Lie theory and control systems defined on spheres

It is shown that in constructing a theory for the most elementary class of control problems defined on spheres, some results from the Lie theory play a natural role. To understand controllability, optimal control, and certain properties of stochastic equations, Lie theoretic ideas are needed. The framework considered here is the most natural departure from the usual linear system/vector space problems which have dominated control systems literature. For this reason results are compared with those previously available for the finite dimensional vector space case

Application of system theory to power processing problems

The work in power processing is reported. Input-output models, and Lie groups in control theory are discussed along with the methods of analysis for time invariant electrical networks

Finite Controllability of Infinite-Dimensional Quantum Systems

Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is finite-dimensional and old results on controllability of systems defined on on Lie groups and quotient spaces provide most of what is needed insofar as controllability of non-dissipative systems is concerned. However, in an infinite-dimensional setting, controlling the evolution of quantum systems often presents difficulties, both conceptual and technical. In this paper we present a systematic approach to a class of such problems for which it is possible to avoid some of the technical issues. In particular, we analyze controllability for infinite-dimensional bilinear systems under assumptions that make controllability possible using trajectories lying in a nested family of pre-defined subspaces. This result, which we call the Finite Controllability Theorem, provides a set of sufficient conditions for controllability in an infinite-dimensional setting. We consider specific physical systems that are of interest for quantum computing, and provide insights into the types of quantum operations (gates) that may be developed.Comment: This is a much improved version of the paper first submitted to the arxiv in 2006 that has been under review since 2005. A shortened version of this paper has been conditionally accepted for publication in IEEE Transactions in Automatic Control (2009

Double bracket dissipation in kinetic theory for particles with anisotropic interactions

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double bracket approach (Double Bracket Vlasov, or DBV). The moments of the DBV equation lead to a nonlocal form of Darcy's law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double bracket kinetic equations is expressed as Lie-Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density--orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.Comment: 19 pages; no figures. Submitted to Proc. Roy. Soc.

Control of trapped-ion quantum states with optical pulses

We present new results on the quantum control of systems with infinitely large Hilbert spaces. A control-theoretic analysis of the control of trapped ion quantum states via optical pulses is performed. We demonstrate how resonant bichromatic fields can be applied in two contrasting ways -- one that makes the system completely uncontrollable, and the other that makes the system controllable. In some interesting cases, the Hilbert space of the qubit-harmonic oscillator can be made finite, and the Schr\"{o}dinger equation controllable via bichromatic resonant pulses. Extending this analysis to the quantum states of two ions, a new scheme for producing entangled qubits is discovered.Comment: Submitted to Physical Review Letter

Parental Influence on the Communicative Behaviors of Black Young Adults

This study examined communicative behaviors of Black young adults and how they were impacted by the relational dynamics of their parents. Data were collected from a convenience sample of 73 Black young adults 18-35 years of age. The survey instrument measured the students\u27 argumentative approach and avoidance behavior in interpersonal relationships. There were three directional hypotheses, but the data collected did not prove or disprove them. The findings revealed that the majority of respondents had parents that were still married. The results showed there to be no significant difference in argumentativeness between the together and strained groups. Verbal and physical abuse however, was found to be more prevalent in the strained group

Kinematically redundant robot manipulators

Research on control, design and programming of kinematically redundant robot manipulators (KRRM) is discussed. These are devices in which there are more joint space degrees of freedom than are required to achieve every position and orientation of the end-effector necessary for a given task in a given workspace. The technological developments described here deal with: kinematic programming techniques for automatically generating joint-space trajectories to execute prescribed tasks; control of redundant manipulators to optimize dynamic criteria (e.g., applications of forces and moments at the end-effector that optimally distribute the loading of actuators); and design of KRRMs to optimize functionality in congested work environments or to achieve other goals unattainable with non-redundant manipulators. Kinematic programming techniques are discussed, which show that some pseudo-inverse techniques that have been proposed for redundant manipulator control fail to achieve the goals of avoiding kinematic singularities and also generating closed joint-space paths corresponding to close paths of the end effector in the workspace. The extended Jacobian is proposed as an alternative to pseudo-inverse techniques

Internal consistency reliability and construct validity of the Attitude toward Muslim Proximity Index (AMPI): a measure of social distance

The Attitude toward Muslim Proximity Index (AMPI) is a six-item scale that uses tolerance to different degrees of social distance to assess prejudice towards Muslims. It was tested on 1777 teenage school children from northern England who indicated their religion as either 'Christian' or 'no religion', and demonstrated good internal reliability (Cronbach's alpha = .81). The index was higher among pupils who supported the views of the British National Party and among those who believed that British Muslims should adopt Western culture; but lower among those who knew Muslims or had Muslim friends. The AMPI is a useful measure of Islamophobic attitudes that does not rely on responses to specific events or on detailed knowledge of the Muslim religion

Network synthesis

A discussion, with numerous examples, on the application of state variable methods to network analysis and synthesis is reported. The state variable point of view is useful in the design of control circuits for regulators because, unlike frequency domain methods, it is applicable to linear and nonlinear problems. The reported are intended as an introduction to this theory