External Description Research Articles

A STRUCTURE THEORY FOR A CATEGORY OF BEHAVIOURS

Abstract A category Bch(X) of behaviours is introduced as a formalization of an external description of systems. It is show that the forgetful functor W: Bch(x) → K2 is algebraic and that therefore Bch(x) has, and W preserves, whatever limits K has. Colimits and an image factorization system for Bch(X) are also investigated.

Triangular canonical forms for bilinear systems

The purpose of this paper is to find necessary and sufficient conditions for the existence of coordinate transformations yielding partially (i.e. triangularly) decoupled canonical forms for bilinear state-pace descriptions. The conditions are found on the internal as well as on the external description, the latter being specified throughout a realizable formal power series.

Estimation of steady-state Kalman filter gain

An external description of multivariable linear stochastic systems gives a new estimation method of the steady, state Kalman filter gain for systems with unknown noise covariances.

The use of frequency transmission concepts in linear multivariate system analysis

Abstract The classical work by Nyquist and Bode and its extensions to the multivariable case are based on a frequency-response approach to feedback systems. Modern state-space techniques, on the other hand, make use of an internal system description as dictated by a set of first-order linear differential equations. Relevant to both approaches is the problem of frequency propagation which in this paper is seen as the means of unifying the external and internal system description. The inextricable association of frequency transmission with the concept of (A, B)-invariant subspaces and controllability subspaces empowers this approach with the ability to effect a penetrating study of a number of aspects of linear system behaviour such as the restriction of the state vector in given subspaces and the characterization of such subspaces, the characterization of multivariate zeros and the categorization of systems into degenerate and non-degenerate. In this paper the study of the transmission of a particular freq...

Feedback realizations in linear multivariable systems

A feedback system consists of two objects, a fixed parent system and a controller connected to it. The relationship between external and internal descriptions of such systems is described. It is shown that redundancy in a feedback system can be expressed as a partial reduction with respect to controllability and observability. Applying this reduction yields a controller of lowest possible order. It is also shown that the requirement of internal stability can be expressed as a requirement on the external description of the feedback system only. This leads to a nice formalism for internally stable control synthesis using rational matrices. This is demonstrated in two important control problems, the model matching problem and the algebraic regulator problem, and by examples.

双線形システムの外部記述モデルの同定と最小双線形実現

双線形システムの外部記述モデルの同定と最小双線形実現

Individuality in the Imperial Constitutions: Hadrian and the Antonines

A considerable number of texts of official pronouncements of Roman emperors (which will be referred to, rather inaccurately, as constitutions, for the sake of brevity) have been preserved on inscriptions, in papyri and in the writings of the classical jurists and the imperial Codes. Such texts provide the kind of documentary evidence which is regarded by historians of more recent periods as primary material, as narrative histories and biographies are not. Such rigour is not possible in Roman history, but it is clearly desirable to make the best use of these documents, especially in a period such as that between Hadrian and Commodus, when they are especially plentiful but, as far as literary sources go, there is not even the doubtful light of a panegyric to supplement the glimmerings of an epitome. But the kind of use to which they are put depends on the question of their authorship: are they to be treated as the work of the individual emperors in whose names they were issued, or of a civil service which continued to operate in much the same way while emperors came and went? The latter hypothesis has commonly been taken for granted until recently, even if not explicitly stated and argued for. In 1967 Millar showed that all the external descriptions of the methods of work of the emperors took it for granted that the emperors normally dealt in person with problems presented to them and produced the constitutions issued in their names themselves: hence those who wished to uphold the second hypothesis described above would have to prove that ‘vast ranges of imperial business were handled by the bureaux in private, systematically concealed from the view of our literary sources.’

External description of multivariable systems

This paper presents a study of the factorized expression of the transfer matrix corresponding to a multivariable system. Two algorithms are developed to bring a transfer matrix to a factorized canonical form; these algorithms are easily programmable in a digital computer.

Exact controllability and observability and realization theory in Hilbert space

In this paper we study in depth a class of infinite dimensional linear time invariant systems. We get concrete analytic conditions characterizing esact controllability and exact observability in the sense of Helton. Also, we characterize the class of transfer functions having realizations that are exactly controllable and esactly observable. There are currently two approaches to the problem of describing linear systems, using external and internal descriptions. The external description gives the input/output relations, whereas the internal description gives the dynamics of the system that produce the given input/output relations. The problem of realization is to find from a given external description all the possible internal descriptions and the relations among them. This is an impossible task unless some additional assumptions are made. One natural assumption is that in some sense a realization should be minimal. Liehen this assumption is made precise, we get a complete theory for finite dimensional time invariant linear systems, whether discrete or continuous. We will quote some of the highlights of the finite dimensional theory, that will serve as reference and motivation for the results of this paper. For a more complete exposition excellent accounts are in [3, 131. Two linear spaces C.r and 5’ are given. U is called the control space and E’ the output space. A (discrete) linear time invariant input/output map is a linear map sending sequences of elements of U into sequences of elements E such that yrl = Cyzt =jljU,_j_l , where 9j E L( CT, I’). The sequence (A,, -4, ,...) is called the impulse response function, whereas z =l# (or x Aizitl) is called the transfer function of the system. Usually we identify

The problem of exact model matching by the use of external description

This paper deals with the problem of exact model matching in multivariable systems. The problem is presented using exclusively a transfer matrix for the description of tho system. A solution is obtained by the use of the minimal bases of rational vector spaces.

Determination of matrix transfer function in the form of matrix fraction from input-output observations

This short paper concerns the identification of a linear time-invariant discrete system represented by a matrix transfer function in the form of a matrix fraction. The relations between external and internal descriptions are discussed, and all matrix transfer functions satisfying given input-output observations are determined.

THE GASTROPTERIDAE OF GUAM, WITH DESCRIPTIONS OF FOUR NEW SPECIES (OPISTHOBRANCHIA : CEPHALASPIDEA)

From 1969 to the present the authors have maintained a regular log of the opistho­ branchs seen on Guam. Most of the study has been done in the area of Bile Bay, near the village of Merizo. During this time over a thousand specimens of Gastropteri­ dae, representing seven species, have been observed. Only a few of each species were collected, external descriptions were made, and color photograph slides taken. Until recently no effort was made by the authors to describe these animals. Gastropteridae are cephalaspid animals with paired parapodia which extend up over the dorsum, an elongate tapered tail, a posterior funnel on the cephalic shield, and a relatively short free mantle margin on the right side with the ctenidium usually located just below the mantle margin. In 1964 Tokioka and Baba divided the Gastro­ pteridae into two genera : Gastropteron characterized by a radular formula of 4-6. 1. 0. 1. 4-6 and with denticulations on the inner edge of the main hook of the first lateral; Sagaminopteron characterized by a radular formula of 9-12. 1. 0. 1. 9-12, with two promi­ nent cusps on the inner edge of the main hook of the first lateral. Carlson and Hoff (1973) described two new species of Sagaminopteron which had fewer marginals than the radular formula given by Tokioka and Baba, but the marginals were still more numerous than in Gastropteron. In 1967 a third genus, Enotepteron, was established by Minichev for a species collected near Tsingtao in the Yellow Sea. Enotepteron has four prominent cusps on the inner edge of the first lateral and a radular formula of 3. 1, 0. 1. 3. Only two of the genera, Gastropteron and Sagaminopteron, have been found on Guam. All external descriptions and comparative measurements presented here are from living animals. Since Gastropteridae change shape as they move, all such comparisons should be considered relative. Specimens of new species described in this paper are deposited in the Bernice P.

A language-oriented instruction set for the BALM language

The availability of microprogramming has increased interest in the design of instruction sets which are oriented towards particular higher-level languages (see (1), for example). We will refer to these as language-oriented instruction sets (or LOISs). In this paper we give a formal definition of a LOIS for the extendable language BALM. This LOIS, which we call MBALM, is used as the basis of the implementation of the current version of the language, BALM4. We will also compare two implementations of the MBALM instruction set, and outline briefly our experiences with them. The external description of BALM4 is given in detail elsewhere (2,3). Briefly, it is an extendable language with an Algol-like syntax and data-types integer, real, logical, string, pair (list), vector, identifier, procedure, and label. Type information is carried with all data-objects, and run-time type testing and conversion is done when necessary. Garbage collection and a run-time compiler are significant attributes of the system. Outlined below are some of the properties of the implementation, which was designed initially for reasons of simplicity and flexibility, but which illustrate some of the advantages of a LOIS-based system.

Construction of minimal linear state-variable models from finite input-output data

An algorithm for constructing minimal linear finite-dimensional realizations (a minimal partial realization) of an unknown (possibly infinite-dimensional) system from an external description as given by its Markov parameters is presented. It is shown that the resulting realization in essence models the transient response of the unknown system. If the unknown system is linear, this technique can be used to find a smaller dimensional linear system having the same transient characteristics. If the unknown system is nonlinear, the technique can be used either 1) to determine a useful nonlinear model, or 2) te determine a linear model, both of which approximate the transient response of the nonlinear system.

A Method for Using Weighting Functions as System Description in Optimal Control

A number of methods of linearised system dynamic identification, particularly those which do not require knowledge of the internal structure of the system, yield a system description in the form of weighting function (impulse response), or its Fourier transform frequency response. However, for optimal control theory it is usual to assume a set of first order differential equations as system description, and there is very little information concerning the use of external descriptions like weighting functions in forming optimal control.

External Morphological Description of the Larva of Exomalopsis Chionura Cockerell, including a Comparison with Other Anthophorids (Hymenoptera: Apoidea)1

Included in this paper is a description of both the mature larva and the first instar of Exomalopsis (Anthophorula) chionura Cockerell. This represents the first relatively complete account of the mature larva of any member of the Exomalopsinae and is of special significance because it tends to clarify the relationship of this subfamily with others of the Anthophoridae. This relationship has been open to question until now (Michener, 1944, 1953).

A New Approach to God

If civilisation is to survive, if the emergent civilisation is to achieve the fulfilment of its potentialities, the coming age must be an age of spiritual as well as social integration.Today the human mind is torn and divided between positivism and irrationalism. The endeavours of pragmatism succeeded in making important discoveries concerning a number of basic attitudes in thought and morality, and in what might be called the sociology of knowledge. As a universal system of knowledge and life, as a philosophy, however, pragmatism has been a failure.What is essentially needed is a renewal of metaphysics. The conceptions of modern science—the unification of matter and energy, physical indeterminism, the notion of space-time, the new reality recognised both as to quality and duration—are invaluable means of deciphering material phenomena. A cosmos of electrons and stars in which the stars are the heavenly laboratories of elements, subjected everywhere to genesis and transmutation, a universe which is finite but whose limits cannot be attained because of the curvation of space, and which dynamically evolves in a definite direction, namely toward the highest forms of individuation and concentration and toward a simultaneous degradation of the quality of its total energy—all this is external description and scientific imagery rather than ontological insight. Such knowledge can never directly serve the purpose of any philosophical or metaphysical extrapolations. Yet all this constitutes at the same time a basic representation of the world incomparably more favourable to the edification of a philosophy of nature and more open to the deepening labour of metaphysical reason than the old Newtonian physics.