دانلود کتاب Information Path Functional and Informational Macrodynamics

The book subject is mathematical formalism, describing the creation of the dynamic and information regularities from stochastics.The formalism is based on the introduction of an informational path functional, defined on trajectories of a controlled random process, and the solution of variation problem for this novel functional.The solution provides both the information dynamic model of a random process and the model of optimal control. This allows building a two-level information model with a random process at the microlevel and a dynamic process at macrolevel. Considering a variation principle (VP) as a mathematical form that expresses some regularity, it is assumed that the VP extremals, represented by the solutions of the above dynamic model, describe a movement possessing these regularities. Such an approach has been used by R. P. Feynman, who introduced the functional on trajectories of an electron’s movement and applied the variation principle for this path functional to obtain the equations of quantum mechanics. Feynman’s path functional is defined on the dynamic trajectories and has not been applied to random trajectories of a controlled process.Table of Contents:PrefaceIntroductionPart 1. The information path functional’s foundation, pp. 1-3321.0. Introduction1.1. The initial mathematical models1.1.1. Model of the microlevel process1.1.2. Model of the macrolevel process1.1.3. The feedback equation-control law1.1.4. Model of the programmable trajectories (as a task) at microlevel1.1.5. Model of the programmable trajectories (as a task) at the macrolevel1.1.6. The equations in deviations1.1.7. Model of disturbances1.1.8. The microlevel process’ functional1.1.9. The Jensen inequality for entropy functional1.2. Dynamic approximation of a random information functional and the path functional1.2.1. The extremal principle and the problem formulation1.2.2. The problem solution. Information path functional1.2.3. The estimation of an accuracy of the probability’s approximation1.3. Variation problem for the information path functional and its solution1.3.1. The problem statements1.3.2. Solution to the variation problem1.3.3. A minimum condition for the microlevel’s functional1.3.4. The optimal control synthesis1.3.5. A summary of the information path functional approach and IMD1.4. The IMD information space distributed macromodels1.4.0. Introduction1.4.1. The variation problem for space distributed macromodel1.4.2. The invariant conditions at the transformation of the space coordinates1.4.3. The parameters of the space transformation and the distributed macromodels1.4.4. The IMD macromodel’s singular points and the singular trajectories1.4.5. The IPF natural variation problem, singular trajectories, and the field’s invariants.1.5. The cooperative information macromodels and information network1.5.1. The time-space movement toward the macromodel's cooperation1.5.2. The consolidation of the model’s processes in a cooperative information network (IN)1.5.3. The IN dynamic structure1.5.4. Geometrical structure of the optimal space distributed cooperative macromodel (OPMC). The IN’s geometric structure1.6. The IMD model’s phenomena and information code1.6.1. The model’s time course and the evaluation of the information contributions into IN. The triplet’s genetic code1.6.2. The model’s information geometry (IG), its specific, and the structure1.6.3. The mode’s uncertainty zone and its evaluation1.6.4. Creation of the IN’s geometry and genetic code of the information cellular geometry1.6.5. The minimal admissible uncertainty and its connection to physics1.6.6 Information structure of the double spiral (DSS) control mechanism1.6.7. Examples of the DSS codes1.6.8. A system’s harmony, regularities, and the VP1.7. The macrodynamic and cooperative complexities1.7.0. Introduction1.7.1. The notion of interactive and cooperative complexities and the information measures1.7. 2. The information indicator of a cooperative complexity1.7.3. Illustration of arising of the information cooperative complexity at discrete points of applied controls1.7.4. The MC complexity invariant measure in a cooperative dynamic process1.7.5. The IN’s cooperative mechanism with the MC complexity’s measures1.7.6. The equations of the spatial information cooperative dynamics. Information attraction and complexity1.8. The regularities of evolutionary dynamics and the information law of evolution1.8.0. Introduction1.8.1. The equations regularities and the evolutionary law1.8.2. A mechanism of an enhancement of the acceptable mutations1.8.3. The conditions of the model’s self-control, adaptation, and self-organization1.8.4. The evolution of the model’s invariants and a potential the macroprocess’ cyclicity1.8.5. Requirements for the model’s self–organization. The results of computer simulations1.8.6. Evaluation of some prognosis parameters of the evolutionary dynamics. Example1.8.7. Information mechanism of assembling the node's frequencies and automatic selection1.8.8. The functional schema of the evolutionary informational mechanisms1.9. The physical analogies related to the information path functional1.9.1. The connection between the information path functional (PF) 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 Mechanics1.9.3. About the invariant transformation of the model's imaginary eigenvalues1.9.4. The superimposing processes, control, and asymmetry. The IMD relation to Nonequilibrium Thermodynamics (NT)Part 2. The information path functional’s and IMD’s applications, pp. 335-4712.1. Solution of the control problems for a complex object2.1.1. The control problems for a complex object2.1.2. Solving the identification problem2.1.2.1. The identification of the concentrated object's models2.1.2.2. The identification of the space distributed object's models2.1.3. Solving the optimal control problem2.1.3.1. A joint solution of the optimal control and identification problems. The basic results2.1.3.2. The procedure of the joint identification, optimal control, and consolidation2.1.3.3. Building the object’s cooperative information network2.2. The information modeling of some biological and cognitive processes2.2.0. The objective and methodology2.2.1. An inner information structure of the IN with the ranged and the nonranged sequences of the starting eigenvalues. The DSS code.2.2.2 Mathematical Model of the IN with an arbitrary sequence of the starting eigenvalues2.2.3. The procedure of encoding, compression, synthesis, and decoding the IN's information2.2.4 Summarized results2.2.5. About other related applications2.2.6. The connections between some physical neuronal functions and mechanisms and their IMD information analogies2.3. Information modeling and control of some industrial technology processes with complex superimposing phenomena2.3.1. Process solidification and its application in casting technology2.3.2. Some electrotechnological processes2.4. An elementary information macrodynamic model of a market economic system2.4.1. About Information Systems Modeling of a Modern Economy. The objectives2.4.2. An Elementary Local Production System (LP)2.4.3. An Information Model of a Local Market2.4.4. Managing the LP. A Bank and a Stock Market2.4.5. Other Information Markets2.4.6. Example2.4.7. Summary2.5. An outline of the computer based methodology2.5.1. The hierarchy of the model’s micro-and macrovariables and their identification2.5.2. The computer’s restoration of the IMD model2.5.3. The structure of the IMD software packageConclusionReferencesIndex