Showing papers in "International Journal of Systems Science in 1975"
TL;DR: In this paper, a state-space procedure for solving linear dynamic systems by the Walsh series is developed, where a new operational matrix plays the main role and a new Kronecker product formula is established.
Abstract: A state-space procedure for solving linear dynamic systems by the Walsh series is developed. A new operational matrix plays the main role and a new Kronecker product formula is established. The laborious use of Corrington'B tables is eliminated. Several examples illustrate the process and demonstrate the power of the approach.
178 citations
TL;DR: In this paper, a preliminary study is made of the dynamic optimization problem for a river with many polluters using a recently developed model of a section of the river Cam near Cambridge in England.
Abstract: In this paper, a preliminary study is made of the dynamic optimization problem for a river with many polluters using a recently developed model of a section of the river Cam near Cambridge in England. Because of the high dimensionality of the system it is computationally prohibitive to obtain optimal solutions. However, the system has a fairly simple structure which could be utilized to alleviate the computational burden. A simple hierarchical structure is proposed for the river pollution control and the strategy is demonstrated on a digital simulation. For the practical implementation of the strategy, it is necessary, however, to have available the state vector of the system. In practice, only certain corrupted measurements of the outputs are available. It is therefore necessary to construct a state estimator. Like the optimal controller, the optimal estimator also requires prohibitive amounts of computation. However, a hierarchical strategy similar to the control strategy could be used to allev...
40 citations
TL;DR: In this article, an approximate non-linear filter is applied to systems described by coupled ordinary and partial differential equations with both volume and boundary disturbances and measurement errors, where measurements are carried out at a discrete number of spatial positions in the distributed portion of the system.
Abstract: An approximate non-linear filter is applied to systems described by coupled ordinary and partial differential equations with both volume and boundary disturbances and measurement errors. Measurements are assumed to be carried out at u discrete number of spatial positions in the distributed portion of the system. The filter is applicable to cases in which the data are available continuously in time and at discrete sampling instants. Both versions of the filter are applied to an ingot heating problem of some interest in steel-making. The numerical results show that the filter is rapidly convergent and quite robust.
29 citations
TL;DR: The notion of connective stability in the mean for large-scale stochastic systems under structural perturbations is introduced, using the decomposition-aggregation method in the context of vector Liapuiiov functions.
Abstract: The procedure of decomposition-aggregation analysis reported by Siljak (1973) and Grujic and Siljak (1973) has been used in a study of the connective-stability aspects of large-scale stochastic systems. An investigation is conducted of the tolerance of a system of interconnected deterministic subsystems to both deterministic and stochastic interactions. The connective stability in the mean is considered and the connective property of stability is defined. The defined concept is included in a modification of the comparison theorem described by Ladde (1975). Attention is also given to a derivation of the sufficient conditions for the connective stability in the mean.
27 citations
TL;DR: In this paper, Chen and Chiu gave additional theorems for evaluating G(s) for certain types of F(s 1, s 2, [tdot], sn ).
Abstract: Let f(t 1 t 2, [tdot], t n rpar; be the inverse Laplace transform ℒ1 −1 F of F(s 1 s 2, [tdot], s n ). Then there exists a function G(s) such that ℒ1 −1 G(s) = f(t 1, t 2, [tdot], t n )|t 1 = t 2,= [tdot] = tn = t-Chen and Chiu (1973) proved three theorems for evaluating the associated transform G(s) for certain types of F(s 1, s 2, [tdot], sn ). In this paper, we give additional theorems for evaluating G(s).
23 citations
TL;DR: This paper proposes a modification of the initial Shannon information theory which takes into account the point of view of the receiver, and obtains the concept of negative information which may explain the practical phenomenon of information loss.
Abstract: This paper is the continuation of two articles which appeared in this journal, and presents an approach to the thermodynamics of general systems via information theory. It is composed of two parts. In the first part one proposes a modification of the initial Shannon information theory which takes into account the point of view of the receiver. The concepts of ‘ effective entropy ’ and ‘ effective information ’ are given, the relation between effective information and Shannon information is exhibited. We then obtain the concept of negative information which may explain the practical phenomenon of information loss. In the second part of the paper, the interpretation of the results of the first part provides a model of state equation which would apply in the thermodynamics of general systems. The counterpart of perfect gas, the perfect system, is investigated via evolution principles and it is emphasized that the results so obtained agree with some practical phenomena. Some suggestions for further research a...
23 citations
TL;DR: It is shown that the theory of tracking systems can be used for the synthesis of control policies such that the system outputs always tend towards the managerial command inputs at a predetermined rate.
Abstract: In this paper, a continuous-time model of a production-inventory system which includes an allowance for the stimulation of sales by advertising is considered. It is shown that the theory of tracking systems can be used for the synthesis of control policies such that the system outputs always tend towards the managerial command inputs at a predetermined rate. The theory is illustrated by the presentation of the results of computer-simulation studies of the response of a particular system of this class to typical command inputs.
22 citations
TL;DR: In this paper, approximate iterative solutions for zero-sum differential games are proposed, and numerical solutions of zero-and non-zero-sum games, available to date, are surveyed and evaluated.
Abstract: Numerical solutions of zero- and non-zero-sum differential games, available to date, are surveyed and evaluated. Alternative approximate iterative solutions for zero-sum differential games are proposed.
21 citations
TL;DR: The problem of deriving frequency-domain conditions that ensure asymptotic stability with probability one (ASWP1) of discrete time non-linear feedback systems with state-dependent noise is considered in this article.
Abstract: The problem of deriving frequency-domain conditions that ensure asymptotic stability with probability one (ASWP1) of discrete time non-linear feedback systems with state-dependent noise is considered. It is shown that if the noise is linearly related with the state of the system, a relatively simple frequency-domain inequality that guarantees ASWPl of the system, exists. The discrete stochastic version of the second method of Liapunov, along with Szego-Kalman typo lemmae are used to derive such conditions, assuming that only sector information or both sector and slope information are available. The case of a difference system with white-noise parameter perturbation is also considered and an illustrative example is presented.
21 citations
TL;DR: Criteria are derived which guarantee that the effect of disturbances on the outputs of a linear feedback system can be reduced as much as desired by means of a suitable state feedback.
Abstract: In this paper criteria are derived which guarantee that the effect of disturbances on the outputs of a linear feedback system can be reduced as much ac desired by means of a suitable state feedback. It is also shown how a suitable feedback strategy can be calculated to achieve the desired degree of decoupling between outputs and disturbances.
20 citations
TL;DR: It is shown that recently developed methods of hierarchical control for dynamic problems lead to economical and efficient algorithms which can be used for a broad class of cost functions and delays in deliveries present little extra difficulty.
Abstract: In this paper the multiproduct inventory holding problem is considered. Joint constraints between product lines and constraints on individual products are allowed. Total costs of holding inventory and backlogging are minimized using recently developed methods of hierarchical control for such dynamic problems. It is shown that such methods lead to economical and efficient algorithms which can be used for a broad class of cost functions and delays in deliveries present little extra difficulty. An algorithm is described for complex costs and stochastic sales. Simulation studies are presented which validate this algorithm. Such hierarchical methods avoid the difficulties of solving two-point boundary problems required by the discrete maximum principle and can be considerably more economical of computer resources than general non-linear programming techniques. The hierarchical algorithms of Lasdon and Tamura are described in full.
TL;DR: In this paper, a best linear policy for a production smoothing problem having a non-quadratic criterion is derived for the ease of an uncorrected and an exponentially correlated sequence of demand.
Abstract: A best linear policy is derived for a production smoothing problem having a non-quadratic criterion. Explicit results are obtained for the ease of an uncorrected and an exponentially correlated sequence of demand. For the uncorrelated case it is shown that in the absence of fixed sot-up costs the optimal linear policy leads almost to the same costs as the exact non-linear policy ; i.e. one can use a linear theory and hence dynamic certainty equivalents.
TL;DR: In this paper, a non-zero-snm differential game of macroeconomic system illustrated in the balance-of-payments adjustment problem between the two countries is considered and the optimal policy solutions of the game model with quadratic performance index are obtained by means of the properties of the pseudo-inverse matrix.
Abstract: The paper is concerned with an application of non-zero-snm differential games of macroeconomic system illustrated in the balance-of-payments adjustment problem between the two countries. The optimal policy solutions of the game model with quadratic performance index are obtained by means of the properties of the pseudo-inverse matrix. Sequentially, necessary and sufficient conditions for the existence of min-min game solutions, which correspond to min—max game solutions, are presented as one of the principal results of the present paper.
TL;DR: In this article, a basis is developed for the systematic design of linear multivariable discrete-time tracking systems, where the required asymptotic behavior may be achieved by a controller incorporating a series of discrete time vector integrators.
Abstract: In this paper a basis is developed for the systematic design of linear multivariable discrete-time tracking systems. It is shown that the required asymptotic behaviour may be achieved by a controller incorporating a series of discrete-time vector integrators. The controllability conditions for such systems are established and the theory is illustrated by a numerical example.
TL;DR: In this article, a gradient algorithm is proposed to compute linear feedback Nash solutions for two examples, and the costs are compared with open loop costs, and several specific strategy structures are shown to dominate the open loop solution.
Abstract: Nash solutions to a class of non-zero-sum differential games are obtained in the form of linear feedback strategies with both constant and time-varying feedback gains. To solve the resulting two-point boundary value problem, a gradient algorithm is proposed. This algorithm is utilized to compute linear feedback Nash solutions for two examples, and the costs are compared with open loop costs. Several specific strategy structures are shown to dominate the open loop solution.
TL;DR: In this article, the authors developed algebraic conditions for uniform practical stability and uniform finite-time stability of large-scale systems, which are related to the prespecified time-varying sets, which yield information about trajectory bounds of the systems.
Abstract: The purpose of the paper is to develop algebraic conditions for uniform practical stability and uniform finite-time stability of large-scale systems. The stability properties are related to the prespecified time-varying sets, which yield information about trajectory bounds of the systems. The conditions guarantee a stability property of the overall system to be implied by the corresponding stability property of all subsystems. The aggregation-decomposition approach used in the paper reduces the dimensionality of an aggregate matrix of the system to the number of its subsystems. Several examples are presented to illustrate application of the obtained stability criteria.
TL;DR: In this article, a mathematical model of the global biogeochemical carbon cycle is presented, and the effect of the projected addition of carbon dioxide into the biosphere resulting from fossil fuel combustion is noted.
Abstract: This paper presents a mathematical model of the global biogeochemical carbon cycle. Through computer simulation of this model, the effect of the projected addition of carbon dioxide into the biosphere resulting from fossil fuel combustion is noted. In particular, the added amount of carbon dioxide in the atmosphere ia predicted, and the concomitant increase in the atmospheric temperature due to this effect is projected. Validation of the model is discussed and u sensitivity analysis ia peformed to test its robustness.
TL;DR: In this paper, singular perturbation methods are used to provide a basis for the analysis of the asymptotic controllability of multivariable linear systems containing small " parasitic " elements.
Abstract: Singular perturbation methods are used to provide a basis for the analysis of the asymptotic controllability of multivariable linear systems containing small ‘ parasitic ’ elements, and for the design of feedback controllers which will effect asymptotic eigenvalue assignment in such systems.
TL;DR: In this paper, simple matricial methods are used to develop a basis for the design of multivariablo tracking systems which incorporate feedforward and feedback controllers, and a composite design which includes a feedforward controller and a feedback controller with both proportional and integral action has a superior tracking performance in certain respects.
Abstract: In this paper, simple matricial methods are used to develop a basis for the design of multivariablo tracking systems which incorporate feedforward and feedback controllers. It is known that the required asymptotic tracking behaviour can be achieved by using only a feedback controller which incorporates integral action (Porter and Bradshaw 1974). However, it is shown in this paper that a composite design which includes a feedforward controller and a feedback controller with both proportional and integral action has a superior tracking performance in certain respects.
TL;DR: In this paper, an approximate method to calculate the expected lost sales for a reorder level system of inventory control in which both the demand per unit time and the lead time are gamma distributed with integer modulus is presented.
Abstract: This paper presents an approximate method to calculate the expected lost sales for a reorder level system of inventory control in which both the demand per unit time and the lead time are gamma distributed with integer modulus. Laplace transforms are used to determine the first four moments of the probability density function (p.d.f.) of demand over lead time. A gamma fit approximation of this p.d.f. is obtained and shown to be quite accurate for a large number of cases. This approximation allows the calculation of expected lost sales to be a simple task.
TL;DR: In this paper, the problem of pollution control of water in a river stream is considered, where the variables to be controlled are the concentration of BOD and the level of Dissolved Oxygen (DO) in the water.
Abstract: This paper is concerned with the application of optimal control techniques to ecological systems. In particular, the control of pollution of water in a river stream is considered. The variables to be controlled are the concentration of Biochemical Oxygen Demand (BOD) and the level of Dissolved Oxygen (DO) in the water. This is proposed to be achieved by controlled dumping of industrial effluents and/or artificial aeration. These constitute the controls. A realistic determination of the optimum values of these controls is subject to several performance criteria relating to water quality. Since some of these criteria are contradictory the problem is tackled (unlike previous investigators) from the point of view of a multi-cost system. Recently published theory on multi-cost system optimization is used. Numerical examples are presented.
TL;DR: This paper uses a relativistic formulation of the classical information theory of Shannon to describe the dynamics of a system in function of its external entropy, and defines the concepts of ‘ organizability ’, ‘ own external entropy ’ and ‘ universe organizable ’.
Abstract: In a preceding article which appeared in this journal we have modified the classical information theory of Shannon (mainly we defined the concepts of ‘ effective information ’ and ‘ negative information ’) and by this way we have inferred a thermodynamic model for describing general systems. In the present paper we improve this approach by using a relativistic formulation which explicitly describes the basic relativistic feature of the information notion. After a careful analysis of the ‘ internal entropy ’ and ‘ external entropy ’ concepts, we apply these notions to the universe and we show that this latter exhibits a universal constant. We introduce a Riemannian space to describe the dynamics of a system in function of its external entropy and the Lorentz transformation is given. We define the concepts of ‘ organizability ’, ‘ own external entropy ’ and ‘ universe organizability ’. Composition laws for the organizability are given. Lastly we define the relativistic dynamics of general systems and some e...
TL;DR: In this article, the multi-level state estimator of Pearson is considered and it is shown why such filters cannot be used for the practical state estimation of large systems, and a computationally efficient suboptimal filter formulated by Shah is described and which is then extended to systems with time lags between the subsystems.
Abstract: This paper discusses certain aspects of multi-level state estimation. In the first part, the multi-level state estimator of Pearson is considered and it is shown why such filters cannot be used for the practical state estimation of large systems. Then a computationally efficient suboptimal filter formulated by Shah is described and which is then extended to systems with time lags between the subsystems. For large serially connected systems, an even simpler state estimator could be used. A number of numerical studies are given comparing the performance of the two sub-optimal estimators and the overall optimal solution.
TL;DR: It is shown how many algorithms for deriving a state variable model for a system defined by a matrix transfer function may be applied to the derivation of state variable models for systems defined by linear constant differential equations.
Abstract: There are many algorithms for deriving a state variable model for a system defined by a matrix transfer function. It is shown how these algorithms may be applied to the derivation of state variable models for systems defined by linear constant differential equations. without the use of polynomial computations.
TL;DR: In this article, the modal control approach is employed to improve the transient response of a power system, by shifting the dominant eigenvalues of the uncontrolled system farther towards the left in the complex plane.
Abstract: In this paper the modal control approach is employed to improve the transient response of a power system, by shifting the dominant eigenvalues of the uncontrolled system farther towards the left in the complex plane. Both complete as well as incomplete state variable feedback are considered. A sector criterion is used for the new locations of the eigenvalues. Comparison of the results obtained by modal control approach with the frequently used approach using optimal linear state regulator formulation is made.
TL;DR: In this article, a generalized pseudo-inverse algorithm is used to estimate the parameters of a discrete-time system from noisy measurements of input-output data, which can be used for on-line identification.
Abstract: Unbiased estimates of the parameters of a discrete-time system from noisy measurements of input-output data can be obtained by using a generalized pseudo-inverse algorithm. Because of its recursive nature, the algorithm can be used for on-line identification. Results of simulation are presented comparing this algorithm with earlier methods.
TL;DR: In this paper, a consistent and sequential method for estimating the orders and parameters of mixed autoregressivu-moving-average (ARMA) processes is described, based on employing sequential least squares estimates of pure autoregressive (AR) models.
Abstract: The paper describes a consistent and sequential method for estimating the orders and parameters of mixed autoregressivu-moving-average (ARMA) processes. The method is based on employing sequential least squares estimates of pure autoregressive (AR) models.
TL;DR: In this article, an algorithm for constructing the inverse of a multivariable finite-dimensional and time-invariant dynamical system is introduced, which is equally applicable to continuous or discrete-time systems.
Abstract: An algorithm for constructing the inverse of a multivariable finite-dimensional and time-invariant dynamical system is introduced. It is equally applicable to continuous or discrete-time systems. Systems may be described in state-space form, by a matrix transfer function or by a set of constant differential equations.
TL;DR: The problem of multiple-objective optimization for the environment development system is formulated and the so-called Pareto-optimal solution set is formulated, related in a one-to-one manner to a family of auxiliary scalar index problems.
Abstract: This paper deals with multiple-objective optimization problems for the environment development system. The model of the environment development system, which was introduced by Kulikowski, is described by a system of non linear differential equations which include interconnected n exogenous and m endogenous controlled factors or processes. The problem of multiple-objective optimization for the environment development system is formulated. A main difficulty of multiple-objective optimization is that it is no longer clear what one means by an optimal solution. A possible remedy for this situation is to refine the concept of optimal solution by introducing the so-called Pareto-optimal solution set. Then multiple-objective optimization problem boils down to determining the set of Pareto-optimal solutions. The Pareto-optimal solution set is related in a one-to-one manner to a family of auxiliary scalar index problems. For an unconstrained multiple-objective optimization problem for the environment deve...
TL;DR: It is shown that sufficient conditions for a weak stability of the system's sample functions, are derived and that these conditions depend heavily on the type of the stochastic partial differential equation which is selected in order to model the system.
Abstract: A stochastic non-linear distributed parameter system of a parabolic typo is dealt with The system is stochastic due to a distributed multiplicative gain The gain is a distributed white (in time) Gaussian noise The distributed parameter system is modelled by two different typos of stochastic partial differential equations By using a stochastic Liapunov type functional, sufficient conditions for a weak stability of the system's sample functions, are derived It is shown that these conditions depend heavily on the type of the stochastic partial differential equation which is selected in order to model the system The conditions for stochastic stability, for the two different models, are compared Also, for the sake of comparison, a deterministic version of the problem is dealt with