Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers

Automated Coronal Hole Identification via Multi-Thermal Intensity Segmentation

Coronal holes (CH) are regions of open magnetic fields that appear as dark areas in the solar corona due to their low density and temperature compared to the surrounding quiet corona. To date, accurate identification and segmentation of CHs has been a difficult task due to their comparable intensity to local quiet Sun regions. Current segmentation methods typically rely on the use of single EUV passband and magnetogram images to extract CH information. Here, the Coronal Hole Identification via Multi-thermal Emission Recognition Algorithm (CHIMERA) is described, which analyses multi-thermal images from the Atmospheric Image Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) to segment coronal hole boundaries by their intensity ratio across three passbands (171 \AA, 193 \AA, and 211 \AA). The algorithm allows accurate extraction of CH boundaries and many of their properties, such as area, position, latitudinal and longitudinal width, and magnetic polarity of segmented CHs. From these properties, a clear linear relationship was identified between the duration of geomagnetic storms and coronal hole areas. CHIMERA can therefore form the basis of more accurate forecasting of the start and duration of geomagnetic storms

The Illawarra at Work: A Summary of the Major Findings of the Illawarra Regional Workplace Industrial Relations Survey

This paper summarises the main results of the Illawarra Regional Workplace Industrial Relations Survey (IRWIRS). The data is unique in that it provides the only comprehensive and statistically reliable source of information about workplace employee relations at the regional level in Australia, and compares regional patterns with national trends. The data collected relates to industrial relations indicators, workplace ownership, market conditions, management organisation and decision- making in the workplace, among other things. The results reveal a positive pattern of employment relations in the Illawarra, distinctive in many respects from national trends.Illawarra Regional Workplace Industrial Relations Survey, workplace employee relations, Australia

Accretion disk reversal and the spin-up/spin-down of accreting pulsars

We numerically investigate the hydrodynamics of accretion disk reversal and relate our findings to the observed spin-rate changes in the accreting X-ray pulsar GX~1+4. In this system, which accretes from a slow wind, the accretion disk contains two dynamically distinct regions. In the inner part viscous forces are dominant and disk evolution occurs on a viscous timescale. In the outer part dynamical mixing of material with opposite angular momentum is more important, and the externally imposed angular momentum reversal timescale governs the flow. In this outer region the disk is split into concentric rings of material with opposite senses of rotation that do not mix completely but instead remain distinct, with a clear gap between them. We thus predict that torque reversals resulting from accretion disk reversals will be accompanied by minima in accretion luminosity.Comment: 13 pages, 7 figures, accepted for publication in Ap

Chemotactic Collapse and Mesenchymal Morphogenesis

We study the effect of chemotactic signaling among mesenchymal cells. We show that the particular physiology of the mesenchymal cells allows one-dimensional collapse in contrast to the case of bacteria, and that the mesenchymal morphogenesis represents thus a more complex type of pattern formation than those found in bacterial colonies. We finally compare our theoretical predictions with recent in vitro experiments

Fluctuations and stability in front propagation

Propagating fronts arising from bistable reaction-diffusion equations are a purely deterministic effect. Stochastic reaction-diffusion processes also show front propagation which coincides with the deterministic effect in the limit of small fluctuations (usually, large populations). However, for larger fluctuations propagation can be affected. We give an example, based on the classic spruce-budworm model, where the direction of wave propagation, i.e., the relative stability of two phases, can be reversed by fluctuations.Comment: 5 pages, 5 figure

Nonholonomic systems and exponential convergence: some analysis tools

In this paper the authors make a contribution to the analysis of nonholonomic systems with exponential rates of convergence. A key idea is the use of control laws which render the closed loop system homogeneous with respect to a dilation. The analysis is applied to nonholonomic systems in power form and consists of two steps. The first step is a reduction to an invariant set and then the application of an averaging result. The averaging theorem is a stability result for C^0 homogeneous order zero vector fields

Experiments in exponential stabilization of a mobile robot towing a trailer

Applies some previously developed control laws for stabilization of mechanical systems with non-holonomic constraints to an experimental system consisting of a mobile robot towing a trailer. The authors verify the applicability of various control laws which have appeared in the recent literature, and compare the performance of these controllers in an experimental setting. In particular, the authors show that time-periodic, non-smooth controllers can be used to achieve exponential stability of a desired equilibrium configuration, and that these controllers outperform smooth, time-varying control laws. The authors also point out several practical considerations which must be taken into account when implementing these controllers