Showing papers in "International Journal of Systems Science in 1971"

Optimum input test signals for system identification—an information-theoretical approach

Abstract: This paper is concerned with a problem of choosing optimum input test signals for estimating response functions or transfer functions of discrete-time systems. Under the amplitude constraint of signals and some additional appropriate assumptions it is shown that, in the case of identifying response functions, a pseudorandom binary sequence of input signals with as small correlations as possible is optimum in the sense that it maximizes a quantity of information provided by measurements. In the case of estimating unknown coefficients of transfer functions, an optimum scheme of step-by-step choice of input signals is proposed.

I. General description and the problem of universal computing ability

Abstract: The notion of polarity is often used in developmental biology for the explanation of various phenomena. Some authors have considered that polarity is absolutely essential for certain kinds of phenomena to appear. In this paper, we identify polarity of an individual cell with its ability to distinguish in somo sense between its ‘ left’ and its ‘ right’ side. We show, using a developmental model originally duo to Lindenmayer, that even if we restrict ourselves to models in which individual cells have no polarity, the models remain general enough to realize any effective procedure, in other words, they have a universal computing ability. Various special cases are considered, These results, as well as other results concerning regulation and synchronization in development, indicate that polarity is not a necessary con-copt, and may not even he an essential concept, for morphogenesis.

Polynomial operators in non-linear systems theory

Abstract: The concept of generalized polynomial operators is introduced and applied to the theory of non-linear systems. Several properties similar to those previously derived for systems described e.g. by Volterra functional series are studied. The main attention is given to inverting of the operators in question. A local inverse is constructed and the region where it is valid is determined. The construction is applied to solving of certain types of non-linear differential equations and to seeking sufficient conditions for BIBO stability of the corresponding systems.

Modelling and optimal control of a production process

Abstract: An industrial production process is modelled as a discrete-time system with a disturbance input due to sales. The state consists of rates of flow of parts or subassemblies at various work stations, backlogs of parts awaiting processing, and the inventory level of the finished product. The control variables are the man-hours scheduled for various work processes. A quadratic performance criterion is minimized so as to keep state and control variables near desired values. Dynamic programming is used and numerical examples are provided.

Analysis of discontinuous large-scale systems: stability, transient behaviour and trajectory bounds

Abstract: The trajectory bounds of simple and large-scale interconnected discontinuous systems are treated within a stability framework. In doing so, stability is defined in terms of pre-specified subsets of the state space over an infinite time interval (practical stability) and over a finite time interval (finite time stability). The discontinuous systems considered are those which are described by ordinary discontinuous differential equations which may be autonomous or non-autonomous, linear or non-linear, unforced or under the influence of persistent disturbances, simple or interconnected. In all cases it is assumed that the differential equation possesses solutions in the sense of Filippov. The results obtained yield sufficient conditions for practical and finite time stability. The interconnected systems are treated in terms of their subsystems. In order to demonstrate the methods involved, some examples are considered.

Complex BIFORE transform

Abstract: Complex BIFORE (Binary FOurior REpresentation) transform belongs to the family of discrete orthogonal transformations and is analogous to discrete Fourier transform (DFT) when dealing with complex inputs. For real inputs, complex BIFORE transform (CBT) reduces to BIFORE or Hadamard transform (BT or HT) whose bases are Walsh functions. BT has been applied in several phases of information processing and sequency filters and sequency multiplexing equipment have also been built. When dealing with complex signals, CBT has some inherent computational advantages, and can be used to analyse and synthesize complex input functions. In the present paper, CBT is defined and its relationship to BT is shown. Several properties of CBT are developed. Invariance of power spectrum to sequential shift of the sampled data is shown. Using matrix factoring, fast algorithms suitable for digital computation of CBT and its inverse are developed. CBT is extended to multiple dimensions. Fast algorithms and corresponding fl...

General systems from network systems: a philosophy of modelling

Abstract: In recent times there has been some convergence of apparently disparate disciplines like engineering on one hand and social sciences on the other. A portable philosophy of systems analysis and design has evolved through progressive development from loop and node equations to state-space equations, from electrical networks to other physical systems, and from technological systems to transportation and economic systems. This paper addresses itself to the philosophy underlying the modelling side of system theory techniques that are sufficiently powerful to have important application in the planning, operation and control of complex large-scale systems required by modern society.

A generalized system-theoretic framework for modelling large scale national economic systems in dynamic, structural and spatial terms†

Abstract: The paper describes the ‘ physical system ’ theoretic construction developed to model the Canadian economy at a level of ten sectors in each of five regions, but which has general applicability. The national economy is identified here as a collection of interconnected components and the approach taken is that of component-to-system construction. It is believed that the framework is general enough to embrace many ‘ input-output’ models in oconomic literature. Specifically, specialization to a few selected models is demonstrated.

Parameter identification for a class of multivariable non-linear processes

Abstract: A new signal-processing technique is presented and applied to the problem of determining the parameters of processes whoso dynamic behaviour is characterized by a set of ordinary first-order non-linear differential equations. The process signals and certain products of the process signals are used to excite Poisson filter chains. The Poisson filter chains provide exponentially smoothed moments of the signals at the filter chain inputs. Simultaneous sample values of these Poisson filtered signals are then used to form linear algebraic equations in the unknown process parameters. The method of instrumental variables is utilized to combat inaccuracies in the measured process signals. Finally, the method is illustrated by an example and the results of simulation studies are presented to demonstrate the feasibility of the method.

On-line identification of linear systems

Abstract: This paper considers the on-line identification of a linear process in terms of an orthonormal expansion of its impulse response. The undesirable features of the earlier solutions such as flipping back tho input or using unstable networks are avoided by the use of correlation functions. Modified Laguorro functions have boen employed in this work for tho identification of tho impulso response. The scheme developed here is applicable for a wide class of input signals. Further, the use of correlation eliminates the effects of any additive noise uncorrected with the input. Digital computer results have boon included to domonstrate the practicability of the schome. The only significant limitation appears to be the requirement that the process should not change appreciably in one avoraging time.

Set stability of differential equations

Abstract: In recent years numerous definitions of stability having a more quantitative nature than most classical stability definitions have been presented by various investigators. These definitions involve known specific bounds on solutions of tho differential equation in question. In this paper a now type of stability (‘set stability’) is introduced which generalizes upon and in some respects unifies those recent endeavours in ‘ quantitative stability theory ’. The usual ‘Liapunov technique’ is employed in obtaining sufficient conditions for the various forms of set stability.

Completely self-diagnosable digital systems

Abstract: In introducing the concept of ‘complete self-diagnosability’ two basic structural models are described. The models are intended to realize a diagnostic capability that assures the location of faults not only in the main system but also in the auxiliary system which is meant to diagnose the main system, Necessary conditions for the minimum weight of a completely self-diagnosable system which is made up of a large number of modules arc derived.

Domains of capability of manufacturing systems

Abstract: In this paper it is shown that the formalisms of set theory and sentential calculus can be combined to provide a powerful tool for the precise specification of the domains of capability of manufacturing systems. Such a specification is, of course, a pre-requisite for the solution of problems involving the optimal selection of manufacturing resources.

Comparison theorems for set stability of differential equations

Abstract: Set stability and uniform set stability of differential equations involve known specific bounds on solutions of the differential equations under consideration. Comparison theorems are presented giving sufficient conditions for these forms of stability. The conditions include the existence of a Liapunov-Like function and the set stability of a scalar differential equation. Examples are given to demonstrate the method.

New algorithms for estimation with sequentially correlated measurement noise

Abstract: This paper derives new estimation algorithms for use with systems with sequentially correlated observation noise. Both single and two-stage correlation are considered. The algorithms appear much like the well known white noise algorithms and are not much more complex. Error analysis algorithms for the analysis of modelling errors made in using those and white noise estimation algorithms are also presented. Those algorithms permit analysis of the effect of making the white noise assumption when the observation noise is really coloured. Examples and associated illustrations are presented to show this effect The newly derived algorithms are compared with existing, more restrictive algorithms, and Bhown to provide equivalent results for problems where both apply.

Strategic management control

Abstract: Throughout this account, the growing interest in management strategy, as a subject which can be planned, as well as described, by upper-echelon managers has been indicated. The most important concept that has been outlined is that the need for a planned management strategy arises directly from the task which management sets itself when it tries to control its environment. It is not merely a need which becomes apparent at a high level of management complexity, but is inherently part of the function of management. The second important idea, implicit throughout this account, and made explicit in §7, is that models of the organization are baaed on axioms which must be outlined at the highest level of control in an organization—by the board of directors : thus, the board have a direct influence, as well as ultimate responsibility, in the modelling activities of managers who construct and carry out planned strategic decisions.

Control theory and input-output analysis †

Abstract: This paper reviews the use of simulation techniques for the testing and analysis of econometric models. Control theory is shown to be a way of obtaining a concise formulation of the properties of the optimal solution rather than the actual solution. Most problems arising from econometric models cannot be solved algebraically and solutions to such problems are obtained using a series of simulation runs. The relationship between Theil's docision rule algorithm and Leontief's dynamic input-output model is demonstrated. In addition, the continuous-time version of the Leontief model is optimized for a quadratic criterion using dynamic programming. Problems relating to the formulation of the social welfare function are discussed and in particular whether the Leentief model provides the appropriate variables needed for the evaluation of social welfare Tho place of control theory within the framework of the Cambridge Growth Model is presented both in relation to past and proposed future work.

The origins and applications of stochastic integral equations

Abstract: Random or stochastic equations appear frequently in the mathematical description of phenomena in the biological, engineering, and physical sciences. The manner in which these equations arise is elucidated and several important applications of stochastic integral equations of the Volterra type in the engineering and biological sciences are presented in order to acquaint the reader with the importance of stochastic equations and how they are used in physical situations. Included in these applications are problems in control theory, statistical turbulence, and telephone traffic theory. Two biological problems, one concerning a mathematical model for chemotherapy and the other concerning population growth, which have been treated previously us deterministic integral equations, are presenter in a more realistic stochastic framework.

On the convergence of an iterative method for the computation of generalized inverse and associated projections

Abstract: An iterative method, with convergence of any desired finite order, for computing the generalized inverse A + and the associated projections AA + and A + A for any matrix A is developed. The method uses an upper bound on the maximum eigen-value of AAast; (or A∗A). It is also shown that the trace of a sequence of approximations to AA + (or A + A) converges to the rank of A. Finally, examples are given illustrating the computation of the generalized inverse and rank.

Equivalence transformations in linear dynamical systems

Abstract: The authors analyse the equivalonce of the minimal realizations of linear dynamical systems with given properties. To this end thoy review various groups of equivalence transformations, somo of which are already known while others are introduced for the first time in this paper. More particularly, the authors study the equivalence of the minimal and periodic realizations, as well as that of the minimal, bounded and reduced realizations. For these latter they also state tho necessary and sufficient conditions governing their existence.

Numerical solutions of multipoint boundary value problems in non-linear systems

Abstract: A method of solution of multipoint boundary value problems in non-linear systems is presented. Inverse problems, system identification, and parameter estimation are generally special eases of this method.

Some comments on the concepts of regulation and positional information in morphogenesis

Abstract: In this present paper, the rather metaphorical ideas of ‘ positional information ’ and ‘regulation’ as used hy Wolpert (1968, 1960) in connection with morphogenesis are placed in a more general dynamical context in which those ideas are sharply defined in terms of the stability properties of classes of dynamical Systems.

I. Development of basic models

Abstract: Based on the concept that task progress is the growth of developments in a structured work and activity process, mathematical models ore developed to define, identify, and follow work progress and resourco utilization patterns. These models ore developed from the Pearl-Roed Logistic function and describe operating characteristics in the micro resource allocation and control problem. The model3 are the Task Operating Characteristic (TOC) curve and the Resource Operating Characteristic (ROC) curve. A second paper extends the theoretical results and gives examples (Braswell 1971).

Vectorial flow graph—a concept for the analysis of generalized feedback systems

Abstract: The use of flow-graph techniques for the analysis of complex feedback systems like those encountered in real life economic problems has met with considerable difficulty in the enumeration of chain graphs Taking note of a basic feature of such systems, viz the possibility of categorizing the interacting nodes into distinct classes of nodes, the concept of a vectorial flow graph is introduced The axioms governing such graphs, their properties and the rules of manipulation are described The analysis of a complex economic system is given as an illustration

Studies in the modelling and control of a national economy

Abstract: A survey of some elementary macroeconomic models is presented which indicates the potential that exists for the application of control theory in economics. An initial linear model is developed systematically to embrace an increasing degree of economic sophistication leading to a non-linear formulation, the need for which is soon made apparent. Examples are given to demonstrate the use of characteristic root analysis, of the root locus technique to examine parameter sensitivity and of phase plane and stability concepts. At the same time, important economic interpretations which can be drawn from the results are indicated.

Estimation of multi-input systems with ‘noiseless’ outputs

Abstract: A procedure is presented for linear discrete system state estimation in which the observation does not contain additive white noise. The order of the system for estimation is reduced according to the number of noiseless outputs and noiseless output differences (here noiseless implies the absence of white noise). The advantage of this approach is its general application. Unlike earlier methods, it is not necessary for the noise states to be separable or even distinguishable from other system states. A systematic approach to the formulation of the required estimation model from a general system model is presented. The procedure is straightforward but somewhat lengthy to describe for the general problem. However, once the basic scheme is understood, it can be applied without undue difficulty to a large number of problems. For the modified estimation model, required filtering algorithms are derived which are of essentially the same complexity as the usual white noise algorithms. Direct estimation of the origi...

Constraints on the synthesis of optimal manufacturing systems

Abstract: In this paper the formalism of set theory is used to determine the constraints which bear upon the synthesis of optimal manufacturing systems to perform given work loads.

System parameter determination via linear functional estimation

Abstract: The system parameter determination problem is reduced to the solution of a set of algebraic equations by the use of estimates of linear functionals involving the observed time functions, i.e. input and output. The minimum variance unbiased estimates of linear functionals are derived using a variation of the Projection Theorem.

A generalized procedure for the constrained optimization problem

Abstract: The necessary and the sufficient conditions for the solution of the equality constrained optimization problem with N variables and (N−1) constraints are first derived and generalized to N variables and m constraints. Directional derivatives are used in the approach. The necessary and sufficient conditions for the problem with N−1 constraints are shown to be equivalent to the unconstrained one-variable problem, when the ordinary derivatives are replaced by the corresponding directional derivatives of the objective function in the direction tangent to the intersection of the constraints. The general equality constrained optimization problem of N variables and m constraints is then analysed using the directional derivative approach. Feasible direction vectors are defined and obtained in terms of first partial derivatives of the constraints. Necessary and sufficient conditions in terms of directional derivatives are derived and their equivalent with results in the literature. Sufficient conditions hi...

A new method of solution for exchange processes in biology, economics and engineering

Abstract: A class of countercurrent and co-current discrete exchange systems is considered, and the problems of solution and interpolation investigated in terms of discrete Fourier expansions. A method is developed to accommodate transport in either direction within a common, framework, which conveniently yields spatial spectra of the distributed system. This solution is applicable to a wide range of systems that exhibit properties of transport and transfer.