Showing papers in "International Journal of Systems Science in 1985"
TL;DR: An overview of earlier research concerning control theory applications in production and inventory control can be found in this article, where areas given special emphasis are those in which control theory seems to have a stronger potential of practical application.
Abstract: The use of efficient production and inventory control systems is of great importance for industry. Therefore this area could be expected to provide many fruitful applications of control theory techniques. However, control theory has traditionally been aimed at applications in other fields, and results have only limited applicability in production and inventory control. This paper gives an overview of earlier research concerning control theory applications in production and inventory control. Areas given special emphasis are those in which control theory seems to have a stronger potential of practical application.
126 citations
TL;DR: Shifted Chebyshev polynomials for solving variational problems are given in this article, which reduces a variational problem to the solution of algebraic equations, and the computation is straightforward on a digital computer.
Abstract: Shifted Chebyshev polynomials for solving variational problems are given in this study. This technique reduces a variational problem to the solution of algebraic equations, and the computation is straightforward on a digital computer. Two illustrative examples are given. Only a small number of the shifted Chebyshev polynomials are needed to calculate the Chebyshev coefficients, and the result produced is very attractive and accurate.
112 citations
TL;DR: In this article, a general expression of the Fourier operational matrix of integration P is derived which is analogous to that previously derived for other types of orthogonal functions such as Walsh, block-pulse, Laguerre, Legendre and Chebyshev.
Abstract: A general expression of the Fourier operational matrix of integration P is derived which is analogous to that previously derived for other types of orthogonal functions such as Walsh, block-pulse, Laguerre, Legendre and Chebyshev. This matrix P may be used to solve problems like identification, analysis and optimal control.
92 citations
TL;DR: An algorithm is derived which optimally incorporates the real-time measurements of the platform position with the predictive information about its destination which can be efficiently implemented using some results from optimal smoothing.
Abstract: The paper discusses the problem of tracking a platform given probabilistic information concerning its possible destinations. Using a bayesian approach, we derive an algorithm which optimally incorporates the real-time measurements of the platform position with the predictive information about its destination. This algorithm can be efficiently implemented using some results from optimal smoothing. The results are illustrated by a simple example.
56 citations
TL;DR: Non-parametric algorithms, based on Parzen kernels, for the real-time identification of non-stationary systems are presented and weak and strong pointwise convergence of identification procedures are found.
Abstract: Non-parametric algorithms, based on Parzen kernels, for the real-time identification of non-stationary systems are presented. Weak and strong pointwise convergence of identification procedures is s...
52 citations
TL;DR: In this paper, a finite-dimensional shifted Legendre polynomials expansion is applied to approximate the solution of linear time-invariant systems with time delay, and an integration matrix and a delay matrix are derived so that the solution can be reduced to a linear algebraic matrix equation.
Abstract: The finite-dimensional shifted Legendre polynomials expansion is applied to approximate the solution of linear time-invariant systems with time delay. An integration matrix and a delay matrix for the shifted Legendre vector are derived so that the solution of a linear time-delay state equation is reduced to the solution of a linear algebraic matrix equation. In addition, parameters of the delayed state equation are also estimated by using the shifted Legendre expansion and the least-squares method. Two examples are given to demonstrate the accuracy of this approach.
39 citations
TL;DR: In this paper, an attempt has been made to generalize Park's (1983) results on an inventory model for decaying raw materials and to extend the results to finished products which are also subject to decay or deterioration.
Abstract: In this paper, an attempt has been made to generalize Park's (1983) results on an inventory model for decaying raw materials. This paper extends the results to finished products which are also subject to decay or deterioration. The decay of raw materials and the finished product is assumed to be a constant fraction of the on-hand inventory. The finished product is produced in batches and the raw materials are obtained from outside vendors. The objective is to minimize the exact average total cost function and to obtain the inventory characteristics of the system. When there is no decay in the finished product, the model corresponds to the non-decaying finished product model by Park. An example is given to illustrate the derived results.
32 citations
TL;DR: It is demonstrated how optimum reality solutions can be obtained even when large model-reality differences exist, and an algorithm which produces optimum solutions for a wide class of processes is presented.
Abstract: The advantages of several methods for the steady-state control of large-scale systems are combined to give an algorithm which produces optimum solutions for a wide class of processes. It is demonstrated how optimum reality solutions can be obtained even when large model-reality differences exist. The method employs a hierarchical framework where coordination of local decision problems is achieved jointly by price and modifier variables. A three-subsystem process is optimized to illustrate the procedure.
26 citations
TL;DR: In this article, the inverse problem of a heat-conduction model using the finite-element method using the time history of measured temperature at some interior points of the heat-conducting body is considered.
Abstract: The paper is concerned with the inverse problem of a heat-conduction model using the finite-element method. The problem is to estimate the surface temperature and surface heat flux using the time history of measured temperature at some interior points of a heat-conducting body. The finite-element formulation estimates the temperature distribution inside the body, and then the surface heat flux is determined so as to minimize the sum of squares of the difference between the estimated and measured temperatures at the interior points. As a numerical experiment, the technique is applied to the inverse problem of the thin-skinned heat-transfer model with a position-dependent surface heat flux. Numerical results show the effectiveness of the proposed technique from the viewpoint of numerical accuracy.
26 citations
TL;DR: In this paper, the authors present a reduced-order time-varying linear observation technique to estimate the state variables in non-linear systems with unknown system parameters and present a strategy to determine an optimal set of measuring sites from among an excess number of sites in the sense of minimizing the measuring cost for fault detection.
Abstract: This paper describes how to determine the optimal set of measuring sites for identifying faults that can be detected if full information about the state variables can be obtained. We present here a new reduced-order time-varying linear observation technique to estimate the state variables in non-linear systems with unknown system parameters. We present a strategy to employ this observation technique to determine an optimal set of measuring sites from among an excess number of sites in the sense of minimizing the measuring cost for fault detection. We also develop a new theoretical result for state observation of non-linear systems with unknown parameters and, for an example application, demonstrate via simulations how to determine the optimal measuring sites and how to detect faults in a non-linear electrical machine.
24 citations
TL;DR: A shape description technique based on linear measurements from a polygonal approximation of the bones is considered, which is demonstrated on some sections of two typical X-rays of 10–12-year-old boys when histogram equalization, thresholding and edge detection, and octal code generation techniques are included in the preprocessing algorithm.
Abstract: Algorithms for the computer recognition of bones in an X-ray of the hand and wrist are described by analysing age-related changes that take place with growth in the bones. Since a straightforward structural description is inadequate because of these changes, the paper considers a shape description technique based on linear measurements (axial length, width and location) from a polygonal approximation of the bones. The recognition algorithm also needs strong a priori knowledge of the structure of the hand. System effectiveness is demonstrated on some sections of two typical X-rays of 10–12-year-old boys when histogram equalization, thresholding and edge detection, and octal code generation techniques are included in the preprocessing algorithm.
TL;DR: This paper deals with eigenvalue assignment in linear discrete control systems which have a two time-scale property and shows that such systems can be decomposed into a fast subsystem with small eigenvalues and a slow subsystem with large eigen values.
Abstract: This paper deals with eigenvalue assignment in linear discrete control systems which have a two time-scale property. It has been shown that such systems can be decomposed into a fast subsystem with small eigenvalues and a slow subsystem with large eigenvalues. Separate eigenvalue assignment is attained using independent feedback gains.
TL;DR: In this article, the authors used the unique property of the convolution integral of the shifted Legendre polynomials (SLP) to solve convolutional integral equations.
Abstract: The unique property of the convolution integral of the shifted Legendre polynomials is used to solve convolution integral equations. Three important types of integral equations: (i) first-order of the first kind, (ii) second-order of the first kind, and (iii) the integral equation of the second kind, are studied in the present paper. The basic idea in solving the integral equation is that the state variables are expressed in terms of the shifted Legendre polynomial series. Series of the algebraic equations of the expansion coefficients are obtained and are calculated recursively by the powerful proposed computational algorithm. Examples are given for illustration. Very satisfactory computational results are obtained.
TL;DR: In this article, the bilinearization of infinite-dimensional nonlinear systems defined on a Hilbert space H is examined and Volterra series on I2 is also considered, which can be achieved by introducing a new Hilbert space L 2 w [H; R] w
Abstract: The bilinearization of infinite-dimensional non-linear systems defined on a Hilbert space H is examined and Volterra series on I2 are also considered. This will be achieved by introducing a new Hilbert space L2 w [H; R].
TL;DR: In this paper, a closed-loop regulation for the primary section of a solar-power plant consisting of a parabolic concentrator and of a thermal accumulator is considered, and a control law based on a Lyapunov-type approach is determined as a function of the distributed state.
Abstract: The problem of closed-loop regulation is considered for the primary section of a solar-power plant consisting of a parabolic concentrator and of a thermal accumulator. The plant, controlled by the flow rate, is modelled by a bilinear distributed-parameter system of hyperbolic type coupled with a lumped-parameter system, representing the concentrator and the accumulator respectively. The purpose of the feedback control is to react against state perturbations due to transient disturbances acting on the plant. A control law based on a Lyapunov-type approach is determined as a function of the distributed state: such a control guarantees a fast decay of the perturbation. Since only the inlet and outlet temperatures of the concentrator are measured, an output feedback control scheme is proposed, based on a polynomial approximation of the distributed state. Numerical experiments confirm that there is no performance decay for the regulator.
TL;DR: Simulation results have shown that for some non-linear models the new smoothing algorithm performs better than the extended Kalman filter algorithm, while it performs almost as well as the Kalmanfilter algorithm for linear models with gaussian noise.
Abstract: A new smoothing algorithm for discrete models is presented. For the disturbance noise and the observation noise, only independency is assumed. Moreover the models’ functions are not limited to continuous functions, i.e. they can be non-continuous. This algorithm estimates the states by first quantizing them and then using the Viterbi decoding algorithm. Simulation results have shown that for some non-linear models the new algorithm performs better than the extended Kalman filter algorithm, while it performs almost as well as the Kalman filter algorithm for linear models with gaussian noise.
TL;DR: A new recursive algorithm via block-pulse functions is presented for estimating the unknown parameters of a linear continuous system from samples of input-output data that is easy to implement and is especially applicable to those estimation problems in which the parameters vary slowly with time in an unknown way.
Abstract: A new recursive algorithm via block-pulse functions is presented for estimating the unknown parameters of a linear continuous system from samples of input-output data. Compared with other methods via block-pulse functions, there are no integrals of input-output data to be computed and no initial states or values involved for the purpose of identification. This algorithm is therefore easy to implement and is especially applicable to those estimation problems in which the parameters vary slowly with time in an unknown way. The illustrative examples show that the new algorithm gives satisfactory results for identification problems.
TL;DR: In this article, the shift Legendre series is used to simplify the analysis of optimal control systems incorporating observers, and only a small number of shifted Legendre polynomials are needed to obtain a very attractive and excellent result.
Abstract: The analysis of optimal control systems incorporating observers has been approached by way of the shifted Legendre series. The method simplifies the system of equations into the successive solution of a set of linear algebraic equations. One example is illustrated, and only a small number (m = 6) of the Legendre polynomials are needed to obtain a very attractive and excellent result.
TL;DR: In this article, the identification of such linear dynamic systems, whose parameters are working point-, signal-, and/or direction-dependent, is dealt with, where the structure and how the parameters depend on a given signal is a priori not known.
Abstract: The paper deals with the identification of such ‘linear’ dynamic systems, whose parameters are working point-, signal-, and/or direction-dependent. Parameter estimation methods are presented for both cases: (i) the structure and how the parameters depend on a given signal is a priori not known; and (ii) the structure is known, only the parameters are unknown. In the latter case the structure to be identified is generally not linear in the parameters. Applying, however, a proper transformation, the continuous form can be approximated by a difference equation which becomes linear in the parameters but also includes redundant parameters.
TL;DR: In this paper, the modified Laguerre polynomial is defined with an additional parameter from the conventional one and is applied to approach the problems of fractional calculus, and the operational matrices for the integration and the differentiation of the modified laguera polynomials are derived.
Abstract: The modified Laguerre polynomial is defined with an additional parameter from the conventional one and is applied to approach the problems of fractional calculus. First, the operational matrices for the integration and the differentiation of the modified Laguerre polynomials are derived. The generalized operational matrices corresponding to s, 1/s, s/(s2 + 1) 1/2 exp [ − s/(s + 1)] are derived as examples. Comparison of the modified Laguerre series approximate inversions of irrational Laplace transforms with exact solution shows that the present modification method is much better than the conventional one. In addition, the present proposed modified Laguerre polynomials can also be used to approximate the solution of fractional calculus which cannot be obtained from conventional Laguerre polynomials.
TL;DR: In this article, a direct method based on using shifted Legendre polynomials is developed to obtain suboptimal control for linear time-varying systems with multiple state and control delays and quadratic performance index.
Abstract: A direct method based on using shifted Legendre polynomials is developed to obtain suboptimal control for linear time-varying systems with multiple state and control delays and quadratic performance index. In this method, both the control and state variables are first expanded into finite shifted Legendre series. The governing delay-differential equation is then converted to a set of linear algebraic equations through use of the operational matrices of integration and delay. The problem finally becomes the simple one of finding the unknown coefficients of the control variables alone, which minimizes the quadratic form of performance index.
TL;DR: Asymptotic stability of the closed-loop system is proved for a large parameter class, and it is shown that stability is robust with an extent depending on the design parameters.
Abstract: A general suboptimal approach to the finite-time control of linear discrete time systems is introduced. The approach is also valid, with appropriate modifications, for the dual case of finite-time suboptimal state estimation. The method entails the use of a moving cost criterion which is to be minimized. It provides the advantages of constant feedback gain, a minimum number of iterations to find the stabilizing solution, and an extra freedom of transient response adjustment. Asymptotic stability of the closed-loop system is proved for a large parameter class, and it is shown that stability is robust with an extent depending on the design parameters. A special doubling algorithm is proposed to compute the feedback gains. The degree of suboptimality of the controller with respect to the linear quadratic regulator is discussed.
TL;DR: In this article, a model for the study of hierarchically organized economics is proposed, where the input-output analysis method is used to describe the interactions between the economic world level, the economic national level and the level of economic sectors.
Abstract: In this paper a model for the study of hierarchically organized economics is proposed. The input-output analysis method is used to describe the interactions between the economic world level, the economic national level and the level of economic sectors and also the interactions between the national level, the level of economic sectors and the level of subsectors or branches of industry. Perturbation methods are used to describe the weak couplings between the different levels of organization of the economic system. A method is presented to derive a master equation giving the time dependence of total production from fundamental equations governing the time evolution of the production of elementary sectors. This method is then applied to hierarchically organized economics.
TL;DR: In this article, the authors proposed bounds for the extreme and lower half eigenvalues of the solution matrix for the algebraic Riccati equation, which can be applied to determine the region where the eigen values lie.
Abstract: Novel bounds are proposed for the extreme and lower half eigenvalues of the solution matrix for the algebraic Riccati equation. The formulae giving these bounds can easily be applied to determine the region where the eigenvalues lie, and the bounds have the added advantage of being sharper in some cases than the previously proposed ones, as some realistic examples will show. The proposed bounds find many applications which are pointed out in the text.
TL;DR: In this paper, the controllability of the discrete-time linear system xk+1 = Axk + uk; uk∊Ω = 0, 1, …, where the input set n is an arbitrary convex set, is studied.
Abstract: The controllability of the discrete-time linear system xk+1 = Axk + uk; uk∊Ω = 0, 1, …, where the input set n is an arbitrary convex set, is studied. The problem of controllability in finite time is examined, that is, conditions on A, Ω are established which ensure the existence of a finite N such that the system is controllable in N steps for any initial state x0.
TL;DR: An operational matrix for the integration of a Laguerre vector is applied to the parameter identification of time-invariant nonlinear systems with and without noise, proper shape having been given to the non-linear terms.
Abstract: An operational matrix for the integration of a Laguerre vector is applied to the parameter identification of time-invariant non-linear systems with and without noise, proper shape having been given to the non-linear terms. A new approach is developed which is very simple and accurate.
TL;DR: In this paper, the operating characteristics of the total-work-content (TWK) due-date assignment method in a dynamic job shop were studied and an analytical procedure was presented to derive the optimal solution and to show that k ∗ p is a unique absolute minimum point of the strictly convex cost functions included in the cost model.
Abstract: The paper studies the operating characteristics of the total-work-content (TWK) due-date assignment method in a dynamic job shop. The due-date for each job is established by adding a multiple of the job's total processing-time to its arrival time at the shop. It is assumed that there will be penalty costs if the shop quotes excessively long due-dates compared with its competitors' and cannot complete the jobs exactly on their assigned due-dates. A cost model composed of these two opportunity cost components is used. The objective is to find the optimal processing-time multiple k ∗ p that will minimize the expected total cost per job. An analytical procedure is presented to derive the optimal solution and to show that k ∗ p is a unique absolute minimum point of the strictly convex cost functions included in the cost model. It is also shown that determination of the optimal processing-time multiple requires only information readily accessible in the shop. Under certain circumstances, k ∗ p can even be exclu...
TL;DR: An attempt is made to select the most efficient methods for analysis of the stability, controllability and observability, the reduction into canonical forms, the pole assignment synthesis and the synthesis of optimal systems with quadratic cost.
Abstract: This paper presents a brief survey of computational algorithms for the analysis and synthesis of linear control systems described in the state space. An attempt is made to select the most efficient methods for analysis of the stability, controllability and observability, the reduction into canonical forms, the pole assignment synthesis and the synthesis of optimal systems with quadratic cost. Some aspects of the development of mathematical software for solving these problems are also discussed.
TL;DR: Convergence of the algorithm is proved for linear-quadratic systems and it is shown that the algorithm exploits the special structure of serially connected systems.
Abstract: A two-level algorithm is presented for decentralized control of a serially connected dynamic system. The algorithm exploits the special structure of serially connected systems. Convergence of the algorithm is proved for linear-quadratic systems.
TL;DR: A class of semi-Markov decision processes is introduced with a view to modelling such phenomena as machine breakdowns, restrictions on switching between jobs, deadlines and batch processing and the structure of optimal processing strategies is looked at.
Abstract: A single machine is available to process a collection of stochastic jobs. A class of semi-Markov decision processes is introduced with a view to modelling such phenomena as machine breakdowns, restrictions on switching between jobs, deadlines and batch processing. The paper looks at the structure of optimal processing strategies and develops procedures for evaluating suboptimal strategies. For those instances where there is a non-empty partial ordering on the job set delimiting the set of possible processing strategies, the problem becomes exceedingly complex. In such cases the paper studies only the performance of strategies which are a fixed permutation of the job set.