Systems tableau : an integrated approach to systems theory Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/tt44pp89f

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  • Systems Tableau is suggested as a convenient tool for the integration of the three phases of systems theory: the synthesis of a model from the analysis of a system; the evaluation of the model; and the decision-making process for the design and control of the resulting system. From a basic consideration of Man-Nature communications, several mathematical, biological, engineering, and management examples of systems models are examined to develop a unified definition of a system. Logical, physical, mathematical, graphic, and computational requirements are postulated for the methodology of models for systems meeting the definition. These requirements are used to formulate the basic tableau as a hybrid of a mathematical mapping matrix and a graphical flowgraph that expresses the interrelationships among the components of a given system. Thus, a tableau is at once a matrix and a network representation of the system. The general (connecting), ordinal (dominating), and technological (directing) relations in the observation (phase) space are illustrated on tableaux for social, economic, management, and engineering examples. Related mathematics of relations are examined. The relationships of these descriptive models to normative models are discussed as synthesis techniques. Orthogonalization of bases, parametric representations (in frequency space as probabilities and statistical distributions), and reductions in state (solution) space are methods introduced with examples in queueing, communication, and information models. In normative models, we are afforded some degrees of freedom expressed in terms of choice of alternatives. This decision requires at least an ordinal, if not cardinal, characterization of each alternative. The ordinally normative models are based on comparatively quantifiable relations originally afforded by the uni-directional flow of time. Theories of Information, Algorithms, and Games were found useful in drawing valuable conclusions (decisions) from these models. Puzzles, games, Turing machines, and biological examples are discussed. The cardinally normative models require decisions based on numerical values. A truly cardinal model must be cardinal resource-wise, time-wise, and information-wise. This inter-dependency of resources in phase space and information in state space, as functions of time expressible in frequency space, is the basis for the proposal of the Cardinal Utility Hypotheses. This concept allows the development of relations as peculiar Laplace-Z transform-pairs, with the utility of Information (usefulness of data for decision-making) serving as the Channel Capacity for a corresponding communication model. The Principle of Optimality of Dynamic Programming was found most useful in Tableau, andits continuous counterpart of Maximum Principle is expected to take a respective place in the Calculus of Variations in Control Theory. The relationship of the controllability and observability of a system and the diagonalization of its Tableau is also illustrated. The linear models of the traditional Tableaux are reviewed and interpreted in the light of Systems Tableau Method, These include Quesney-Leontief Tableau Economique, Hellerman's Tableau, and Critical Path Scheduling Tableau. The obvious advantages afforded by the applications of Huggins' (and others) Signal Flowgraph techniques are briefly illustrated. Mention is made of a tableau-based computer program that will produce the dual network for Ford-Fulkerson's Minimum-cut-maximal-flow Method. A brief discussion of the future of Systems Theory concludes the treatise.
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