Showing papers in "International Journal of Systems Science in 1976"
TL;DR: In this article, the problem of finding a strategy of allocating service which minimizes the total expected costs of all jobs in the system and which observes the order constraints is addressed.
Abstract: A collection of jobs requires service. Each job has an associated cost function; normally costs accrue when a job is completed. The amount of service needed to complete a job is a random variable with a known probability distribution. Service may be allocated to jobs according to a sot of order constraints between the jobs. The problem is to find a strategy of allocating service which minimizes the total expected costs of all jobs in the system and which observes the order constraints.
56 citations
TL;DR: A sufficient condition is given for “ chaotic” behaviour of trajectories of systems of difference equations.
Abstract: A sufficient condition is given for “ chaotic” behaviour of trajectories of systems of difference equations.
51 citations
TL;DR: Following developments in non-linear least pth optimization by the authors it is possible to derive two new methods of non- linear minimax optimization.
Abstract: Following developments in non-linear least pth optimization by the authors it is possible to derive two new methods of non-linear minimax optimization. Unlike the Polya algorithm in which a sequenc...
45 citations
TL;DR: A method for the analysis of the effects of subjective and objective tolerances in networks and systems is presented and networks representing humanistic systems may be analysed using this method.
Abstract: A method for the analysis of the effects of subjective and objective tolerances in networks and systems is presented in this paper. The imprecision of the components is represented using fuzzy sets and then the value of the desired attribute is computed. The resulting attribute is also fuzzy and is obtained in the form of a fuzzy set. This fuzzy set contains the extremal and other values of the desired attribute along with their grades of membership. Thus, apart from getting the extremel values, we get the overall picture of the attribute. Since this method is directly applicable for the analysis of subjective tolerances, networks representing humanistic systems may be analysed using this method.
43 citations
TL;DR: Methods developed for the reduction in order of single-input/single-output systems are extended to the reduction of linear, constant, equal input/equal output multivariable systems.
Abstract: Methods developed for the reduction in order of single-input/single-output systems are extended to the reduction of linear, constant, equal input/equal output multivariable systems. The methods considered are the continued fraction and the Pade approximation techniques. Examples are given to illustrate the method.
33 citations
TL;DR: Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient.
Abstract: Among the iterative schemes for computing the Moore — Penrose inverse of a woll-conditioned matrix, only those which have an order of convergence three or two are computationally efficient. A Fortran programme for these schemes is provided.
30 citations
TL;DR: A recursive pseudo-inverse algorithm is presented for estimating the parameters of the transfer-function matrix of a multiple-input-multiple-output discrete-time system from the samples of the input-output data.
Abstract: A recursive pseudo-inverse algorithm is presented for estimating the parameters of the transfer-function matrix of a multiple-input-multiple-output discrete-time system from the samples of the input-output data. The algorithm is suitable for on-line identification of linear multivariable systems.
27 citations
TL;DR: In this article, the problem of the approximate reconstruction of the unknown state variables in distributed-parameter systems is examined, and the results on the observer theory for important classes of linear and non-linear operator, partial differential, and partial differential-integral equations are presented.
Abstract: This paper examines the problem of the approximate reconstruction of the unknown state variables in distributed-parameter systems. New results on the observer theory for important classes of linear and non-linear operator, partial differential, and partial differential-integral equations in describing distributed-parameter systems are presented. The specific developments employ the recent results on Lyapunov stability theory, along with the theory of linear and non-linear semigroup operators, and their infinitesimal generators. The questions of observability, stability of the state reconstruction error dynamics associated with the proposed observer structure are discussed. The theoretical results are illustrated with some applications to problems of the kinetic lumping of complex distributed-parameter chemical reaction systems, as well as the observer design for linear and non-linear distributed-parameter diffusion systems.
23 citations
TL;DR: In this article, a generalization of the direct continued fraction method was made by using the squared magnitude continued fraction and factorization technique to obtain reduced models which are always stable, for single-input, single-output and multi-input-output cases.
Abstract: The direct continued fraction method of model reduction for single-input-output and multi-input—output cases sometimes produces unstable reduced models. A generalization is made by using the squared magnitude continued fraction and factorization technique to obtain reduced models which are always stable.
18 citations
TL;DR: In this article, it is shown that the method of D-partition can be used to investigate the stabilizability of a class of continuous-time production-inventory systems in which the control policies are retarded by finite time-delays.
Abstract: In this paper it is shown that the method of D-partition can be used to investigate the stabilizability by linear state feedback of a class of continuous-time production-inventory systems in which the control policies are retarded by finite time-delays. The theory is illustrated by the presentation of typical transient and steady-state response characteristics of controlled production-inventory systems of this class.
18 citations
TL;DR: In this article, the Brunovsky canonical form is used to synthesize piecewise-constant control policies for a class of production-inventory systems which consist of a set of production inventory sub-systems connected in cascade.
Abstract: n this paper the Brunovsky canonical form is used to synthesize piecewise-constant control policies for a class of production-inventory systems which consist of a set of production-inventory sub-systems connected in cascade. It is shown that each production-inventory sub-system can be controlled in isolation but that control policies based on this approach lead to undesirable transient behaviour. The alternative approach whereby the control policies are formulated for the composite system leads to improved transient behaviour.
TL;DR: In this paper, the stability of the trivial equilibrium solution of a class of non-linear differential equations with a non-stationary absolutely integrable random coefficient is studied and the mean square stability of random systems is discussed and stability theorems of Bertram and Sarachik (1959) are stated.
Abstract: The stability of the trivial equilibrium solution of a class of non-linear differential equations with a non-stationary absolutely integrable random coefficient is studied. The mean square stability of random systems is discussed and stability theorems of Bertram and Sarachik (1959) are stated. It is shown that the equilibrium null solution is mean square stable under some mild conditions. Some examples are also considered.
TL;DR: In this paper, the interaction prediction method and the goal coordination method for the multi-level optimization of large-scale interconnected dynamical systems with separable quadratic coat functions and linear dynamics are compared.
Abstract: In this note the interaction prediction method and the goal coordination method for the multi-level optimization of large-scale interconnected dynamical systems with separable quadratic coat functions and linear dynamics are compared. The vehicle for the comparison is a twelth-order complex counter-current example taken from the literature. The computational load for the two methods is compared qualitatively whereas the convergence characteristics arc tested on the example. A simple condition is also given for the convergence of the interaction prediction method. This is also tested on the example.
TL;DR: In this paper, the class of linear multivariable continuous-time plants which are amenable to high-gain error-actuated control is characterized in terms of the relatively prime polynomial matrix factors of the transfer function matrices of such plants.
Abstract: In this paper, the class of linear multivariable continuous-time plants which are amenable to high-gain error-actuated control is characterized in terms of the relatively prime polynomial matrix factors of the transfer function matrices of such plants. It is shown that this characterization greatly facilitates the design of high-gain error-actuated controllers, and the resulting synthesis technique is illustrated by designing such a controller for a third-order plant with two inputs and two outputs.
TL;DR: In this article, a particular class of linear parametric stochastic systems is considered and the moment stability problem is analyzed: it is shown that the stability conditions do not depend on the noise bandwidth.
Abstract: In this paper a particular class of linear parametric stochastic systems is considered. For this class the moment stability problem is analysed: it is shown that the stability conditions do not depend on the noise bandwidth. An equivalent Ito equation is derived. Explicit criteria for the stability of the moments, for pth mean stability and for almost sure stability are obtained.
TL;DR: In this article, modern control theoretical principles are used to derive necessary conditions for the optimal linear control of a general linear production-inventory system with non-linear costs per period, where the main assumptions are stationary normal distribution of all random"variables and optimization of the average expected costs.
Abstract: Modern control theoretical principles are used to derive necessary conditions for the optimal linear control of a general linear production-inventory system with non-linear costs per period. The main assumptions are stationary normal distribution of all random"variables and optimization of the average expected costs per period.
TL;DR: In this paper, the stability of complex systems composed of interconnected subsystems is investigated by studying a comparison system, the dimension of which is equal to the number of subsystems, and special attention is given to the estimation of the stability region of the complex system.
Abstract: In this paper the stability of complex systems composed of interconnected subsystems is investigated. The results are derived by studying a comparison system, the dimension of which is equal to the number of subsystems. Special attention is given to the estimation of the stability region of the complex system. The stability analysis of the comparison system is carried out without using a Lyapunov function. This approach permits an extension of the results of Weissenberger (1973) who treated an analogous problem.
TL;DR: A method with wide applicability is outlined for the hierarchical control of large non-linear interconnected dynamical systems with separable cost functions and the method is applied to the problem of optimal control of synchronous machine excitation.
Abstract: In this paper a method with wide applicability is outlined for the hierarchical control of large non-linear interconnected dynamical systems with separable cost functions, The method is applied to the problem of optimal control of synchronous machine excitation The system considered comprises a single generator connected by a transmission line to an infinite bus-bar and for this system the trajectory of the optimal voltage to be applied to the field winding is computed using the two-level method
TL;DR: A rigorous basis for the formerly ill-defined notion of ‘ constraint ’ is established and four interrelated viewpoints of a mathematical model are defined: the set-theoretic relation space, the submodel family, the bipartite graph, and the constraint matrix.
Abstract: The purpose of this paper is to develop an analytic foundation—called Constraint Theory—for the systematic determination of mathematical model consistency and computational allowability. Constraint Theory's primary application is the more efficient construction and use of heterogeneous, multidimensional mathematical models, especially when interdisciplinary technical teams, system analysts, and managers are involved. A rigorous basis for the formerly ill-defined notion of ‘ constraint ’ is established and four interrelated viewpoints of a mathematical model are defined : (a) the set-theoretic relation space, (b) the submodel family, (c) the bipartite graph, and (d) the constraint matrix. The first two viewpoints represent complete models ; the second two represent metamodels. Many correspondences are proved between the topological properties of a model's graph and its constraint properties, Variables located in different connected components of a graph are always mutually consistent, but computations perf...
TL;DR: The proposed approach involves the estimation of the information transfer between the modules of the system, which necessitates the creation of a multivariate binary probability measure representing the problem, which leads in turn to a general criterion for the decomposition of theSystem into its most independent subsystems, or modules.
Abstract: The hierarchical decomposition of a general system is a powerful tool in the reduction of complexity, as has been recognized by various authors. It may be used either to simplify an already existing system, or as an aid to the design of a new system. This paper is concerned with decomposition in the latter sense, being an approach to the modular design of complex systems. The proposed approach involves the estimation of the information transfer between the modules of the system. This necessitates the creation of a multivariate binary probability measure representing the problem, which leads in turn to a general criterion for the decomposition of the system into its most independent subsystems, or modules. As an application, the detection of the modular structure of a computer operating system is discussed.
TL;DR: In this paper, the stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration, and the deterioration of the equipment with age is modelled as a random process.
Abstract: The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example.
TL;DR: In this paper, the authors present a method for generating near optimal closed-loop solutions to zero-sum perfect information differential games by periodically updating the solution to the two-point boundary value problem (TPBVP) obtained from the application of the necessary conditions for a saddle-point solution.
Abstract: This paper presents a method for generating near optimal closed-loop solutions to zero-sum perfect information differential games. Such a near-optimal solution is generated by periodically updating the solution to the two-point boundary-value problem (TPBVP) obtained from the application of the necessary conditions for a saddle-point solution. This procedure is accomplished by updating the co-state vector at each updating time based on the state error from a reference TPBVP solution. The relationship between the required change in the co-state vector and the state error is obtained using the transition matrices for the linearized TPBVP. Between updating times the player using this method plays his open-loop control determined from the updated TPBVP solution. A number of examples are presented to illustrate the advantages and shortcomings of this method.
TL;DR: Lower bounds for a quadratic cost functional, applicable to certain optimal control problems, have been derived in this paper, and these bounds are found to be useful in determining the quality of suboptimal controls.
Abstract: Lower bounds for a quadratic cost functional, applicable to certain optimal control problems, arc derived. These bounds are tight, and are found to bo useful in determining the quality of suboptimal controls. The use of a cost functional lower bound in the snboptimal control of a linear distributed parameter system is included.
TL;DR: In this paper, the controllability conditions for R n and R n null controllabilities were derived for two special cases of the problem of controllable admissible control inputs.
Abstract: An important problem in system theory is whether a dynamic system is controllable with inputs from the class of admissible controls. This paper treats the case whore the dynamic system is described by differential-difference equations and the class of admissible control inputs consists of piecewise constant functions. This situation arises in practice in the on-line control of some industrial processes. Euclidean space and function space controllability are studied, and controllability conditions which are both necessary and sufficient are derived for R n and R n null controllability. Simple algebraic conditions are also given for two special cases. In the study of function space null controllability the concept of j-controllability is introduced and a sufficiency theorem is stated in terms of this new concept.
TL;DR: It is shown that modal control theory can be used to synthesize control policies for production-inventory systems which incorporate unfilled-order backlogs.
Abstract: In this paper it is shown that modal control theory can be used to synthesize control policies for production-inventory systems which incorporate unfilled-order backlogs. The theory is illustrated by the presentation of typical transient and steady-state response characteristics of controlled production-inventory systems of this class.
TL;DR: In this paper, an optimal control formulation of the preview control problem is presented and optimal tracking results reviewed and an information weighting pattern for previewed input information is developed and used to obtain a control realizable with finite preview which closely approximates the optimal control which requires infinite preview.
Abstract: An optimal control formulation of the preview control problem is presented and optimal tracking results reviewed. An information weighting pattern for previewed input information is developed and used to obtain a control realizable with finite preview which closely approximates the optimal control which requires infinite preview, The information weighting pattern is also used to establish bounds on the preview requirements for the class of systems considered.
TL;DR: The algorithms are based on an appropriate sequence of elementary similarity transformations and are well suited to digital computer implementation and provide considerable improvement over existing methods particularly when the transformation matrix as well as the canonical form is required.
Abstract: In this paper algorithms far the computation of all four Luonbarger canonical forms are presented. The algorithms are based on an appropriate sequence of elementary similarity transformations and are well suited to digital computer implementation. They also provide considerable improvement over existing methods particularly when the transformation matrix as well as the canonical form is required.
TL;DR: In this paper, the problem of designing dynamic output feedback compensators to achieve arbitrary polo assignment in linear multivariable systems is considered, and a procedure is developed for the design of unit rank dynamic compensators for arbitrary pole placement.
Abstract: The problem of designing dynamic output feedback compensators to achieve arbitrary polo assignment in linear multivariable systems is considered. By extending a reeent pole assignment technique using constant output feedback to include dynamic output feedback, a procedure is developed for the design of unit rank dynamic compensators for arbitrary pole placement. The design is carried out entirely in the frequency domain and the key step in the design is the formation of a set of linear equations relating the parameters of the compensator to the desired closed-loop characteristic polynomial. The problem of assigning the poles of the compensator which achieves arbitrary pole placemont is also considered.
TL;DR: In this article, the matrix continued fraction and the mixed method are extended to obtain reduced models of multivariable systems with various numbers of inputs and outputs, where the ratio of the rank and the dimension of a transfer function matrix is not an integer or the ratio is an integer but there exist numerically ill-conditioned elements in the matrix, a technique is proposed to deal with these cases.
Abstract: Two methods arc presented in the frequency domain for obtaining reduced models of multivariable systems with various numbers of inputs and outputs. The method of matrix continued fraction and the mixed method are extended to obtain the reduced models. When the ratio of the rank and the dimension of a transfer-function matrix is not an integer or the ratio is an integer but there exist numerically ill-conditioned elements in the matrix, a technique is proposed to deal with these cases.
TL;DR: It is shown that the unknown parameters in the model can be identified while simultaneously controlling the economy, and a comparison of the average value of the criterion function is made to emphasize the importance of using the adaptive systems approach in econometrics.
Abstract: In this paper the problem of simultaneous estimation and Control in macroeconometric models is considered, Using the adaptive control scheme of Deshpande et al. (1073)on a linear 28-variable model of the U.S. economy, it is shown that the unknown parameters in the model can be identified while simultaneously controlling the economy, A comparison of the average value of the criterion function (with and without ‘ learning ’) is made to emphasize the importance of using the adaptive systems approach in econometrics.