Stabilization Control of the Differential Mobile Robot Using Lyapunov Function and Extended Kalman Filter

This paper presents the design of a control model to navigate the differential mobile robot to reach the desired destination from an arbitrary initial pose. The designed model is divided into two stages: the state estimation and the stabilization control. In the state estimation, an extended Kalman filter is employed to optimally combine the information from the system dynamics and measurements. Two Lyapunov functions are constructed that allow a hybrid feedback control law to execute the robot movements. The asymptotical stability and robustness of the closed loop system are assured. Simulations and experiments are carried out to validate the effectiveness and applicability of the proposed approach.Comment: arXiv admin note: text overlap with arXiv:1611.07112, arXiv:1611.0711

Fine strand-like structure in the solar corona from MHD transverse oscillations

Current analytical and numerical modelling suggest the existence of ubiquitous thin current sheets in the corona that could explain the observed heating requirements. On the other hand, new high resolution observations of the corona indicate that its magnetic field may tend to organise itself in fine strand-like structures of few hundred kilometres widths. The link between small structure in models and the observed widths of strand-like structure several orders of magnitude larger is still not clear. A popular theoretical scenario is the nanoflare model, in which each strand is the product of an ensemble of heating events. Here, we suggest an alternative mechanism for strand generation. Through forward modelling of 3D MHD simulations we show that small amplitude transverse MHD waves can lead in a few periods time to strand-like structure in loops in EUV intensity images. Our model is based on previous numerical work showing that transverse MHD oscillations can lead to Kelvin-Helmholtz instabilities that deform the cross-sectional area of loops. While previous work has focused on large amplitude oscillations, here we show that the instability can occur even for low wave amplitudes for long and thin loops, matching those presently observed in the corona. We show that the vortices generated from the instability are velocity sheared regions with enhanced emissivity hosting current sheets. Strands result as a complex combination of the vortices and the line-of-sight angle, last for timescales of a period and can be observed for spatial resolutions of a tenth of loop radius.Comment: Accepted for publication in ApJ

On Rotations as Spin Matrix Polynomials

Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an alternate derivation. The central factorial numbers play key roles in both derivations.Comment: 6 Figures. References updated in v2, along with some editing of tex

Muskrats on tidal marshes of Dorchester County

This bulletin reports, in a non-technical manner, investigations on the Virginia muskrat, prevalent in Maryland, from July, 1949 to June, 1951

Advice to a Princess: the literary articulation of a religious, political and cultural programme for Mary Queen of Scots, 1562

No abstract available

The Renaissance uses of a medieval Seneca: murder, stoicism, and gender in the marginalia of Glasgow Hunter 297

Examines, transcribes, and annotates the extensive marginalia in a medieval manuscript of Seneca\u27s tragedies made by Sir William Sinclair of Mey (1582-1643), exploring some of the links between the original text, the marginal additions, the events of Sinclair\u27s life, and the culture of Renaissance Scotland

Coexistence of fish species with strongly similar life histories - population dynamical feedback forces species to pick sides

Fish generally grow several orders of magnitude between the larval and adult stage. Many ecological properties of organisms are related to body size, and hence small fish often have very different ecological roles than large conspecifics. This also implies that omnivory, the feeding on more than one trophic level by individuals of the same species, is a common phenomenon in fish. Intraguild predation is omnivory in its simplest form, where two species compete for the same resource, but one of the species can also eat its competitor. In models, persistence of both species in such a configuration is difficult to obtain. In marine fish communities however, it is observed routinely. One way in which persistence of omnivorous species can be established is by incorporating it as an ontogenetic diet shift, where small individuals of both species compete, and large individuals of one can feed on the small individuals of the others species. We show in this study that this mechanism can not only lead to persistence of a single omnivorous species, but also to persistence of multiple omnivorous species. This is possible given that the adults have sufficiently different diets. It is shown that, while adults of both species can feed both on small competitors or on the basic resource, due to the population dynamical feedback, one species will in practice act as a predator, while the other acts as prey. This way, a system with two omnivores in practice persists as a tritrophic system. Which of the species assumes which role depends on the specific community characteristics. We show here that by incorporating complex size-dependent feeding relationships in food webs, many more species may be able to coexist than is possible based on either species-level considerations or size spectrum models which do incorporate within-population size differences, but relate diet only to individual body size irrespective of species identity. The mechanism underlying our result may be part of the explanation why fish species with seemingly similar life histories do coexist in marine ecosystems