Stable observer-based trajectory controller for asymptotic model matching of a rigid robot

This paper considers a control problem that requires the design of an observed-based compensator in order to guarantee the asymptotic convergence of the output (namely, the joint generalized coordinates of ann-degree of freedom robot) to a corresponding output produced by a linear reference model. It is shown that, for a model having a relative degree vector {r ₁, ...,r _n}, withr _i 2, it is possible to determine a controller-observer yielding a robot output that converges exponentially to the desired model output. Moreover, the combined system comprising the plant and the controller is internally stable in the semiglobal sense. The solution to the standard trajectory-following problem in robotics is obtained as a simplified case of the underlying model matching problem. While the controller-observer is nonlinear, its dynamic part is linear time-varying; in addition, the construction does not assume a priori the knowledge or even the existence of an upper bound to the model state vector.This research was supported in part by the Paul Ivanier Center for Robotics Research and Production Management, Ben Gurion University of the Negev, Beer Sheva, Israel.The authors wish to thank Evgany Landau from the Department of Electrical and Computer Engineering, Ben Gurion Univeersity of the Negev, for designing and performing the computer simulation.     

The Geometry of Cauchy's Fluxes

A formulation of the Cauchy theory for balance laws of scalar valued quantities is considered from a general geometric point of view. It is assumed only that the ambient space is an orientable m-dimensional manifold. The analog of the usual flux vector field is an (m−1)-differential form. Both the Cauchy theorem and differential version of the balance laws are formulated in this context. Accepted December 9, 1999?Published online July 12, 2000     

Holographic solitons

We propose a new kind of an optical spatial soliton: the holographic soliton. This soliton consists of two mutually coherent field components that interfere, induce a periodic change in the refractive index, and simultaneously are Bragg diffracted from the grating. Holographic solitons are formed when the broadening tendency of diffraction is balanced by phase modulation that is due to Bragg diffraction from the induced grating. Holographic solitons are solely supported by cross-phase modulation arising from the induced grating, not involving self-phase modulation at all.     

Optical parametric oscillation in soliton-induced waveguides

We demonstrate experimentally an optical parametric oscillator constructed in a waveguide induced by a photorefractive spatial soliton and show that the pumping threshold is reduced considerably.     

Photorefractive solitons and light-induced resonance control in semiconductor CdZnTe

We demonstrate the formation of (1+1) - and (2+1) -dimensional solitons in photorefractive CdZnTe:V, exploiting the intensity-resonant behavior of the space-charge field. We control the resonance optically, facilitating a 10-mus soliton formation times with very low optical power.     

Self-regulated complexity in cultured neuronal networks

New quantified observables of complexity are identified and utilized to study sequences (time series) recorded during the spontaneous activity of different size cultured networks. The sequence is mapped into a tiled time-frequency domain that maximizes the information about local time-frequency resolutions. The sequence regularity is associated with the domain homogeneity and its complexity with its local and global variations. Shuffling the recorded sequence lowers its complexity down to artificially constructed ones. The new observables are utilized to identify self-regulation motifs in observed complex network activity.     

Two-dimensional higher-band vortex lattice solitons

We study self-localized second-band vortex states in two-dimensional photonic lattices and find stable ring solitons whose phase forms an array of counterrotating vortices. We also identify composite solitons in which a second-band vortex is jointly trapped with a mode arising from the first band and study their stability. When such a composite entity is unstable, it disintegrates while exchanging angular momentum between its constituents, eventually stabilizing into another form of composite soliton.     

Incoherent matter-wave solitons and pairing instability in an attractively interacting Bose-Einstein condensate

The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.