Showing papers in "International Journal of Systems Science in 1982"
TL;DR: In this article, the authors demonstrate how to detect instrument faults in non-linear time-varying processes that include uncertainties such as modelling error, parameter ambiguity, and input and output noise.
Abstract: We demonstrate how to detect instrument faults in non-linear time-varying processes that include uncertainties such as modelling error, parameter ambiguity, and input and output noise. The design of state estimation filters with minimum sensitivity to the uncertainties and maximum sensitivity to the instrument faults is described together with existence conditions for such filters. Simulations based on a non-linear chemical reactor with heat exchange and feedback control illustrate the validity of the proposed method.
235 citations
TL;DR: In this paper, a deterministic inventory model for situations in which, during the stockout period, a fraction j8 of the demand is backordered and the remaining fraction 1 − β is lost is presented.
Abstract: This article presents a deterministic inventory model for situations in which, during the stockout period, a fraction j8 of the demand is backordered and the remaining fraction 1 — β is lost. By defining a time proportional backorder cost and a fixed penalty cost per unit lost, a convex objective function representing the average annual cost of operating the inventory system is obtained. The optimal operating policy variables are calculated directly. At the extremes β = 1 and β = 0 the model presented reduces to the usual backorders and lost sales case, respectively.
127 citations
TL;DR: Some characterizations and theoretical results are derived here for some specific types of random variations of the multivariate input-output system and potential applications are briefly indicated.
Abstract: Measuring efficiency of systems with multiple inputs and multiple outputs is most difficult when market, prices for these inputs and outputs are unavailable as for example in most public sector decision-making units. Two types of measures related to Pareto-efficiency could still be defined in such a framework, one related to the productivity of a common set of inputs and the other to a ratio of weighted index of outputs and inputs. These measures however are ordinal and useful in ranking purposes only and may have stochastic variations when the multivariate input-output system contains random components. Some characterizations and theoretical results are derived here for some specific types of random variations. Potential applications are also briefly indicated.
99 citations
TL;DR: In this paper, an operational matrix for the integration of the Laguerre vector whose elements are the Lagaerre polynomials is introduced and applied to parameter identification of time invariant linear systems.
Abstract: An operational matrix for the integration of the Laguerre vector whose elements are the Laguerre polynomials is introduced and applied to parameter identification of time invariant linear systems. Due to the unique property of the operational matrix, the algorithms to formulate the algebraic equations to estimate unknown parameters are recursive and suitable for computer programming. Examples with satisfactory results are given.
95 citations
TL;DR: In this article, an operational matrix for the integration of the shifted Legendre vector whose elements are the shift Legendre polynomial functions is developed and applied to the parameter identification of time invariant linear systems.
Abstract: An operational matrix for the integration of the shifted Legendre vector whose elements are the shifted Legendre polynomial functions is developed and applied to the parameter identification of time invariant linear systems. By employing operational matrix of shifted Legendre polynomials to approach identification problem, the algorithms for computation are effective and straightforward, and the computational results are accurate, compared to other numerical values in the literature.
64 citations
TL;DR: In this paper, a Laguerre series method for the solution of a functional differential equation of the type (d/dt)y(t) = Ay(λt) + By(t), with given initial conditions is presented.
Abstract: This paper presents a Laguerre series method for the solution of a functional differential equation of the type (d/dt)y(t) = Ay(λt) + By(t), with given initial conditions. The method consists of the following steps : (1) represent y(t) and y(λt), respectively, by series of the Laguerre polynomials gi(t) and gi(λt) ; (2) expand gi(λt) into Laguerre series of gi(t) ; (3) integrate the Laguerre series approximation of the functional differential equation by an operational matrix approach. Two numerical examples are given with satisfactory results.
56 citations
TL;DR: The reachability property for a pair of matrices (A, B) over the polynomial ring ℛ = R[d1..., dk] in k symbols with real coefficients is considered in this paper.
Abstract: The formal reachability property for a pair of matrices (A, B) over the polynomial ring ℛ = R[d1..., dk] in k symbols with real coefficients is considered where A is n by n, B is n by m with integers m being fixed. Reachability is defined as the property that ImRscr;[A|B]= ℛn n where [A |B] = [B, AB,..., A n−1B] is the formal reachability matrix for the pair (A, B). This abstract property is first characterized by a numerical rank criterion over the field of complex numbers. Then it is shown that reachability is generic if and only if k < m. It is hoped that the results presented will stimulate further research on polynomial output feedback controllers' for the delay-differential and multidiscrete-type systems.
40 citations
TL;DR: In this article, the elegant Laplace transform technique is used to integrate the block pulse convolution matrix in terms of block pulse functions, and the solutions of integral equations can be recursively calculated.
Abstract: A new method to obtain the explicit solutions of integral equations via block pulse functions is proposed. The elegant Laplace transform technique is used to integrate the block pulse convolution matrix in terms of the block pulse functions. Based on these results, the solutions of integral equations can be recursively calculated. The first and second order integral equations of the first kind, and the integral equations of the second kind arc all solved via this new approach.
39 citations
TL;DR: Using the elegant operational properties of block-pulse functions, a new recursive algorithm for identifying single-input-single-output (SISO) dynamic systems on-line is developed that is much simpler and more convenient for use in computers.
Abstract: Using the elegant operational properties of block-pulse functions, a new recursive algorithm for identifying single-input-single-output (SISO) dynamic systems on-line is developed. Compared with the Walsh function approach, the proposed method is much simpler and more convenient for use in computers. Some examples are presented to illustrate the use of this method
34 citations
TL;DR: In this article, the linear system Mx¨ + (∝ M+ β) K[xacute] + KX= F with M singular, is decomposed into two linear systems, one singular and one non-singular.
Abstract: The linear system Mx¨ + (∝ M+ β) K)[xacute] + KX= F with M singular, is decomposed into two linear systems, one singular and one non-singular. The singular ono is solved explicitly in terms of M, K, f, a, S and analysed.
33 citations
TL;DR: The extension of Luenberger's observer theory to 2D systems is considered and equations are developed for the design of 2D observers and conditions are given for the use of these observers in the stabilization of2D systems through state feedback.
Abstract: The extension of Luenberger's observer theory to 2D systems is considered. Equations are developed for the design of 2D observers Conditions are given for the use of these observers in the stabilization of 2D systems through state feedback.
TL;DR: In this paper, a procedure is developed for the computation of a state space realization from two dimensional transfer functions with separable denominator, which relies on a canonic form for the state-space realization.
Abstract: In this paper a procedure is developed for the computation of a state space realization from two dimensional transfer functions with separable denominator. The procedure relies on a canonic form for the state space realization.
TL;DR: In this paper, a frequency domain approach is employed in which the 3D prototype system (model) is given in transfer function matrix of the form G m(p, w, z).
Abstract: For a general state space model of three-dimensional (3-D) systems, the exact model-matching control problem via state and output feedback ia considered. A frequency domain approach is employed in which the 3-D prototype system (model) is given in transfer function matrix of the form G m(p, w, z). The approach is based on equating the closed-loop transfer matrix function G c(p, w, z) to G m(p, w, z) and solving for the required feedback matrix gains through an application of Kronecker matrix product concept. We start with the static feedback case, and then treat the dynamic feedback problem for the important case of proportional plus integral plus derivative (PID) control. The approach leads to a set of linear algebraic equations, which involve the necessary and sufficient conditions for the exact model matching problem to have a solution. Two simple, but non-trivial examples, are computed.
TL;DR: In this paper, the authors explore the relationship between the κ-stop-ahead prediction approach and the state space approach, and is a generalization of the earlier work of Caines to include control weighting and time delay on the control.
Abstract: Distinct approaches to sampled data control system design use either a state space model or a ‘ controlled autoregressive moving average ’ (CARMA) model, sometimes known as Astrom's representation, One reason for the current interest in the CARMA model is that it is a useful basis for self-tuning controllers as its parameters can be readily estimated on-line. Moreover, simple transfer function controllers can be derived using κ-step-ahead prediction theory. On the other hand, these controllers can be interpreted as minimizing a single stage cost function in state space terms, and the corresponding performance can sometimes be poor. This paper explores the relationship between the κ-stop-ahead prediction approach and the state space approach, and is a generalization of the earlier work of Caines to include control weighting and time delay on the control. Two forms of state space model are used (‘ explicit ’ and ‘ implicit’ time delay models) and a new representation of the steady state Kalman filter is sho...
TL;DR: Syntactic methods for segmentation of connected handwritten numeral and for recognition of individual handwritten numerals are described, in which the size of individual numerals present in the same chain of connected numerals is required to be nearly uniform.
Abstract: Syntactic methods for segmentation of connected handwritten numerals and for recognition of individual handwritten numerals are described. In the first part the size of individual numerals present in. the same chain of connected numerals is required to be nearly uniform. But the recognition procedure for individual numerals is invariant under shape and size. After segmentation and before recognition handwritten numerals are divided into two groups. Handwritten numerals consisting mainly of curves form one group while those consisting of vertical and horizontal strokes form the other. Recognition procedures for the two groups are different but similar. In both cases, for recognition of a numeral only the information about its border is made use of. The extracted border is in fact a sort of skeleton of the numeral pattern and is stored in one-dimensional strings of eight direction codes. On the basis of these one-dimensional strings certain subpatterns are recognized through some automata. The numeral patte...
TL;DR: In this paper, an analytical method is presented which emphasizes the link that exists between the generating word of an organism (in the language consisting of the possible cell transformations) and the successive structures of the developmental process.
Abstract: A great number of organism development processes can be accounted for by the elementary mechanisms of cell partition and cell transformation. In the present article an analytical method is presented which emphasizes the link that exists between the generating word of an organism (in the language consisting of the possible cell transformations) and the successive structures of the developmental process. The viewpoints of analysis (types of structures generated by a given type of word) and of synthesis (type of word generating a given type of structure) are considered. As an illustration of the method models of development are constructed which have already been proposed empirically to account for two types of plant development.
TL;DR: In this paper, a method of analysis of non-linear systems with and without time delay via single term Walsh series approach is presented, where piecewise constant solutions and discrete solutions are obtained with minimal mean square error.
Abstract: This paper presents a new method of analysis of certain non-linear systems with and without time delay via single term Walsh series approach. The piecewise constant solutions and discrete solutions are obtained with minimal mean-square error. The method is easily amenable to digital computer. Examples are presented to illustrate the simplicity of the method. 'This method is better than the previous block pulse function and Walsh function techniques
TL;DR: A decentralized procedure for planning advertising-production decisions is designed for a recently proposed model of a marketing-production system based upon the goal-coordination principle in control theory.
Abstract: Marketing-production decisions mo planned in a decentralized fashion in most firms. Most of the research in this field, however, assumes that the decisions in the two firms are planned in a centralized fashion. In this paper, a decentralized procedure for planning advertising-production decisions is designed for a recently proposed model of a marketing-production system. The procedure is based upon the goal-coordination principle in control theory. An example is presented to illustrate the performance of the procedure.
TL;DR: In this article, the general formulation of the linear quadratic Gaussian (LQG) problem for stochastic singularly perturbed linear systems with a white noise component has been presented.
Abstract: This paper addresses the general formulation of the linear-quadratic-gaussian (LQG) problem for stochastic singularly perturbed systems. It has been found that the time-Scale phenomena between the fast state variable and the stochastic variable plays a crucial role in formulating a meaningful LQG problem for the above system. A well-posed LQG problem for the stochastic singularly perturbed linear system with the fast state having a white noise component has been presented.
TL;DR: The single step method of block pulse functions (b.p.f.) is successfully applied to the analysis of stiff systems and is proved to be better than the Runge-Kutta method.
Abstract: The single step method of block pulse functions (b.p.f.) is successfully applied to the analysis of stiff systems. The efficiency of the new method has been demonstrated by considering a few standard examples. The present method is proved to be better than the Runge-Kutta method. It has been found that the new approximate solution becomes extremely close to exact solution when the step length is decreased
TL;DR: In this article, the problem of constructing stable (right) inverses for linear time-invariant multivariable systems is studied, where the poles of an inverse which are invariant are determined.
Abstract: In this paper we study the problem of constructing stable (right) inverses for linear time-invariant multivariable systems. We show how the poles of an inverse which are ‘ invariant ’ and therefore common to all inverses of a given system can be determined. A method is described which allows us to position the remaining non-invariant- poles at any desired locations in the complex plane, so that if the invariant poles are all stable, we can construct stable inverses. Some examples are given to illustrate the main results of the paper.
TL;DR: Conditions for asymptotic stability of linear systems with time varying delays are obtained by specific application of a comparison method and used to design stable sampled-data feedback controllers for linear systems governed by time invariant differential-difference equations.
Abstract: Conditions for asymptotic stability of linear systems with time varying delays are obtained by specific application of a comparison method. The conditions are used to design stable sampled-data feedback controllers for linear systems governed by time invariant differential-difference equations.
TL;DR: In this paper, a piecewise linear functional approximation of planar curves is introduced, which is based on an adaptive segmentation procedure that alleviates the need for segment number estimation and error norm minimization.
Abstract: A now method of piece-wise linear functional approximation of planar curves is introduced. This method is baaed on an adaptive segmentation procedure that alleviates the need for segment number estimation and error norm minimization. It is shown that this approach results in a higher computational efficiency than existing methods with comparable accuracy
TL;DR: In this paper, the error estimation of the block-pulse series expansion method in analysing a linear time-invariant system is derived based on the point-wise convergence of a continuous integrable function and the block pulse series of the integral of a function.
Abstract: The error estimation of the block-pulse series expansion method in analysing a linear time-invariant system is derived. The result is based on the point-wise convergence of the block-pulse series of a continuous integrable function and the block-pulse series of the integral of a function. These two convergent properties are proved first and then the convergence of the block-pulse series of the solution of a class of linear time-invariant systems is concluded.
TL;DR: In this paper, a general approach is presented to analyse linear systems by the use of the Walsh series expansion of composite functions, which is applied to analyze linear delay systems, in which the solution can be calculated directly without time-partition.
Abstract: A general approach is presented to analyse linear systems by the use of the Walsh series expansion of composite functions. The result is applied to analyse linear delay systems, in which the solution can be calculated directly without time-partition.
TL;DR: In this paper, the authors deal with the feedback stabilization of a class of bilinear systems with disjunct linear and multiplicative control inputs, and the controller design involves the solution of a dynamic optimization problem with fourth-order performance criterion.
Abstract: The present paper deals with the feedback stabilization of a class of bilinear systems with disjunct linear and multiplicative control inputs. The controller design involves the solution of a dynamic optimization problem with fourth-order performance criterion. The main characteristics of the resulting closed loop system are its global stability and the progressive damping of large disturbances.
TL;DR: It is shown that multi-objective programming problems are closely connected with vector-valued lagrangian problems and corresponding multiplier vectors are saddle points of vector- valued lagrangians.
Abstract: This paper deals with saddle points of vector-valued functions and duality in multi-objective programming. First, saddle points for vector-valued functions are defined as a generalization of those for scalar-valued functions. Some properties of them are derived. Secondly, it. is shown that multi-objective programming problems are closely connected with vector-valued lagrangians. Solutions to multi-objective programming problems and corresponding multiplier vectors are saddle points of vector-valued lagrangians. Multiplier vectors are also sub-gradients for perturbation maps. Finally, there exists a corresponding multiplier vector, which is a solution to the dual problem, for each solution to some class of primal problems (stable problems).
TL;DR: Two methods are presented for evaluating the cellular composition and volume of a developmental system at each stage of its evolution using an annihilating polynomial of the evolution matrix and recursive equations that describe the evolution of the system.
Abstract: Two methods are presented for evaluating the cellular composition and volume of a developmental system at each stage of its evolution. The first is based on the use of an annihilating polynomial of the evolution matrix. The second is based on the recursive equations that describe the evolution of the system. Both load to an explicit expression of the cellular composition and of the volume of the system.
TL;DR: In this article, the authors discuss the optimum repair limit policies with a time constraint and obtain the optimum policies which minimize the expected total discounted cost, under certain conditions, and present a numerical example using a mixed Weibull distribution.
Abstract: In this paper, we discuss the optimum repair limit policies with a time constraint. We apply the expected total discounted cost as a criterion and obtain the optimum policies which minimize it. We show that, under certain conditions, there exists a finite and unique optimum policy. Finally, we present a numerical example using a mixed Weibull distribution.