Information Path Functional and Informational Macrodynamics.
Lerner, Vladimir S.
Information Path Functional and Informational Macrodynamics. - 1st ed. - 1 online resource (507 pages)
Intro -- INFORMATION PATH FUNCTIONAL AND INFORMATIONAL MACRODYNAMICS -- INFORMATION PATH FUNCTIONAL AND INFORMATIONAL MACRODYNAMICS -- CONTENTS -- ABSTRACT -- PREFACE -- ACKNOWLEDGMENTS -- INTRODUCTION -- PART 1. THE INFORMATION PATH FUNCTIONAL'S FOUNDATION -- Chapter 1.0 INTRODUCTION -- Chapter 1.1 THE INITIAL MATHEMATICAL MODELS* -- 1.1.1. Model of Microlevel Process -- 1.1.2. Model of the Macrolevel Process -- 1.1.3. The Feedback Equation-Control Law -- 1.1.4. Model of Programmable Trajectories (as a Task) at Microlevel -- 1.1.5. Model of Programmable Trajectories (as a Task) at the Macrolevel -- 1.1.6. The Equations in Deviations -- 1.1.7. Model of Disturbances -- 1.1.8. The Microlevel Process' Functional -- 1.1.9. The Jensen's Inequality for the Entropy Functional -- Chapter 1.2 DYNAMIC APPROXIMATION OF A RANDOM INFORMATION FUNCTIONAL AND THE PATH FUNCTIONAL -- 1.2.1. The Extremal Principle and the Problem Formulation -- 1.2.2. The Problem Solution. Information Path Functional -- 1.2.3. The Estimation of an Accuracy of the Probability's Approximation -- Chapter 1.3 THE VARIATION PROBLEM FOR THE INFORMATION PATH FUNCTIONAL AND ITS SOLUTION -- 1.3.1. The Problem Formulation -- 1.3.2. Solution to the Variation Problem -- 1.3.3. The Minimum Condition for the Microlevel Functional -- 1.3.4. The Optimal Control Synthesis -- 1.3.5. A Summary of the Information Path Functional Approach. The IPF invariants -- Chapter 1.4 THE INFORMATION SPACE DISTRIBUTED MACROMODELS DEVELOPED BY THE SOLUTIONS OF THE IPF VARIATION PROBLEM -- 1.4.1. Introduction -- 1.4.2. The Variation Problem for Space Distributed Macromodel -- 1.4.3. The Invariant Conditions at the Transformation of the Space Coordinates -- 1.4.4. The Parameters of the Space Transformation and the Distributed Macromodels. 1.4.5. The IPF Macromodel's Singular Points and the Singular Trajectories -- 1.4.6. The IPF Natural Variation Problem, Singular Trajectories, and The Field's Invariants for the IPF -- Chapter 1.5 THE COOPERATIVE INFORMATION MACROMODELS AND INFORMATION NETWORK -- 1.5.1. Introduction -- 1.5.2. The Time-Space Movement Toward the Macromodel's Cooperation -- 1.5.3. The Consolidation and Aggregation of the Model Processes. Forming an Information Network (IN) -- 1.5.4. The IN Dynamic Structure -- 1.5.5. Geometrical Structure of the Optimal Space Distributed Cooperative Macromodel (OPMC). The IN Geometrical Structure -- Chapter 1.6 THE IMD MODEL'S PHENOMENA AND INFORMATION CODE -- 1.6.1. The Model Time Course and the Evaluation of the Information Contributions into IN. The Triplet Genetic Code -- 1.6.2. The Model Information Geometry (IG), Its Specific, and the Structure -- 1.6.3. The Model Uncertainty Zone and Its Evaluation -- 1.6.4. Creation of the IN geometry and a Genetic Code of the Information Cellular Geometry -- 1.6.5. The Minimal Admissible Uncertainty and Its Connection to Physics -- 1.6.6. Information Structure of the model Double Spiral's (DSS) Control Mechanism -- 1.6.7. Examples of the DSS codes -- 1.6.8. A System's Harmony, Regularities, and the VP -- Chapter 1.7 THE MACRODYNAMIC AND COOPERATIVE INFORMATION COMPLEXITIES -- 1.7.1. Introduction -- 1.7.2. The Notion of Interactive and Cooperative Complexities and Their Information Measures -- 1.7.3. The Information Indicator of a Cooperative Complexity -- 1.7.4. Illustration of Arising of the Information Cooperative Complexity at Discrete Points of Applied Controls -- 1.7.5. The Complexity Invariant Measure in a Cooperative Dynamic Process -- 1.7.6. The IN Cooperative Mechanism with the Complexity Measure. 1.7.7. The Equations of the Spatial Information Cooperative Dynamics. Information Attraction and Complexity -- 1.7.8. Connection to Kolmogorov's Complexity -- Chapter 1.8 THE EVOLUTIONARY DYNAMICS AND THE INFORMATION LAW OF EVOLUTION -- 1.8.1. Introduction -- 1.8.2. The Equations Regularities and the Evolutionary Law -- 1.8.3. A Mechanism of an Enhancement of the Acceptable Mutations -- 1.8.4. The Conditions of the Model's Self-control, Adaptation, and Self-organization -- 1.8.5. The Evolution of the Model Invariants and a Potential Macroprocess' Cyclicity -- 1.8.6. Requirements for the Model Self-organization. The Results of Computer Simulations -- 1.8.7. Evaluation of Some Prognostic Parameters of the Evolutionary Dynamics. Example -- 1.8.8. Information Mechanism of Assembling the Node's Frequencies and Automatic Selection -- 1.8.9. The Functional Schema of the Evolutionary Informational Mechanisms. A Summary -- A Summary -- Chapter 1.9 THE PHYSICAL ANALOGIES RELATED TO THE INFORMATION PATH FUNCTIONAL -- 1.9.1. The Connection between the Information Path Functional (IPF) and the Kolmogorov's (K) Entropy of a Dynamic System, and the Relations to Physics -- 1.9.2. An IPF Analogy with the Feynman Path Functional in Quantum Mechanics and Informational Form of Schrödinger's Equation -- 1.9.3. About the Invariant Transformation of the Model Imaginary Eigenvalues and Information -- 1.9.4. The Superimposing Processes, Control and Asymmetry. The IMD Relation to Nonequilibrium Thermodynamics (NT) -- 1.9.5. About the Notion of a System -- PART 2.THE INFORMATION PATH FUNCTIONAL'SAND IMD'S APPLICATIONS -- Chapter 2.1 SOLUTION OF THE CONTROL PROBLEMS FOR A COMPLEX OBJECT -- 2.1.1. The Control Problems for a Complex Object -- 2.1.2. Solving the Identification Problem -- 2.1.2.1. The Identification of the Concentrated Object's Models. 2.1.2.2. The Identification of the Space Distributed Object's Models -- 2.1.3. Solving the Optimal Control Problem -- 2.1.3.1. A Joint Solution of the Optimal Control and Identification Problems. The Basic Results -- 2.1.3.2. The Procedure of the Joint Identification, Optimal Control, and Consolidation -- 2.1.3.3. Building the Object Cooperative Information Network -- Chapter 2.2 THE INFORMATION MODELING OF THE ENCODING-DECODING PROCESSES AT TRANSFORMATION OF BIOLOGICAL AND COGNITIVE INFORMATION -- 2.2.1. The Objective and Methodology -- 2.2.2. An Inner Information Structure of the IN with the Ranged and the Nonranged Sequences of the Starting Eigenvalues. The DSS Code -- Example of the Bio-process' Code -- 2.2.3. Mathematical Model of the IN with an Arbitrary Sequence of the Starting Eigenvalues -- 2.2.4. The Procedure of Encoding, Compression, Synthesis, and Decoding of the IN Information -- 2.2.5. Summarized Results -- 2.2.6. About Other Related Applications -- 2.2.7. The Connections between Some Physical Neuronal Functions and Mechanisms and Their IMD Information Analogies -- Chapter 2.3 INFORMATION MODELING AND CONTROL OF SOME INDUSTRIAL TECHNOLOGY PROCESSES WITH COMPLEX SUPERIMPOSING PHENOMENA -- 2.3.1. Process Solidification and its Application in Casting Technology -- Example of the Technological Object's Code -- 2.3.2. Some Electrotechnological Processes -- Appendix. Additional Practical Results -- A.3.1. Control System in the Casing Technology -- The Automatic Control System Design and Development -- A.3.2. Control System in the Electrotechnology -- Chapter 2.4 AN ELEMENTARY INFORMATION MACRODYNAMIC MODEL OF A MARKET ECONOMIC SYSTEM -- 2.4.1. About Information Systems Modeling of a Modern Economy. The Objectives -- 2.4.2. An elementary Local Production System (LP) -- 2.4.3. An Information Model of a Local Market. 2.4.4. Managing the LP. A Bank and a Stock Market -- 2.4.5. Other Information Markets -- 2.4.6. Example -- 2.4.7. Summary -- Chapter 2.5 AN OUTLINE OF THE COMPUTER BASED METHODOLOGY -- 2.5.1. The Hierarchy of the Model's Micro-and Macrovariables and Their Identification -- 2.5.2.The Computer's Restoration of the IMD Model -- 2.5.3. The Structure of the IMD Software Package -- CONCLUSION -- REFERENCES -- References to chs. 1.1-1.6 -- References to ch. 1.7 -- References to ch. 1.8 -- References to ch. 1.9 -- References to ch. 2.1 -- References to ch. 2.2 -- References to ch. 2.3 -- References to ch. 2.4 -- Selected Author's Publication in Russian [R] (translated) -- ABOUT THE AUTHOR -- INDEX -- Blank Page.
9781614700920
Stochastic control theory.
Variational principles.
System analysis -- Mathematical models.
Electronic books.
QA402.37 -- .L47 2010eb
629.8/312
Information Path Functional and Informational Macrodynamics. - 1st ed. - 1 online resource (507 pages)
Intro -- INFORMATION PATH FUNCTIONAL AND INFORMATIONAL MACRODYNAMICS -- INFORMATION PATH FUNCTIONAL AND INFORMATIONAL MACRODYNAMICS -- CONTENTS -- ABSTRACT -- PREFACE -- ACKNOWLEDGMENTS -- INTRODUCTION -- PART 1. THE INFORMATION PATH FUNCTIONAL'S FOUNDATION -- Chapter 1.0 INTRODUCTION -- Chapter 1.1 THE INITIAL MATHEMATICAL MODELS* -- 1.1.1. Model of Microlevel Process -- 1.1.2. Model of the Macrolevel Process -- 1.1.3. The Feedback Equation-Control Law -- 1.1.4. Model of Programmable Trajectories (as a Task) at Microlevel -- 1.1.5. Model of Programmable Trajectories (as a Task) at the Macrolevel -- 1.1.6. The Equations in Deviations -- 1.1.7. Model of Disturbances -- 1.1.8. The Microlevel Process' Functional -- 1.1.9. The Jensen's Inequality for the Entropy Functional -- Chapter 1.2 DYNAMIC APPROXIMATION OF A RANDOM INFORMATION FUNCTIONAL AND THE PATH FUNCTIONAL -- 1.2.1. The Extremal Principle and the Problem Formulation -- 1.2.2. The Problem Solution. Information Path Functional -- 1.2.3. The Estimation of an Accuracy of the Probability's Approximation -- Chapter 1.3 THE VARIATION PROBLEM FOR THE INFORMATION PATH FUNCTIONAL AND ITS SOLUTION -- 1.3.1. The Problem Formulation -- 1.3.2. Solution to the Variation Problem -- 1.3.3. The Minimum Condition for the Microlevel Functional -- 1.3.4. The Optimal Control Synthesis -- 1.3.5. A Summary of the Information Path Functional Approach. The IPF invariants -- Chapter 1.4 THE INFORMATION SPACE DISTRIBUTED MACROMODELS DEVELOPED BY THE SOLUTIONS OF THE IPF VARIATION PROBLEM -- 1.4.1. Introduction -- 1.4.2. The Variation Problem for Space Distributed Macromodel -- 1.4.3. The Invariant Conditions at the Transformation of the Space Coordinates -- 1.4.4. The Parameters of the Space Transformation and the Distributed Macromodels. 1.4.5. The IPF Macromodel's Singular Points and the Singular Trajectories -- 1.4.6. The IPF Natural Variation Problem, Singular Trajectories, and The Field's Invariants for the IPF -- Chapter 1.5 THE COOPERATIVE INFORMATION MACROMODELS AND INFORMATION NETWORK -- 1.5.1. Introduction -- 1.5.2. The Time-Space Movement Toward the Macromodel's Cooperation -- 1.5.3. The Consolidation and Aggregation of the Model Processes. Forming an Information Network (IN) -- 1.5.4. The IN Dynamic Structure -- 1.5.5. Geometrical Structure of the Optimal Space Distributed Cooperative Macromodel (OPMC). The IN Geometrical Structure -- Chapter 1.6 THE IMD MODEL'S PHENOMENA AND INFORMATION CODE -- 1.6.1. The Model Time Course and the Evaluation of the Information Contributions into IN. The Triplet Genetic Code -- 1.6.2. The Model Information Geometry (IG), Its Specific, and the Structure -- 1.6.3. The Model Uncertainty Zone and Its Evaluation -- 1.6.4. Creation of the IN geometry and a Genetic Code of the Information Cellular Geometry -- 1.6.5. The Minimal Admissible Uncertainty and Its Connection to Physics -- 1.6.6. Information Structure of the model Double Spiral's (DSS) Control Mechanism -- 1.6.7. Examples of the DSS codes -- 1.6.8. A System's Harmony, Regularities, and the VP -- Chapter 1.7 THE MACRODYNAMIC AND COOPERATIVE INFORMATION COMPLEXITIES -- 1.7.1. Introduction -- 1.7.2. The Notion of Interactive and Cooperative Complexities and Their Information Measures -- 1.7.3. The Information Indicator of a Cooperative Complexity -- 1.7.4. Illustration of Arising of the Information Cooperative Complexity at Discrete Points of Applied Controls -- 1.7.5. The Complexity Invariant Measure in a Cooperative Dynamic Process -- 1.7.6. The IN Cooperative Mechanism with the Complexity Measure. 1.7.7. The Equations of the Spatial Information Cooperative Dynamics. Information Attraction and Complexity -- 1.7.8. Connection to Kolmogorov's Complexity -- Chapter 1.8 THE EVOLUTIONARY DYNAMICS AND THE INFORMATION LAW OF EVOLUTION -- 1.8.1. Introduction -- 1.8.2. The Equations Regularities and the Evolutionary Law -- 1.8.3. A Mechanism of an Enhancement of the Acceptable Mutations -- 1.8.4. The Conditions of the Model's Self-control, Adaptation, and Self-organization -- 1.8.5. The Evolution of the Model Invariants and a Potential Macroprocess' Cyclicity -- 1.8.6. Requirements for the Model Self-organization. The Results of Computer Simulations -- 1.8.7. Evaluation of Some Prognostic Parameters of the Evolutionary Dynamics. Example -- 1.8.8. Information Mechanism of Assembling the Node's Frequencies and Automatic Selection -- 1.8.9. The Functional Schema of the Evolutionary Informational Mechanisms. A Summary -- A Summary -- Chapter 1.9 THE PHYSICAL ANALOGIES RELATED TO THE INFORMATION PATH FUNCTIONAL -- 1.9.1. The Connection between the Information Path Functional (IPF) and the Kolmogorov's (K) Entropy of a Dynamic System, and the Relations to Physics -- 1.9.2. An IPF Analogy with the Feynman Path Functional in Quantum Mechanics and Informational Form of Schrödinger's Equation -- 1.9.3. About the Invariant Transformation of the Model Imaginary Eigenvalues and Information -- 1.9.4. The Superimposing Processes, Control and Asymmetry. The IMD Relation to Nonequilibrium Thermodynamics (NT) -- 1.9.5. About the Notion of a System -- PART 2.THE INFORMATION PATH FUNCTIONAL'SAND IMD'S APPLICATIONS -- Chapter 2.1 SOLUTION OF THE CONTROL PROBLEMS FOR A COMPLEX OBJECT -- 2.1.1. The Control Problems for a Complex Object -- 2.1.2. Solving the Identification Problem -- 2.1.2.1. The Identification of the Concentrated Object's Models. 2.1.2.2. The Identification of the Space Distributed Object's Models -- 2.1.3. Solving the Optimal Control Problem -- 2.1.3.1. A Joint Solution of the Optimal Control and Identification Problems. The Basic Results -- 2.1.3.2. The Procedure of the Joint Identification, Optimal Control, and Consolidation -- 2.1.3.3. Building the Object Cooperative Information Network -- Chapter 2.2 THE INFORMATION MODELING OF THE ENCODING-DECODING PROCESSES AT TRANSFORMATION OF BIOLOGICAL AND COGNITIVE INFORMATION -- 2.2.1. The Objective and Methodology -- 2.2.2. An Inner Information Structure of the IN with the Ranged and the Nonranged Sequences of the Starting Eigenvalues. The DSS Code -- Example of the Bio-process' Code -- 2.2.3. Mathematical Model of the IN with an Arbitrary Sequence of the Starting Eigenvalues -- 2.2.4. The Procedure of Encoding, Compression, Synthesis, and Decoding of the IN Information -- 2.2.5. Summarized Results -- 2.2.6. About Other Related Applications -- 2.2.7. The Connections between Some Physical Neuronal Functions and Mechanisms and Their IMD Information Analogies -- Chapter 2.3 INFORMATION MODELING AND CONTROL OF SOME INDUSTRIAL TECHNOLOGY PROCESSES WITH COMPLEX SUPERIMPOSING PHENOMENA -- 2.3.1. Process Solidification and its Application in Casting Technology -- Example of the Technological Object's Code -- 2.3.2. Some Electrotechnological Processes -- Appendix. Additional Practical Results -- A.3.1. Control System in the Casing Technology -- The Automatic Control System Design and Development -- A.3.2. Control System in the Electrotechnology -- Chapter 2.4 AN ELEMENTARY INFORMATION MACRODYNAMIC MODEL OF A MARKET ECONOMIC SYSTEM -- 2.4.1. About Information Systems Modeling of a Modern Economy. The Objectives -- 2.4.2. An elementary Local Production System (LP) -- 2.4.3. An Information Model of a Local Market. 2.4.4. Managing the LP. A Bank and a Stock Market -- 2.4.5. Other Information Markets -- 2.4.6. Example -- 2.4.7. Summary -- Chapter 2.5 AN OUTLINE OF THE COMPUTER BASED METHODOLOGY -- 2.5.1. The Hierarchy of the Model's Micro-and Macrovariables and Their Identification -- 2.5.2.The Computer's Restoration of the IMD Model -- 2.5.3. The Structure of the IMD Software Package -- CONCLUSION -- REFERENCES -- References to chs. 1.1-1.6 -- References to ch. 1.7 -- References to ch. 1.8 -- References to ch. 1.9 -- References to ch. 2.1 -- References to ch. 2.2 -- References to ch. 2.3 -- References to ch. 2.4 -- Selected Author's Publication in Russian [R] (translated) -- ABOUT THE AUTHOR -- INDEX -- Blank Page.
9781614700920
Stochastic control theory.
Variational principles.
System analysis -- Mathematical models.
Electronic books.
QA402.37 -- .L47 2010eb
629.8/312