Synergetics of Measurement, Prediction and Control

1. Introduction.- 1.1 Goal.- 1.2 Relation to Other Scientific Fields.- 1.3 Plan of the Monograph.- 2. A Quantitative Description of Nature.- 2.1 Synergetics of Natural Phenomena.- 2.2 A Description of Nature.- 2.3 Fundamentals of Quantitative Description.- 2.4 Fundamentals of Physical Laws.- 2.5 The Random Character of Physical Variables.- 2.6 Expression of Natural Laws by Differential Equations.- 2.7 Methods of Empirical Modeling.- 2.7.1 The Role of Models.- 2.7.2 Piecewise Linear Models of Empirical Natural Laws.- 2.8 Introduction to Modeling by Neural Networks.- 2.8.1 Functional Properties of a Neuron.- 2.8.2 Empirical Modeling by a Perceptron.- 3. Transducers.- 3.1 The Role of Sensors and Actuators.- 3.2 Sensors and Actuators of Biological Systems.- 3.2.1 Performance Characteristics of Biological Sensors.- 3.2.2 Structure of Biological Sensors.- 3.2.3 Transduction Characteristics of Biological Sensors.- 3.3 Operational Characteristics of Transducers.- 3.3.1 Transducer Classification.- 3.3.2 Transduction Characteristics.- 3.3.3 Sensor Loading Effects.- 3.3.4 Transducer Field Characteristics.- 3.4 Fabricated Transducers.- 3.4.1 Microsensors and Integrated Sensors.- 3.4.2 Synthetic Bio-sensors and Neurobiology.- 3.5 Transducers in Intelligent Measurement Systems.- 3.6 Future Directions in Transducer Evolution.- 4. Probability Densities.- 4.1 Estimation of Probability Density.- 4.1.1 Parzen Window Approach.- 4.1.2 An Optimal Selection of the Window Function.- 4.1.3 Nearest Neighbor and Maximal Self-Consistency Approach.- 4.1.4 The Self-Consistent Method in the Multivariate Case..- 4.1.5 Numerical Examples.- 4.1.6 Conclusions About Filtering of the Empirical PDF.- 5. Information.- 5.1 Some Basic Ideas.- 5.2 Entropy of Information.- 5.3 Properties of Information Entropy.- 5.4 Relative Information.- 5.4.1 Information of Continuous Distributions.- 5.4.2 Information Gain from Experiments.- 5.5 Information Measure of Distance Between Distributions.- 6. Maximum Entropy Principles.- 6.1 Gibbs Maximum Entropy Principle.- 6.2 The Absolute Maximum Entropy Principle.- 6.3 Quantization of Continuous Probability Distributions.- 6.3.1 Quadratic Measure of Discrepancy Between Distributions.- 6.3.2 Information Divergence as a Measure of Discrepancy.- 6.3.3 Vector Quantization and Reconstruction Measure of Discrepancy.- 7. Adaptive Modeling of Natural Laws.- 7.1 Probabilistic Modeler of Natural Laws.- 7.2 Optimization of Adaptive Modeler Performance.- 7.3 Stochastic Approach to Adaptation Laws.- 7.4 Stochastic Adaptation of a Vector Quantizer.- 7.5 Perturbation Method of Adaptation.- 7.6 Evolution of an Optimal Modeler and Perturbation Method.- 7.7 Parametric Versus Non-Parametric Modeling.- 8. Self-Organization and Formal Neurons.- 8.1 Optimal Storage of Empirical Information in Discrete Systems.- 8.2 Adaptive Vector Quantization and Topological Mappings.- 8.3 Self-Organization Based on the Absolute Maximum-Entropy Principle.- 8.4 Derivation of a Generalized Self-Organization Rule.- 8.5 Numerical Examples of Self-Organized Adaptation.- 8.6 Formal Neurons and the Self-Organization Process.- 9. Modeling by Non-Parametric Regression.- 9.1 The Problem of an Optimal Prediction.- 9.2 Parzen’s Window Approach to General Regression.- 9.3 General Regression Modeler, Feedback and Recognition.- 9.4 Application of the General Regression Modeler.- 9.4.1 Empirical Modeling of Acoustic Phenomena.- 9.4.2 Prediction of the Seismic Capacity of Walls.- 9.4.3 Modeling of a Periodontal Disease Healing Process.- 10. Linear Modeling and Invariances.- 10.1 Relation Between Parametric Modeling and Invariances.- 10.2 Generalized Linear Regression Model.- 10.2.1 An Example of Iterative Determination of a Linear Regression Model.- 10.3 Sequential Adaptation of Linear Regression Model.- 10.4 Transition from the Cross- to Auto-Associator.- 10.4.1 Application of the Auto-Associator to Analysis of Ultrasonic Signals.- 11. Modeling and Forecasting of Chaotic Processes.- 11.1 Modeling of Chaotic Processes.- 11.2 Examples of Chaotic Process Forecasting.- 11.3 Forecasting of Chaotic Acoustic Emission Signals.- 11.4 Empirical Modeling of Non-Autonomous Chaotic Systems.- 11.4.1 Example of Economic Time-Series Forecasting.- 11.5 Cascade Modeling of Chaos Generators.- 11.5.1 Numerical Experiments.- 11.5.2 Concluding Remarks.- 12. Modeling by Neural Networks.- 12.1 From Biological to Artificial Neural Networks.- 12.1.1 Basic Blocks of Neural Networks and Their Dynamics.- 12.2 A Linear Associator.- 12.3 Multi-layer Perceptrons and Back-Propagation Learning.- 12.4 Radial Basis Function Neural Networks.- 12.5 Equivalence of a Radial Basis Function NN and Perceptrons.- 13. Fundamentals of Intelligent Control.- 13.1 Introduction.- 13.2 Basic Tasks of Intelligent Control.- 13.2.1 Empirical Description of a Controlled System.- 13.2.2 General Identification by Non-Parametric Modeling.- 13.3 The Tracking Problem.- 13.4 Cloning.- 13.5 An Empirical Approach to Optimal Control.- 13.5.1 The Theoretical Problem of Optimal Control.- 13.5.2 Experimental Description of Plant Performance and Optimal Control.- 13.5.3 Design of an Intelligent Optimal Controller.- 13.5.4 The Influence of the Environment on Optimal Control.- 13.5.5 The Problem of Phase Space Exploration.- 13.5.6 Numerical Simulations of Optimal Control.- 13.5.7 Summary and Conclusions.- 14. Self-Control and Biological Evolution.- 14.1 Modeling of Natural Phenomena by Biological Systems.- 14.2 Joint Modeling of Organism and Environment.- 14.3 An Operational Description of Consciousness.- 14.4 The Fundamental Problem of Evolution.- A. Fundamentals of Probability and Statistics.- A.1 Sample Points, Sample Space, Events and Relations.- A.2 Probability.- A.3 Random Variables and Probability Distributions.- A.4 Averages and Moments.- A.5 Random Processes.- A.6 Sampling, Estimation and Statistics.- B. Fundamentals of Deterministic Chaos.- B.1 Instability of Chaotic Systems.- B.2 Characterization of Strange Attractors.- B.3 Experimental Characterization of Chaotic Phenomena.- References.