Showing papers in "International Journal of Systems Science in 1973"
TL;DR: In this paper, a study is made of several algorithms for computing the greatest common divisor g(λ) of two or mora polynomials a1(λ), with real coefficients.
Abstract: A study is made of several algorithms for computing the greatest common divisor g(λ) of two or mora polynomials a1(λ) with real coefficients. Brief descriptions are given of methods including the Routh array form of Euclid's algorithm, a recent approach using the companion matrix of one of the polynomials, another matrix method due to Blankinship and an iterative scheme of Weinstock. The problem of finding multipliers, polynomials x1(λ)such that Σa1x1=g1 also discussed. Estimates are given of the numbers of operations which each method involves when calculating the g.c.d. Numerical results obtained when testing a variety of examples are also presented. By virtue of these considerations it is concluded that for the general problem of finding g(λ)and the multipliers Blankinship's method is the best, both for reasons of accuracy (i.e. ability to distinguish between nearly identical factors) and of computing time and storage requirements. For the case when it is only required to find the g.c.d. of two polynom...
36 citations
TL;DR: In this paper, a transformation of the control variables is introduced which overcomes matrix singularity problems arising out of the transposition of the dynamic input-output model into the 9tato-sp formulation.
Abstract: A transformation of the control variables is introduced which overcomes matrix singularity problems arising out of the transposition of the dynamic input-output model into the 9tato-sp formulation.
34 citations
TL;DR: In this article, several stability criteria are obtained for a class of stochastic feedback systems containing a multiplicative white noise element; continuous time as well as discrete time systems are dealt with.
Abstract: In this paper several stability criteria are obtained for a class of stochastic feedback systems containing a multiplicative white noise element ; continuous time as well as discrete time systems are dealt with. Mean square stability properties are derived by means of Lyapunov theory ; the Lyapunov functions are generated by means of the Lyapunov equation, the path integral technique, and the Kalman-Yacoboviteh lemma. Results similar to the Routh-Hurtwitz conditions and the circle criteria for deterministic feedback systems are discussed. Different interpretations of the white noise element (Ito, Stratonovitch, etc.) are considered.
29 citations
TL;DR: In this paper, the Gauss-Markov theorem is extended to the distributed-parameter ease and a dynamic estimator is derived governing the minimal variance linear unbiased estimate of the state of the system at hand.
Abstract: Some results concerning the state estimation problem of distributed-parameter systems corrupted by white, in time, stochastic disturbances and noises are presented. The least-squares technique is adopted throughout. First, the Gauss-Markov theorem is extended to the distributed-parameter ease and a dynamic estimator is derived governing the minimal variance linear unbiased estimate of the state of the system at hand. Second, the innovations approach to least-squares estimation is invoked and the filtering, fixed-interval, fixed-point, and fixed-lag smoothing problems are studied and solved. Finally, the stability properties of the optimal filter derived are studied by employing the controllability and observability properties of the system under consideration. The results of the paper provide new tools for dealing with distributed data, thus substantially enlarging the existing distributed-parameter estimation theory.
25 citations
TL;DR: In this article, three new theory of association for non-linear systems analysis is presented, compared with the inspection method of Brilliant, the pair listing method of Lubbock, and the new approach is much simpler and easier.
Abstract: In non-linear systems analysis, multiple dimensional Laplace transform is often applied in solving the volterra model. The special technique for the inverse Laplace transform solution is called the association of variables. Three new thoorems are developed for the theory of association. Compared with the inspection method of Brilliant, the pair listing method of Lubbock, the new approach is much simpler and easier and more systematic. Several illustrative examples are included.
25 citations
TL;DR: In this paper, a non-separable problem of power scheduling in a hydroelectric system is described, representing an example of a typical nonseparable optimization problem, and the decomposition methods (recognition of coupling variables, introduction of pseudo-variables) and the coordination algorithms arc described.
Abstract: The multilevel control of large systems intended to distribute between several control levels the calculation of optimum set points and the use and calculation of optimum control laws is based upon the concept of decomposition-coordination of the overall optimization problem For the non-separable problems examined in this paper, it is necessary to use a formulation of the decomposition-coordination principle different from that usod for separable problems In the first part of the discussion, the decomposition methods (recognition of coupling variables, introduction of pseudo-variables) and the coordination algorithms arc described In the second part, a problem of optimum power scheduling in a hydroelectric system is described, representing an example of a typical non-separable optimization problem.
18 citations
TL;DR: The power of Probabilistic reinforcement algorithms for the reconstruction of digital pictures, consisting of two or more grey levels, from their projections, is illustrated by a few examples, as reconstructed by a digital computer.
Abstract: Probabilistic reinforcement algorithms are described for the reconstruction of digital pictures, consisting of two or more grey levels, from their projections. The power of those algorithms are illustrated by a few examples, as reconstructed by a digital computer,
15 citations
TL;DR: The sufficient conditions under which a multivariable time varying system with multiple delays in the state and/or the control vector can be decoupled are derived and used to effect the controller design.
Abstract: In this paper the problem of designing a linear feedback controller for decoupling a multivariable time varying system with multiple delays in the state and/or the control vector is considered. The sufficient conditions under which such a system can be decoupled are derived and used to effect the controller design. Two application examples are thoroughly investigated and reported to illustrate the applicability and usefulness of the theory.
14 citations
TL;DR: A method for the decomposition of complex problems which uses as coordination magnitudes the variables of interconnection between subsystems and the associated Lagrangian parameters to solve static and dynamic optimization problems.
Abstract: In this article, the authors present a method for the decomposition of complex problems which uses as coordination magnitudes the variables of interconnection between subsystems and the associated Lagrangian parameters. This method thus uses a combined coordination by simultaneous action on the criterion function and on the model of each subsystem. The principles of the method are discussed along with static and dynamic optimization problems while defining the local lower-level optimization subproblems, proposing coordinating algorithms for the higher level, and presenting the con vergence studies relative to these algorithms.
13 citations
TL;DR: In this article, conditions are given under which, for any particular application of the model, each species in the community will either oscillate about its unique equilibrium value continuously in a limit cycle or approach it asymptotically.
Abstract: A general Volterra model for describing the dynamics of interacting populations is proven to be inherently stable. Conditions are given under which, for any particular application of the model, each species in the community will either oscillate about its unique equilibrium value continuously in a limit cycle or approach it asymptotically. The asymptotic approach to the steady state is proven to be exponential eventually. An estimate of the decay constant indicates faster convergence to the steady state the larger the size of the equilibrium populations, the intra-species interaction, and the ‘ nutritional value ’ of the inter-species interaction.
12 citations
TL;DR: A comparison has been made between the Fletcher—Powell method, the new Fletcher method and the Jacobson-Oksman method by obtaining second- and third-order models of a seventh-order system so that the stop-response of the model approximates that of the system in the least-squares sense.
Abstract: Three gradient optimization methods have been applied to the problem of determining on optimum low-order model for a high-order system. A comparison has been made between the three methods (the highly regarded Fletcher—Powell method, the new Fletcher method and the Jacobson-Oksman method) by obtaining second- and third-order models of a seventh-order system so that the stop-response of the model approximates that of the system in the least-squares sense.
TL;DR: In this article, the main results on finite time pseudoequilibrium are briefly reviewed while the problem of infinite time-pseudoe-quilibrium is more deeply investigated, and the main result on finite-time pseudo-quilibria is discussed.
Abstract: Pseudoequilibrium states of a dynamical system arc first defined as states which can be approximated at will by suitable motions oven if they are not equilibrium states. Then the main results on finite time pseudoequilibrium are briefly reviewed while the problem of infinite time-pseudoequilibrium is more deeply investigated
TL;DR: A production-inventory problem with advertising control of the sales is cast in a form amenable to solution by discrete-time optimal control theory and the results are interpreted so as to establish guidelines for decisions by management.
Abstract: A production-inventory problem with advertising control of the sales is cast in a form amenable to solution by discrete-time optimal control theory. Uncertainty in the process dynamics and the measurements is included. The versatility of the approach is demonstrated by two examples. The results are interpreted so as to establish guidelines for decisions by management.
TL;DR: In this paper, the performance deterioration of optimal regulators caused by the introduction of Kalman filters as state estimators is investigated and it is shown that, in the ease of single-input single-output (SISO) systems, performance deterioration cannot be made arbitrarily small unless the optimal control law can be implemented by direct output feedback.
Abstract: In this paper, the performance deterioration of optimal regulators caused by the introduction of Kalman filters as state estimators is investigated. It is shown that, in the ease of single-input single-output systems, the performance deterioration cannot be made arbitrarily small unless the optimal control law can be implemented by direct output feedback.
TL;DR: Optimal policies for the pontrol of a class of production-inventory systems are derived and typical response characteristics are presented which illustrate the effects of using different weighting parameter values in the performance cost functional.
Abstract: Optimal policies for the pontrol of a class of production-inventory systems are derived. Typical response characteristics are presented which illustrate the effects of using different weighting parameter values in the performance cost functional.
TL;DR: In this paper, a non-parametric feature selection criterion with an explicit learning scheme is presented, based on the well-known concept of inter-class and intra-class Euclidean distances as a measure of the separability of the pattern classes in a given feature space.
Abstract: A now method of pattern classification, evolved by integrating in a sequential mode a non-parametric feature selection criterion with an explicit learning scheme, is presented. This feature selection criterion is based on the well-known concept of inter-class and intra-class Euclidean distances as a measure of the separability of the pattern classes in a given feature space. An ‘ effective figure of merit’ is denned and the feature subset in which this figure of merit attains the maximum value is construed as the best feature subset. Usually in most of the existing techniques, a single feature subset is chosen as the hest for the multi-class problem as a whole. A distinctive departure from this practice has been made here in that an individual best feature subset is determined for each of the pattern classes. The values of the effective figure of merit for the best feature subsets of the different pattern classes are sorted to determine the best separable pattern class. The learning scheme developed here ...
TL;DR: In this paper, three main forms of representations arc introduced: (causal) parameter mapping, state mapping, and state transition mapping, where the causality and state are defined independently on each other, but they turn out to be intimately connected via properties and interrelations of those forms.
Abstract: The subject is considered in n general set-theoretic formalism. A time system is hero a set of ordered pairs of functions on a common time domain ; extensions to more general forms are also noted. A representation of a system S is an ‘ aggregate ’ of sets and structures by the aid of which each pair of S can be generated. Leading principles of the work arc : (i) Just a representation is a primarily interesting description of S, and it is a starting-point in analysis in most practical eases, (ii) Tbo concepts, like causality and state, are primarily defined as properties of representations. Three main forms of representations arc introduced : (i) (causal) parameter mapping ; (ii) state mapping ; and (iii) state transition mapping. The causality and state are here defined independently on each other. However, they turn out to be intimately connected via properties and interrelations of those forms, presented by some propositions. The aim of the work is to present an alternative formalism which is m...
TL;DR: By filtering the output of a non-linear element, whose input consists of the normal low frequency input signal with a high frequency (dither) signal added, the equivalent nonlinearity of the element can be obtained as discussed by the authors.
Abstract: By filtering the output of a non-linear element, whose input consists of the normal low frequency input signal with a high frequency (dither) signal added, the equivalent non-linearity of the element can be obtained. Illustrative examples of equivalent non-linearities for several non-linear elements are given. It is shown that the technique of dither injection permits the identification of certain types of open and closed-loop systems. Practical results are included to show the accuracy of the method.
TL;DR: In this article, a unified survey of multivariate control theory aspects and techniques applied to linear sequential machines over a Galois field GF(p) is presented, where the concepts of controllability and observability for a Mealy-type machine are studied.
Abstract: This paper presents a unified survey of some modern multivariate control theory aspects and techniques applied to linear sequential machines over a Galois field GF(p), Utilizing the concepts of controllability and observability for a Mealy-type machine the canonical decomposition problem, the state minimization problem, the identification problem, the transformation to canonical form problem, and the controllability/observability problem of combined machines are studied. Then the problem of designing a linear feedback controller for driving any state of a linear machine to the zero state after a minimum number of time steps A(clock periods), as well as the dual problem of designing a time-optimal state reconstructor for the same machine are solved. Finally, the problems of inverting a linear sequential machine and decoupling its inputs and outputs by using state feedforward and feedback are examined. Several examples illustrate the theoretical results.
TL;DR: The simulation methods for analysing dynamic behaviour in industrial and economic systems have been available for more than 10 years, but they have not been widely used as mentioned in this paper, and the reasons for their lack of application are discussed.
Abstract: The simulation methods for analysing dynamic behaviour in industrial and economic systems have been available for more than 10 years, but they have not been widely used. This paper traces the development of the techniques, discusses the reasons for their lack of application, and suggests some areas for future research.
TL;DR: It is shown that a system which is isolated from its environment cannot increase its organization and the basic foundations of a new approach to self-organizing systems are proposed.
Abstract: Self-organizing systems are investigated and the basic foundations of a new approach arc proposed. Mainly based upon the notion of information exchange, this tentative defines the physical entropy of a system and some other characteristic functions. It is shown that a system which is isolated from its environment cannot increase its organization.
TL;DR: In this article, it was shown that the parameters of the input-output (deterministic) port of the model may first be estimated consistently when a pure auto-rogressive structure of that part is considered.
Abstract: The problem of consistently estimating all parameters of an input-output noise model is considered. It is shown that the parameters of the input-output (deterministic) port of the model may first be estimated consistently when a pure auto-rogressive structure of that part is considered. Subsequently, if a consistent estimation procedure of the noise model is employed, a consistent estimate of the parameters of the complete input-output-noise model is shown to be obtainable.
TL;DR: Two now techniques for the synthesis of open-loop optimal controls in distributed systems are presented and applied to a number of teat problems and necessary conditions for optimality in the form of a two-point boundary-value problem are found to be preferable for the solution of distributed optimal control problems.
Abstract: Two now techniques for the synthesis of open-loop optimal controls in distributed systems are presented and applied to a number of teat problems. Results thus obtained are compared with the results obtained via application of existing techniques to the test problems. Necessary conditions for optimality in the form of a two-point boundary-value problem are found to be preferable from the computational point of view for the solution of distributed optimal control problems.
TL;DR: In this article, an iterative hyperpower method of any finite-order for computing generalized inverse A + and the associated projections AA + and A + A for any complex matrix A was developed.
Abstract: In an earlier paper (Gupta 1971), an iterative hyperpower method of any finite- order for computing generalized inverse A + and the associated projections AA + and A + A for any complex matrix A was developed. In this paper, hyperpower methods of different orders are compared and it is shown that there exists an optimum hyperpower method of order three.
TL;DR: In this paper, the problems involved in finding a set of state variables for a dynamical system are formulated, and the definition of topologies in which these presumptive state variables become jointly continuous, or in which a particular system dynamics is continuous.
Abstract: Some of the problems involved in finding a set of state variables for a dynamical system are formulated. Particular attention is given to the definition of topologies in which these presumptive state variables become jointly continuous, or in which a particular system dynamics is continuous. These ideas are illustrated in a number of particular examples with a bearing also on recursive function theory and on pattern recognition.
TL;DR: Two numerical algorithms are applied to non-linear planning models under optimal controls in order to test their sensitivity, convergence, and stability properties around the steady-state solution.
Abstract: Two numerical algorithms are applied to non-linear planning models under optimal controls in order to test their sensitivity, convergence, and stability properties around the steady-state solution. In general, the Davidon algorithm is found to be more efficient in terms of faster convergence and the choice of the search direction parameter.
TL;DR: In this article, it was shown that a sequence of successive approximations, xn)tω converges to the unique random solution at each t ≥ 0 with probability one and in mean square under the conditions of Tsokos' theorem.
Abstract: A non-linear random integral equation of the Volterra type of the form was considered by Tsokos (1960), where ω∊Ω, the underlying set of the probability measure space (Ω A, P). He was concerned with the existence of a unique random solution to this equation, where a random solution is defined to be a second-order stochastic process, x(t; ω), which satisfies the equation almost surely. The present paper shows that a sequence of successive approximations, xn)tω) converges to the unique random solution at each t≥0 with probability one and in mean square under the conditions of Tsokos' theorem. The rate of convergence of the successive approximations and a bound on the mean square error of approximation are also given.
TL;DR: In this article, the projection operator usually associated with the steepest descent solution of constrained optimal control problems is developed by analogy to the familiar finite-dimensional projection matrix, and a simple parameter is introduced to provide both insight into the geometrie relationship of the performance and constraint contours and a measure of the convergence of the gradient descent algorithm.
Abstract: The projection operator usually associated with the steepest descent solution of constrained optimal control problems is developed by analogy to the familiar finite-dimensional projection matrix. The equivalence of two different derivations appearing in the literature is shown, and the geometric significance of various terms in the control variation equation of steepest descent is presented. A full derivation of the auxiliary differential equations used to implement the projection operator has not appeared previously bnt is given here for completeness. A simple parameter is introduced to provide both insight into the geometrie relationship of the performance and constraint contours and a measure of the convergence of the steepest descent algorithm. The application of the projection operator to other direct gradient search algorithms is discussed and illustrated by an application to the conjugate gradient method.
TL;DR: In this article, Liapunov-like theorems are presented which yield sufficient conditions for the set stability of such systems, and examples are given to demonstrate the method.
Abstract: Set stability and uniform set stability involve known specific bounds on the solutions of differential equations. These concepts are extended to include the case of differential equations with time delay. Liapunov-like theorems are presented which yield sufficient conditions for the set stability of such systems. Examples are given to demonstrate the method.
TL;DR: In this paper, the formulation of a class of Lyapunov functions for time-varying nonlinear control systems which occur in the stability analysis of control systems is considered.
Abstract: The formulation of a class of Lyapunov functions for time-varying nonlinear control systems which occur in the stability analysis of control systems is considered. A new approach is presented, which is an extension of a generation technique for time-invariant non-linear systems. This approach, which uses by analogy the classical theory of Hamilton, permits stability and transient information to be obtained from system equations with time-varying damping as well as time-varying gain. A second and third-order example is used to illustrate the application of this new result.