Abstract: Given a stress-free system as a perfect crystal with points or atoms ordered in a three dimensional lattice in the Euclidean reference space, any defect, external force or heterogeneous temperature change in the material connection that induces stress on a previously stress-free configuration changes the equilibrium configuration. A material has stress in a reference which does not agree with the intrinsic geometry of the material in the stress-free state. By stress we mean forces between parts when we separate one part from another (tailing the system), the stress collapses to zero for any part which assumes new configurations. Now the problem is that all the new configurations of the parts are incompatible with each other. This means that close loop in the earlier configuration now is not closed and that the two paths previously joining the same two points now join different points from the same initial point so the final point is path dependent. This phenomenon is formally described by the commutators of derivatives in the new connection of the stress-free parts of the system under the control of external currents. This means that we lose the integrability property of the system and the possibility to generate global coordinates. The incompatible system can be represented by many different local references or Cartan moving Euclidean reference, one for any part of the system that is stress-free. The material under stress when is free assumes an equilibrium configuration or manifold that describes the intrinsic “shape” or geometry of the natural stress—the free state of the material. Therefore, we outline a design system by geometric compensation as a prototypical constructive operation.
Abstract: We survey some of the rich history of control over the past century with a focus on the major milestones in adaptive systems. We review classic methods and examples in adaptive linear systems for both control and observation/identification. The focus is on linear plants to facilitate understanding, but we also provide the tools necessary for many classes of nonlinear systems. We discuss practical issues encountered in making these systems stable and robust with respect to additive and multiplicative uncertainties. We discuss various perspectives on adaptive systems and their role in various fields. Finally, we present some of the ongoing research and expose problems in the field of adaptive control.
Abstract: Modern general system theory proposed a holistic integrative approach based on input-state-output dynamics as opposed to the traditional reductionist detail based approach. Information complexity and uncertainty required a fuzzy system theory, based on fuzzy sets and fuzzy logic. While successful in dealing with analysis, synthesis and control of technical engineering systems, general system theory and fuzzy system theory could not fully deal with humanistic and human-like intelligent systems which combine technical engineering components with human or human-like components characterized by their cognitive, emotional/motivational and behavioral/action levels of operation. Such humanistic systems are essential in artificial intelligence, cognitive and behavioral science applications, organization management and social systems, man-machine systems or human factor systems, behavioral knowledge based economics and finance applications. We are introducing here a “postmodern fuzzy system theory” for controlled state dynamics and output fuzzy systems and fuzzy rule based systems using our earlier postmodern fuzzy set theory and a Kabbalah possible worlds model of modal logic and semantics type. In order to create a postmodern fuzzy system theory, we “deconstruct” a fuzzy system in order to incorporate in it the cognitive, emotional and behavioral actions and expressions levels characteristic for humanistic systems. Kabbalah offers a structural, fractal and hierarchic model for integrating cognition, emotions and behavior. We obtain a canonic deconstruction for a fuzzy system into its cognitive, emotional and behavioral fuzzy subsystems.
Abstract: Some observations are presented starting with the well-known article by Vladimir Fock “Quantum Physics and Philosophical Problems”, published in 1971. In this article, which summarizes for Western readers a long and complicated reflection of the foundations of quantum mechanics (QM), Fock illustrates his “minimal” interpretation of this theory. By minimal, we mean that it only uses concepts related to the operational aspects of the measurement procedures, avoiding any mention of definite quantum ontologies (Bell’s beables). It is argued that, by taking into account the time reversal invariance of the microscopic processes and introducing the notion of irreversibility in an appropriate manner, Fock’s description becomes an anticipation of the “transaction” notion introduced by Cramer a decade later. So, the concept of “collapse” does retain the features of a QM “freak” postulate to become a new way to look at the elementary quantum processes.
Abstract: Different accounts have been given in order to face the problem of the emergence of musical consonance and dissonance. Getting a more adequate comprehension of such phenomenology may require a systemic view to integrate such multidimensionality into a unitary picture in which every partial solution enlightens a particular aspect of the very same problem. Such a systemic viewpoint shifts the focus from different explanations to analytic dimensions that seem to be embedded in music perception. Taking into consideration these dimensions means understanding consonance and dissonance in an embodied context, in which arithmetic, physics, psychology and physiology are part of a complex anddynamic process of understanding, which is not reducible to any privileged explanatory level.
Abstract: A system is something that can be separated from its surrounds, but this definition leaves much scope for refinement. Starting with the notion of measurement, we explore increasingly contextual system behaviour and identify three major forms of contextuality that might be exhibited by a system: (1) between components; (2) between system and experimental method; and (3) between a system and its environment. Quantum theory is shown to provide a highly useful formalism from which all three forms of contextuality can be analysed, offering numerous tests for contextual behaviour, as well as modelling possibilities for systems that do indeed display it. I conclude with the introduction of a contextualised general systems theory based on an extension of this formalism.