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General systems theory : mathematical foundations /
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrang...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1975.
|
| Colección: | Mathematics in science and engineering ;
v. 113. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
MARC
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| 100 | 1 | |a Mesarovi�c, Mihajlo D. | |
| 245 | 1 | 0 | |a General systems theory : |b mathematical foundations / |c M.D. Mesarovic and Yasuhiko Takahara. |
| 260 | |a New York : |b Academic Press, |c 1975. | ||
| 300 | |a 1 online resource (xii, 268 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Mathematics in science and engineering ; |v v. 113 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Cover13; -- General Systems Theory: Mathematical Foundations -- Copyright Page -- Contents -- Preface -- Chapter I. Introduction -- 1. General Systems Theory: What Is It and What Is It for? -- 2. Formalization Approach for the Development of the Mathematical Theory of General Systems -- Chapter II. Basic Concepts -- 1. Set-Theoretic Concept of a General System -- 2. General Time and Dynamical Systems -- 3. Auxiliary Functions and Some Basic Classification of Systems -- 4. Causality -- Chapter III. General Realization Theory -- 1. Realizability and Dynamical Representation -- 2. Canonical Representation (Decomposition) of Dynamical Systems and Characterization of States -- 3. Constructive Origin of State-Space Representation -- Chapter IV. Linearity -- 1. Linear Time Systems -- 2. Decomposition of Systems Response: State- and Input-Response Functions -- 3. Realization Theory -- 4. Construction of the State Space for a Linear System -- Chapter V. Past-Determinacy -- 1. On the Class of Past-Determined Systems -- 2. State-Space Representation -- 3. Characterization of Past-Determined Systems -- Chapter VI. Stationarity and Time Invariance -- 1. State-Space Stationarity and Time Invariance -- 2. Realization Theory of Time-Invariant Systems -- 3. Stationary Past-Determined Systems -- 4. Axiomatic Construction of a Class of Dynamical Systems -- 5. Abstract Transfer Function -- Chapter VII. Controllability -- 1. Basic Concepts -- 2. Some General Conditions for Controllability -- 3. Controllability of Time Systems -- 4. Overview of Some Basic Linear Time Systems Properties Related to Controllability -- Chapter VIII. Minimal Realization -- 1. Concepts of Minimal Realizations -- 2. Characterization of the Minimal Realization of Stationary Systems -- 3. Uniqueness of Minimal Input-Response Realization -- Chapter IX. Stability -- 1. General Concept of Stability -- 2. Stability of Sets for General Systems -- Chapter X. Interconnections of Subsystems, Decomposition, and Decoupling -- 1. Connecting Operators -- 2. Subsystems, Components, and Decomposition -- 3. Feedback Connection of Components -- 4. Decoupling and Functional Controllability -- 5. Abstract Pole Assignability -- 6. Simplification through Decomposition of Discrete-Time Dynamical Systems -- Chapter XI. Computability, Consistency, and Completeness -- 1. Computation as Dynamical Process -- 2. Fundamental Diagonalization (Goedel) Theorem -- 3. Application of the Fundamental Theorem to Formal Systems -- 4. Realization by Turing Machines -- Chapter XII. Categories of Systems and Associated Functors -- 1. Formation of Categories of General Systems and Homomorphic Models -- 2. Categories of General Systems -- 3. Categories of Time Systems -- 4. Categories of Dynamical Systems -- Appendix I. References and Historical Account -- Appendix II. Alternative Basis for Mathematical General Systems Theory -- 1. Axiomatic Logic Structures -- 2. Topological. Functional Analysis, and Quantitative Approaches -- 3. Algebraic Systems Theory -- 4. Restricted Notion of a System -- Appendix III. Open Systems and Goal-Seeking Systems -- 1. Open Systems -- 2. Goal-Seeking Systems -- Appendix IV. Basic Notions in Category Theory -- Index. | |
| 520 | |a In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;<BR id="CRLF">methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and<BR id="CRLF">methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.<BR id="CRLF"><BR id="CRLF">As a result, the book represents a blend of new methods in general computational analysis, <BR id="CRLF">and specific, but also generic, techniques for study of systems theory ant its particular<BR id="CRLF">branches, such as optimal filtering and information compression. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a System analysis. | |
| 650 | 6 | |a Analyse de syst�emes. |0 (CaQQLa)201-0007674 | |
| 650 | 7 | |a systems analysis. |2 aat |0 (CStmoGRI)aat300077662 | |
| 650 | 7 | |a SCIENCE |x System Theory. |2 bisacsh | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Operations Research. |2 bisacsh | |
| 650 | 7 | |a System analysis |2 fast |0 (OCoLC)fst01141385 | |
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| 650 | 7 | |a Systemtheorie |2 gnd |0 (DE-588)4058812-9 | |
| 650 | 7 | |a Mathematik |2 gnd |0 (DE-588)4037944-9 | |
| 650 | 7 | |a SYSTEMS ANALYSIS. |2 nasat | |
| 653 | |a General systems theory | ||
| 700 | 1 | |a Takahara, Yasuhiko, |d 1935- | |
| 776 | 0 | 8 | |i Print version: |a Mesarovi�c, Mihajlo D. |t General systems theory: mathematical foundations. |d New York, Academic Press, 1975 |z 9780124915404 |w (DLC) 74001639 |w (OCoLC)900956 |
| 830 | 0 | |a Mathematics in science and engineering ; |v v. 113. | |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780124915404 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/bookseries/00765392/113 |z Texto completo |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/publication?issn=00765392&volume=113 |z Texto completo |