Consistent Approximations for the Optimal Control of Constrained Switched Systems

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In this paper, we devise an algorithm for the computation of an optimal control of constrained nonlinear switched dynamical systems. The control parameter for such systems include a continuous-valued input and discrete-valued input, where the latter corresponds to the mode of the switched system that is active at a particular instance in time. Our approach, which we prove converges to local minimizers of the constrained optimal control problem, first relaxes the discrete-valued input, then performs traditional optimal control, and then projects the constructed relaxed discrete-valued input back to a pure discrete-valued input by employing an extension to the classical Chattering Lemma that we prove. We extend this algorithm by formulating a computationally implementable algorithm which works by discretizing the time interval over which the switched dynamical system is defined. Importantly, we prove that this implementable algorithm constructs a sequence of points by recursive application that converge to the local minimizers of the original constrained optimal control problem. Four simulation experiments are included to validate the theoretical developments

Airborne 20-65 micron spectrophotometry of Comet Halley

Observations of Comet Halley with a grating spectrometer on board the Kuiper Airborne Observatory on four nights in Dec. 1985 to Apr. 1986 are reported. Low resolution 20 to 65 micrometer spectra of the nucleus with a 40 arcsec FWHM beam was obtained on 17 Dec. 1985, and on 15 and 17 Apr. 1986. On 20 Dec. 1985, only a 20 to 35 micrometer spectrum was obtained. Most of the data have been discussed in a paper where the continuum was dealt with. In that paper, models were fit to the continuum that showed that more micron sized particles of grain similar to amorphous carbon were needed to fit the spectrum than were allowed by the Vega SP-2 mass distribution, or that a fraction of the grains had to be made out of a material whose absorption efficiency fell steeper than lambda sup -1 for lambda greater than 20 micrometers. Spectra was also presented taken at several points on the coma on 15 Apr. which showed that the overall shape to the spectrum is the same in the coma. Tabulated values of the data and calibration curves are available. The spectral features are discussed

A Theoretical mechanistic investigation of asymmetric aziridination by N-Aryl-O-acylhydroxylamines

This paper reports a theoretical investigation of the most probable mechanism for the asymmetric aziridination of olefins by N‐aryl‐O‐acylhydroxylamines. The transition states of two possible mechanisms (Scheme 2) were studied. The transition state for pathway 2 (oxaziridine as intermediate) has a lower energy of activation than the energy of the transition state for pathway 1. The anionic transition state of pathway 2 is more stable than the neutral transition state

Turning light into a liquid via atomic coherence

We study a four level atomic system with electromagnetically induced transparency with giant $\chi^{(3)}$ and $\chi^{(5)}$ susceptibilities of opposite signs. This system would allow to obtain multidimensional solitons and light condensates with surface tension properties analogous to those of usual liquids

A Spitzer Study of Comets 2P/Encke, 67P/Churyumov-Gerasimenko, and C/2001 HT50 (LINEAR-NEAT)

We present infrared images and spectra of comets 2P/Encke, 67P/Churyumov-Gerasimenko, and C/2001 HT50 (LINEAR-NEAT) as part of a larger program to observe comets inside of 5 AU from the sun with the Spitzer Space Telescope. The nucleus of comet 2P/Encke was observed at two vastly different phase angles (20 degrees and 63 degrees). Model fits to the spectral energy distributions of the nucleus suggest comet Encke's infrared beaming parameter derived from the near-Earth asteroid thermal model may have a phase angle dependence. The observed emission from comet Encke's dust coma is best-modeled using predominately amorphous carbon grains with a grain size distribution that peaks near 0.4 microns, and the silicate contribution by mass to the sub-micron dust coma is constrained to 31%. Comet 67P/Churyumov-Gerasimenko was observed with distinct coma emission in excess of a model nucleus at a heliocentric distance of 5.0 AU. The coma detection suggests that sublimation processes are still active or grains from recent activity remain near the nucleus. Comet C/2001 HT50 (LINEAR-NEAT) showed evidence for crystalline silicates in the spectrum obtained at 3.2 AU and we derive a silicate-to-carbon dust ratio of 0.6. The ratio is an order of magnitude lower than that derived for comets 9P/Tempel 1 during the Deep Impact encounter and C/1995 O1 (Hale-Bopp).Comment: Accepted for publication in the Astrophysical Journal 48 pages, 15 figures, 10 table

Stabilized vortex solitons in layered Kerr media

In this letter we demonstrate the possibility of stabilizing beams with angular momentum propagating in Kerr media. Large propagation distances without filamentation can be achieved in layered media with alternating focusing and defocusing nonlinearities. Stronger stabilization can be obtained with the addition of an incoherent beam.Comment: 4 pages, 3 figures. We have removed the sentence "Thus, they erroneously point out to the existence of fully stabilized vortex solitons" in page 2, column 2, line 7-8, because it might be confusin

Dba-free" Palladium Intermediates Of The Heck-matsuda Reaction."

The dba-free Heck-Matsuda reaction was investigated via direct ESI-MS(/MS) monitoring. Palladium species involved in the reduction of Pd(II) during a Wacker type reaction and several dba-free arylpalladium transient complexes were detected and characterized. Based on these findings, a more comprehensible catalytic cycle for this pivotal reaction is suggested.113277-8