modelling, as well as the use of models, remains very much an art rather than a science.
14 citations
TL;DR: In this article, it is shown that certain problems of optimal control of stochastic systems can be reduced to an optimal control problem of a class of nonstandard distributed parameter systems (with controls appearing in the coefficients).
Abstract: In this paper it ia shown that certain problems of optimal (feedback) control of stochastic systems can be reduced to an optimal control problem of a class of nonstandard distributed parameter systems (with controls appearing in the coefficients). Fixed time problems reduce to optimal control problems of distributed parameter system with Canchy condition and Markov time problems reduce to those with first boundary condition. (Il'In, Kalashnikov and Oleinik 1962, p. 40.)
13 citations
TL;DR: In this article, the problem of finding n-vectors x and y such that Ax = b + y, xTy = 0, x≥ bk and y≥ 0, is solved by solving a number of linear systems.
Abstract: Let A be a real symmetric positive definite n × n matrix and b a real column n-veetor. The problem of finding n-vectors x and y such that Ax = b + y, xTy = 0, x ≥ 0 and y ≥ 0, occurs when the method of Christopherson is used to solve free boundary problems for journal bearings. In this case A is a ‘ finite difference ’ matrix. We present a direct method for solving the above problem by solving a number of linear systems Akx = bk. Each system can be solved using one of the recently developed fast direct or iterative procedures. We consider the solution by factorization techniques.
TL;DR: In this paper, a modified definition of coordinability is proposed to remedy this situation, in which a decision-making system may be coordinable by that definition and yet intuitively seem uncoordinable.
Abstract: Coordinability of a multi-level decision-making system is one of the most fundamenta concepts in hierarchical systems theory. The definition of coordinability according to Mesarovic et al. is stated. By means of an example it is demonstrated that that definition may load to anomalous results, in that a decision-making system may be coordinable by that definition and yet intuitively seem uncoordinable. To remedy this situation a modified definition of coordinability is proposed.
TL;DR: In this article, a unified treatment of filtering in stochastic distributed systems using a function space approach is presented using an infinite-dimensional analogue of the well-known matrix inversion lemma and used in developing explicit and computationally efficient representations for the estimate and covariance equations.
Abstract: A unified treatment of filtering in stochastic distributed systems is presented using a function space approach. An infinite-dimensional analogue of the well-known matrix inversion lemma is established and used in developing explicit and computationally efficient representations for the estimate and covariance equations. It also enables us to pursue the analogy to the finite-dimensional case and certain new results are obtained for the case of intermittent measurements. The equations for the case of continuous-time measurements follow easily from the above under passage to the limit. Measurements over the entire region as well as those at a finite number of locations are considered.
TL;DR: In this article, an identification algorithm for a pollution source distributed along a river is presented, where the water quality is described by a couple of partial differential equations of the first order or a parabolic one.
Abstract: An identification algorithm is presented for a pollution source distributed along a river. The water quality is described by a couple of partial differential equations of the first order or a parabolic one. This problem, after transformation, results in the Fredholm integral equation of the first kind, which is non-well posed in the sense of Hadamard. The solution does not continuously depend on the observed data. The application of the regularization method proposed by Tikhonov (1963) yields a stable algorithm for the identification problem. Some simulation examples are given to illustrate the applicability of this method to environmental control systems based on the convective or dispersive phenomena.
TL;DR: It has been demonstrated how efficiently extremely near minimax results can be achieved on a discrete sot of sample points using this approach and the programmes written verify this.
Abstract: User-oriented computer programmes in FORTRAN IV for discrete least pth approximation with a single specified function, and more generalized discrete least pth approximation with various specifications, which may also be used for non-linear programming, are presented. Values of p up to 10" can be used successfully in conjunction with efficient gradient minimization algorithms such as the Fletcher-Powell method and a method due to Fletcher. It has been demonstrated how efficiently extremely near minimax results can be achieved on a discrete sot of sample points using this approach and the programmes written verify this. The programmes may be applied to a wide variety of design problems with a wide range of specifications. They are suitable for electrical network and system design and such problems as filter design.
TL;DR: In this paper, a solution is presented to the timing of advertising expenditure, using a differential equation to model the relationship between the sales and advertising rates and using profit as a criterion.
Abstract: In this paper a solution is presented to an important marketing problem : the timing of advertising expenditure. Using a differential equation to model the relationship between the sales and advertising rates and using profit as a criterion, a synthesis of the optimal dynamic advertising policy as a function of the current sales level and length of the campaign is derived. In addition, using profit as a criterion, the profitability under an optimal dynamic advertising policy is compared with the profits obtained using an optimal static policy. It is shown that a significant increase in profits can result from employing the optimal dynamic policy.
TL;DR: In this article, the synchronization of a digital communication network of general structure by the method of discrete-control-correction is investigated, where periodic corrections are made to the frequencies of the local clocks, according to changes in the local buffer-levels.
Abstract: The synchronization of a digital communication network of general structure by the method of discrete-control-correction is investigated. In this method, periodic corrections are made to the frequencies of the local clocks, according to changes in the local buffer-levels. Conditions under which synchronization is achieved are derived, and the frequency of synchronism and the steady-state buffer levels are calculated.
TL;DR: In this article, the problem of optimal selection of the pair {u, φ} for a class of non-linear systems with finite heredity in both the states and the control is considered.
Abstract: In this paper the problem of optimal selection of the pair {u, φ} for a class of non-linear systems with finite heredity in both the states and the control is considered. With the initial data {u(t),φ(t;)/te[α,t0)] directly penalized in the cost functional, a Pontryagintype Maximum Principle is derived. An example illustrates the results.
TL;DR: In this article, a stochastic distributed parameter system of a parabolic type is dealt with, and sufficient conditions for n weak stability of the system's solutions are derived by applying a finite-difference scheme on the spatial coordinate.
Abstract: A stochastic distributed parameter system of a parabolic type is dealt with. The system is stochastic duo to a distributed multiplicative gain. The gain is a non-linear function of a Wiener process. By applying a finite-difference scheme on the spatial coordinate, and using a stochastic Linpunov type functional, sufficient conditions for n weak stability of the system's solutions, are derived.
TL;DR: In this article, the Nyquist plot of a single variate transfer function is used to analyze selected system sensitivity problems in the Hilbert space setting, which is relevant to linear and non-linear operators on a Hilbert space.
Abstract: The Nyquist plot of a single variate transfer function provides the motivation for a graphical technique relevant to linear and non-linear operators on a Hilbert space. The graphical method is developed so as to retain the geometrical interpretation and physical insight which characterizes the conventional Nyquist plot. The extended Nyquist plot is then utilized to analyze selected system sensitivity problems in the Hilbert space setting.
TL;DR: An electronic model of a cardiac pacemaker cell is developed from a study of the Hodgkin—Huxley equations describing the dynamic behaviour of excitable tissue membranes, based on the functional hypothesis that the controlling factor is the leakage conductance of the membrane to sodium ions.
Abstract: An electronic model of a cardiac pacemaker cell is developed from a study of the Hodgkin—.Huxley equations describing the dynamic behaviour of excitable tissue membranes. The model is based on the functional hypothesis that the controlling factor is the leakage conductance of the membrane to sodium ions and that this is increased by stimulation of the sympathetic nerves and decreased by stimulation of the parasympathetic nerves. The resulting model shows close agreement with experimental results obtained by Levy and Ziesko on the heart of the anaesthetised dog. The model forms part of an circulatory-parameter analogue of the human circulatory system currently being constructed as an aid to studying the manner in which the parameters and control loops of this system adapt to prolonged periods of heavy exercise.
TL;DR: In this article, the main properties of martingales from an engineering point of view are discussed, followed by applications of the theory to optimal linear as well as non-linear estimation problems.
Abstract: The main properties of martingales »are discussed from an engineering point of view. This is followed by applications of the theory to optimal linear as well as non-linear estimation, problems†
TL;DR: In this article, the vector valued bandlimited functions have been used as the class of admissible controls and the properties of attainable sets and the set of trajectories of the dynamical system under consideration are presented.
Abstract: In this paper (vector valued) bandlimited functions have been used as the class of admissible controls. Essential properties of the class of admissible controls are developed. Properties of attainable sets and the set of trajectories of the dynamical system under consideration are presented. These results are proved without the convexity condition usually imposed on the ‘ velocity field ’ of the dynamical system. In the final section several interesting optimal control problems are solved using the compactness properties of attainable sots and admissible trajectories.
TL;DR: In this article, a weaker notion of equivalence between DTOLs, called similarity, was introduced and proved decidability for the sequence equivalence problem for some particular cases.
Abstract: Deterministic Informationless Lindenmayer Sytems with Tables (DTOL) aro systems introduced for the mathematical modelling of the development of Filainontoita organisms under changing environmental conditions. The sequence equivalence problem for DTOL, i.e. the problem of determining whether the sequences of organisms produced by two given DTOL are equal, is open in the general case. We introduce hero a weaker notion of equivalence between DTOL, to be called similarity, and prove its decidability. We also prove the decidability of the original sequence-equivalence problem for some particular cases.
TL;DR: An approach to self-organizing systems based upon information theory is presented and it is shown that the capacity of an information source is given by the logarithm of its inverse entropy rather than by its negative entropy.
Abstract: This paper is the continuation of a preceding one which appeared in this journal, and presented an approach to self-organizing systems based upon information theory. To begin with, some illustrating examples try to show why one can think that the concept of information should play a crucial role in a theory of general systems. Then the concept of ‘ structural entropy ’, and the ‘ evolution principle ’ that we have previously introduced, are improved here in a definitive form. The concept of ‘ information potential ’ is defined and we show that the capacity of an information source is given by the logarithm of its inverse entropy rather than by its negative entropy. Composition laws for the structural entropy are stated and it is shown that these concepts provide an approach to information balance. Some simple examples are outlined to connect this approach with well known existing results.
TL;DR: In this paper, a new algorithm for calculating a state space minimal realization of a rational transfer function matrix is given, which consists of four major steps: calculation of the least common denominators of the columns of the transferred function matrix; calculation of a greatest common right divisor of two polynomial matrices; factoring the divisors from the two matrices ; and expansion of the resulting relatively right prime matrices into constant matrices.
Abstract: A complotely new algorithm for calculating a state space minimal realization of a rational transfer function matrix is given. Tho algorithm consists of four major steps : calculation of the least common denominators of the columns of the transfer function matrix ; calculation of the greatest common right divisor of two polynomial matrices ; factoring the divisor from the two matrices ; and expansion of the resulting relatively right prime matrices into constant matrices. The transfer function matrix need not be proper and the result of the calculations leaves the polynomial part of the transfer function matrix unaltered, thus allowing a useful check on the accuracy of the computations to be incorporated. The results of several examples show that this new algorithm is superior in terms of computing time to other methods and is very accurate.
TL;DR: It is shown that this procedure minimizes the expected number of necessary tests for some classes of functions and probably will do so for others.
Abstract: The paper considers the determination of the value of a boolean function by examining its variable. The function's value is deterministically determined by the variables which arc binary and random. A sequential testing procedure of the variables is presented. It is shown that this procedure minimizes the expected number of necessary tests for some classes of functions and probably do so for others. The presence of such problem is described in file searching, reliability systems, switching circuits and graph connectivity.
TL;DR: A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed and the feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non- linear model and a higher order linear model.
Abstract: A non-linear model, construed as a generalized version of the models put forth earlier for the study of bi-state social interaction processes, is proposed in this study. The feasibility of deriving the dynamics of such processes is demonstrated by establishing equivalence between the non-linear model and a higher order linear model.
TL;DR: Differential transformation techniques developed elsewhere in the literature are seen to be effective tools of dynamic analysis of this non-linear non-conservative mode! of social interaction process.
Abstract: A mathematical model of social interaction in the form of two coupler! first-order non-linear differential equations, forms the topic of this study. This non-conservative model io representative of such varied social interaction problems as coexisting sub-populations of two different species, arms race between two rival countries and the like. Differential transformation techniques developed elsewhere in the literature are seen to be effective tools of dynamic analysis of this non-linear non-conservative mode! of social interaction process.
TL;DR: In this paper, the authors extended the differential transformation technique for non-linear, time invariant systems to the domain of time-varying systems by modifications to differential transformation laws proposed therein.
Abstract: The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.