Preservation of controllability-observability in expanded systems

The result contributed by the article is that controllability-observability of an original continuous-time LTI dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices. This new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases, such as aggregations and restrictions, which enable such preservation only in certain special cases. A complete unrestricted transmission of these qualitative properties from the original controllable-observable system to its expansion is a basic requirement on the expansion/contraction process, mainly when controllers/observers are designed in expanded systems to be consequently contracted for implementation in initially given systems. An original system composed of two overlapped subsystems is adopted as a general prototype ease. A numerical example is suppliedPeer ReviewedPostprint (published version

Controllability-observability of expanded composite systems

The relation between original and expanded systems within the Inclusion Principle from the point of view of controllability–observability of both subsystems and composite systems is studied. It is proved that complementary matrices always exist ensuring that the subsystems and the overall expanded system are simultaneously controllable–observable. Two practically important large classes of complementary matrices are identified to offer results computationally attractive. First, the existence of complementary matrices ensuring controllability–observability of decoupled subsystems is proved. Then, using this result, the same property is proved for the composite expanded system.Peer ReviewedPostprint (published version

A design procedure for overlapped guaranteed cost controllers

© 2008 the authors. This work has been accepted to IFAC for publication under a Creative Commons Licence CC-BY-NC-NDIn this paper a quadratic guaranteed cost control problem for a class of linear continuous-time state-delay systems with norm-bounded uncertainties is considered. We will suppose that the systems are composed by two overlapped subsystems but the results can be easily extended to any number of subsystems. The main objective is to design overlapping guaranteed cost controllers with tridiagonal gain matrices for these kind of systems by using a linear matrix inequality (LMI) approach. With this idea in mind, we present a design strategy to reduce the computational burden and to increase the feasibility in the LMI problem. In this context, the use of so-called complementary matrices play an important role. A simple example to illustrate the advantages achieved by using the proposed method is supplied.Peer ReviewedPostprint (published version

Overlapping guaranteed cost control for uncertain continuous-time delayed systems

Overlapping guaranteed cost control design problem is solved for a class of linear continuous-time uncertain systems with state as well as control delays. Unknown arbitrarily time-varying uncertainties with known bounds are considered. A point delay is supposed. Conditions preserving closed-loop systems expansion-contraction relations including the identical bounds of performance indices are proved. A linear matrix inequality (LMI) delay independent procedure is used for control design in the expanded space. The results are specialized on the overlapping decentralized control design. A numerical illustrative example is supplied.Peer ReviewedPostprint (published version

Quantum Gravity and Taoist Cosmology: Exploring the Ancient Origins of Phenomenological String Theory

In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (phenomenological) action pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature’s fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory entails the dialectical interplay of symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper closes by considering the role of the analyst per se in the further evolution of the cosmos

Optimal complementary matrices in systems with overlapping decomposition: a computational approach

© 2006 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The paper deals with linear quadratic (LQ) optimal control of linear time-invariant (LTI) systems which are decomposed into overlapped subsystems. A mathematical framework (inclusion principle) is available to formalize different structural properties and relations between the initial and the expanded systems, in which the so called complementary matrices play an important role. Up to now, only the structure and conditions on these matrices have been studied in the literature, but not the way to obtain their numerical values systematically. This paper presents a computational approach to select complementary matrices, which can be useful for a practical use of overlapping decompositions. The specific objective is to obtain the complementary matrices such that the quadratic performance for the expanded optimal control problem is minimum. An example is supplied to illustrate the use of the proposed algorithm.Peer ReviewedPostprint (published version

Semi-decentralized Strategies in Structural Vibration Control

In this work, the main ideas involved in the design of overlapping and multi-overlapping controllers via the Inclusion Principle are discussed and illustrated in the context of the Structural Vibration Control of tall buildings under seismic excitation. A detailed theoretical background on the Inclusion Principle and the design of overlapping controllers is provided. Overlapping and multi-overlapping LQR controllers are designed for a simplified five-story building model. Numerical simulations are conducted to asses the performance of the proposed semi-decentralized controllers with positive results

Control strategies for large-scale structural systems: high-raise buildings and multi-building systems

This work presents an overview of some recent developments made by the authors in the field of vibrational control of largescale structural systems subject to seismic excitations. The structural systems under consideration are classified in two broad categories: (i) high-rise buildings, and (ii) multi-building systems. When dealing with high-rise buildings, the inclusion principle can be used as a powerful mathematical tool to design semi-decentralized state-feedback and output-feedback controllers. In the case of multi-building systems, a passive-active structural vibration control for adjacent buildings consisting in a combination of passive linking elements with an active decentralized control system is designed. Numerical simulations show that the overall active-passive control system achieves excellent results when the active control system works; in case of full or partial failure of the active control system, a remarkable reduction in the vibrational response is guaranteed by the passive linking elements. Three different building models serve as example to clarify the theoretical results and, at the same time, to show the advantages of the proposed control approachesPostprint (published version

Fast sampling control of a class of differential linear repetitive processes

Repetitive processes are a distinct class of 2D linear systems of practical and theoretical interest. Most of the available control theory for them is for the case of linear dynamics and focuses on systems theoretic properties such as stability and controllability/observability. This paper uses an extension of standard, or 1D, feedback control schemes to control a physically relevant sub-class of these processes

A quantum-mechanical perspective on linear response theory within polarizable embedding

The derivation of linear response theory within polarizable embedding is carried out from a rigorous quantum-mechanical treatment of a composite system. Two different subsystem decompositions (symmetric and nonsymmetric) of the linear response function are presented, and the pole structures as well as residues of the individual terms are analyzed and discussed. This theoretical analysis clarifies which form of the response function to use in polarizable embedding, and we highlight complications in separating out subsystem contributions to molecular properties. For example, based on the nonsymmetric decomposition of the complex linear response function, we derive conservation laws for integrated absorption cross sections, providing a solid basis for proper calculations of the intersubsystem intensity borrowing inherent to coupled subsystems and how that can lead to negative subsystem intensities. We finally identify steps and approximations required to achieve the transition from a quantum-mechanical description of the composite system to polarizable embedding with a classical treatment of the environment, thus providing a thorough justification for the descriptions used in polarizable embedding models