Showing papers in "International Journal of Systems Science in 1972"

Modal control of production-inventory systems

Abstract: In this paper, control policies for a class of production-inventory systems are derived using modal control theory, lb is shown that control policies which result in both good transient and good steady-state behaviour may readily be synthesized.

Models for cellular interactions in development without polarity of individual cells II. Problems of synchronization and regulation

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. It has been shown, using a developmental model originally due to Lindenmayer, that oven 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. However, it has been conjectured that, in a linear array of cells, the individual cells must have polarity in order to exhibit certain kinds of regulatory behaviour, i.e. the regaining of certain global properties of the array after a significant external disturbance (for example, the breaking of the array into two disconnected arrays). We demonstrate that one suc...

The identification of many-dimensional relations

Abstract: Any system, no matter how general or complex, can be described by a relationship amongst nominal variables. In this paper we investigate the problem of identifying snob a relationship, and the properties of the system corresponding to it, when the data descriptive of the system have been gathered from diverse and uncorrelated sources. We represent this problem theoretically as one of reconstructing and identifying an n-dimensional relation from its projections, and discuss the practical implications of this representation. We show that such reconstruction and identification is possible only if certain basic features of the corresponding system are constrained in ft very definite manner. For example, if the relation is to be identifiable, i.e. if the sot of relevant variables is to be ’ perfectly constrained ’, then the system must contain no more than a certain number of functionally determined variables, and no more than a certain number of independent variables. Furthermore, as the number of variables b...

A Nash algorithm for a class of non-zero sum differential games

Abstract: An algorithm is proposed for solving a class of non-zero sum differential games. The ‘ping-pong’ algorithm assumes initial discrete control values, and then integrates a set of state equations forward and the corresponding set of co-state equations backward, alternately, until a stopping criterion is met. Cost calculation on each forward integration run provides a means of measure of cost improvement, and hence the stopping criterion based on convergence within some small value. This algorithm is tested on an appropriate nonzero sum differential game: the Apartment Heating Problem. In this problem, the conflict arises from the system equations. Each tenant desires to heat his apartment at a minimum cost. Each tenant is free to adjust his control such that his desires are met. But since these tenants share a common wall, their desires may not be achieved, as heat can flow through this wall. In addition, each tenant cannot measure the state, so the problem is ‘open loop’ in the sense of control theory. This...

Transient stability of a power system by the second method of Lyapunov

Abstract: The second method of Lyapunov has been applied to the transient stability analysis of a power system ; and the Lyapunov functions have been generated systematically by a method developed recently. The stability boundaries obtained have been compared with those obtained by other workers and have been found to give better results.

Determination of Volterra kernels from input-output data

Abstract: In this paper a class of system identification problems of non-parametric type is considered. Specifically, given an unknown deterministic system whose input-output relation can be expressed by a Volterra expansion, some basic structural aspects related to the problem of determining Volterra kernels from input-output records are discussed from a coordinate-free point of view. The model adopted for the system input—output relation is general enough to cover a number of situations ranging from problems of identification where the kernels are time-varying to those where the kernels must be constrained in Hilbert spaces of well-behaved functions. The emphasis is on establishing what, in principle, can be recovered of the system kernels through a noiseless identification process, and the ultimate limitations imposed by the presence of observation or measurement noise. An application of the steepest descent iteration to the ill-posed estimation problem resulting from the presence of observation noise is considered.

Principles of an abstract theory of systems

Abstract: A general definition of the notion of ‘ system ’ ia given. Starting from this definition, some basic principles of an abstract system theory are developed. The theory loads to a specification of several terms often used in this field, such as ‘ model ’, ‘ continuous or discrete system ’, ‘ discrete model of a continuous system ’, etc. Also some properties of the systems are specified, under extremely general conditions.

Concerning controllability and observability of linear sequential machines

Abstract: The concept of output–controllability for linear sequential machines over a GF(p) is studied and conditions for k output-controllability are given. Then the concept of k observability is introduced which is the dual of the k state–controllability concept. discussed by Cohn. The duality of controllability and observability is revealed and several examples are studied which illustrate the theoretical results.

Synthesis of control policies for manufacturing systems using eigenvalue-assignment techniques †

Abstract: In this paper, eigenvalue–assignment techniques are used to synthesize control policies for a manufacturing system. This system is modelled as a diserete–time multivariate dynamical system with a disturbance input duo to sales. The state variables of the system are the rotes of flow of parts at the various work stations, the backlogs of parts, and the inventory level of the finished product. The control inputs ore the man–hours–per–week required for the various work processes involved in the manufacturing system.

Mathematical models in health-planning research

Abstract: The authors suggest, several factors which may be used to identify classes of modelling techniques appropriate to a given planning problem. Those factors are the degrees of (a) the decision makers’ authority to specify control measures, (b) the consistency of the decision makers’ objectives, (c) the decision makers’ ability to describe the casual relationships involved, and (d) the ‘ complexity’ of these relationships. The effect of these factors on suitable modelling approaches is discussed, and examples given from the field of health planning.

A Newton-like optimization algorithm for digital systems with time delay

Abstract: The design and computation problems of optimum nonlinear digital time-delay control systems is considered. A minimum principle is presented which solves the design problem, and a second-order computational algorithm is developed which solves the computation problem. The minimum principle is shown to be a special case of a generalized minimum principle in. Hilbert space. The computational algorithm is actually a Newton-like hill-climbing technique for iteratively improving the guessed initial values of the conjugate vector λ so as to satisfy the final condition of the problem. The main advantage of the present algorithm is that it does not require excess memory as in other algorithms.

Dyadic feedback laws for linear multivariable systems

Abstract: The extent to which it is possible to assign the eigenvalues of the system Where K is constrained to have the dyadic structure. K = qpT, is investigated. It is shown that a necessary and sufficient condition for the existence of a dyadic feedback law to assign arbitrary eigenvalues, in so for as this can be accomplished by any state variable feedback law, is that the system matrix of the controllable part of the system is non-derogatory. The proof furnishes a constructive procedure for computing a vector q in this case. The treatment is based on the Anderson-Luenberger approach, and a now result is presented regarding the information which can be extracted from their canonical form.

Probability of stability of a class of linear dynamical systems

Abstract: In this paper, simple formulas for the probability of stability of a class of linear dynamical systems arc presented. The theoretical results thus obtained are compared with certain empirical results obtained by Ashby (1952).

On buffer design for Erlang arrivals and multiple synchronous periodically regular outputs

Abstract: The buffer design problem is studied for the case of Erlang arrivals, multiple, synchronous servicing channels, and periodically regular removal rates. Using traffic intensity, Erlang constant, and number of servicing channels as parameters the analytical expressions among buffer size, overflow probability, mean queue length and expected queuing delay due to buffering are derived. These relationships are computed for a sot of parameter values and are plotted to provide a basis for the buffer design. The results of the paper should be valuable in many engineering applications such as time-sharing computer systems, information compression, telephone exchanges, statistical multiplexing of data communication, and simulation of road traffic systems. As an example, a time-sharing computer system, servicing a large number of remote terminals, is studied.

L2-stability of time-varying systems with global conditions on the time-varying gain

Abstract: The L2-stability of linear und non-linoar time-varying systems is considered and integral typo condition on the time-varying gain is obtained through the positive operator theory.

The tactile discrimination of complex systems

Abstract: The elementary modalities of sensation such as touch and pressure may be taken as basic units of perception, and the tactile perception of more complex systems such as matter in its various states viewed as a structured combination of these units. When the system which is discriminated or perceived is not too complex, then the relationship between the external system and the internal, physiological perceiving system may be explored. It is seen in several examples that an interesting parallel exists between discriminating and discriminated (internal and external) systems.

Synthesis of optimal suspension systems subjected to stochastic disturbances

Abstract: In this paper, a synthetic approach to the design of optimal suspension systems subjected to stochastic disturbances is presented. The method is illustrated by synthesizing a single-degree-of-freedom suspension system and a two-degree-of-freedom suspension system subjected to white gaussian forces and torques.

A test for periodic effects in time series data

Abstract: Systems modelling frequently is dependent upon the analysis of sample data to enable establishment of functional relationships. This may be concerned with the evaluation of periodic or cyclical effects in time series data. Autocorrelation, using a Student's t text statistic, is often utilized to ‘investigate’ such effects. However, this test statistic is not applicable since basic assumptions are violated. Thus, an alternative statistic and the relatively unknown Wald and Wolfowitz non-parametric circular serial correlation coefficient, is discussed in this paper. To facilitate use of this test statistic, a FORTRAN subroutine is included.

Transfer function matrices and state-space representations of multivariable linear systems

Abstract: Several new theorems concerning the transfer function matrices associated with different representations of linear time-invariant multivariable dynamical systems are presented. These theorems are derived using modal systems theory and are expressed in terms of the eigenvalue, mode-controllability, and mode-observability matrices associated with different system representations.

Choice of complex systems based on past experience

Abstract: The choice of new systems based on the properties and performance of previous systems, of the same class, is considered, A two-phase selection procedure, consisting of curve-fitting and optimization, is proposed. An example illustrating the procedure for the choice of a Satellite Attitude Control System is presented.

Heuristic programming: A survey

Abstract: This survey of heuristic programming starts by considering the nature of an algorithm as an automatic and precise process. A heuristic, by contrast, in an approximate and uncertain process, although algorithms and heuristics should be regarded as lying on a continuum. An examination of various applications of heuristics follows, showing the wide range of their use from game playing and logic theorem proving to shop floor scheduling and natural language programming.

Suboptimal feedback control of a distributed linear regulator with control and observation structure constraints

Abstract: The problem of feedback control of a linear distributed parameter system with quadratic cost where the number of control and measurement locations is finite is considered. An average cost is used to reduce the sensitivity to changes in initial conditions. A suboptimal scheme is developed to evaluate the feedback coefficients. Two examples arc solved where the feedback coefficients are evaluated in a piecewise constant form using the matrix Maximum Principle and matrix gradient.

A max-min differential game in Hilbert space

Abstract: A game with quadratic pay-off, whose dynamics are described by evolution equations in Hilbert space, is considered. One player, trying to maximize the pay-off, chooses his control function for the game at the outset and we first investigate how the opposing player, who knows this choice, will use his controls to minimize the payoff. The controls of the minimizing player may vary throughout a Hilbert space, whilst the controls of the maximizing player are possibly restricted to a subset of a Hilbert space. An unexpected linear simplification shows that the maximizing player should try, roughly speaking, to get as far away as possible from the free motion of the minimizing player, and with this information a maximum principle is obtained.

δ state controllability by admissible controls for linear time-invariant systems

Abstract: The necessary and sufficient conditions for a linear time-invariant continuous system to be δ state controllable by admissible controls are developed. The corresponding conditions for a linear time-invariant discrete system are stated without proof.

Parameter estimation and control in non-linear systems with perfect measurements I. Parameters appearing linearly †

Abstract: Many chemical processes are characterized by significant process disturbances, but negligible measurement noise. By combining the state and measurement equations, and considering the parameter drift equation to be the new ‘ state ’ equation, parameter estimation algorithms in the presence of feedback control can be developed. A Bayesian approach is used herein to develop the estimate of a parameter appearing linearly in a non-linear state equation.

Weighting sequence estimation using pseudo-random sequences with arbitrary experiment length

Abstract: A method is derived whereby cross-correlation techniques using pseudo-random sequences can be used to estimate the weighting sequence from experimental data of arbitrary lengths without incurring error duo to partial pseudo-random sequence periods. The method consists of forming an ensemble average of the output data before cross-correlation is performed. Slight modifications of the method give increased accuracy when the non-zero off-peak value of the autocorrelation function is not ignored, or when it is known that the weighting sequence is shorter than the pseudo-random sequenco period.

Transmission of stochastic signals through a class of non-linear systems†

Abstract: A separable, not necessarily stationary, stochastic process is passed through a nonlinear system represented by a functional polynomial of the Hammerstein type. Functional relations between the multivariate characteristic function of the output and the multivariate distribution, density and characteristic functions and multiple moments of various orders of the input are developed. Methods of evaluating these relations are discussed. Three examples arc worked out.

Dynamics of a non-linear spatial trade model

Abstract: This paper deals with n nonlinear economic model consisting of a collection of suppliers and markets. The markets and suppliers are assumed to be separated by a constant transport cost. A social payoff function is proposed. The existence, uniqueness, and stability of equilibrium states are related to the properties of the optimal social payoff.

Toward a systems science market valuation model

Abstract: This research note makes a modest attempt to view the valuation of common shares, in part, in terms of a simple feedback mechanism. In so doing, the authors hope to shed light upon one of the underlying dynamics of the often mentioned tendency of the market to ‘over-react’ to changes in its environment.