Linear regulator design for stochastic systems by a multiple time scales method

A hierarchically-structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems is considered. The controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short period modes of the longitudinal dynamics of the F-8 aircraft

A finite-state, finite-memory minimum principle, part 2

In part 1 of this paper, a minimum principle was found for the finite-state, finite-memory (FSFM) stochastic control problem. In part 2, conditions for the sufficiency of the minimum principle are stated in terms of the informational properties of the problem. This is accomplished by introducing the notion of a signaling strategy. Then a min-H algorithm based on the FSFM minimum principle is presented. This algorithm converges, after a finite number of steps, to a person - by - person extremal solution

C^+ distribution around S1 in rho Ophiuchi

We analyze a [C II] 158 micron map obtained with the L2 GREAT receiver on SOFIA of the emission/reflection nebula illuminated by the early B star S1 in the rho-OphA cloud core. This data set has been complemented with maps of CO(3-2), 13CO(3-2) and C18O(3-2), observed as a part of the JCMT Gould Belt Survey, with archival HCO^+(4-3) JCMT data, as well as with [O I] 63 and 145 micron imaging with Herschel/PACS. The [C II] emission is completely dominated by the strong PDR emission from the nebula surrounding S1 expanding into the dense Oph A molecular cloud west and south of S1. The [C II] emission is significantly blue shifted relative to the CO spectra and also relative to the systemic velocity, particularly in the northwestern part of the nebula. The [C II] lines are broader towards the center of the S1 nebula and narrower towards the PDR shell. The [C II] lines are strongly self-absorbed over an extended region in the S1 PDR. Based on the strength of the [13C II] F = 2-1 hyperfine component, [C II] is significantly optically thick over most of the nebula. CO and 13CO(3-2) spectra are strongly self-absorbed, while C18O(3-2) is single peaked and centered in the middle of the self-absorption. We have used a simple two-layer LTE model to characterize the background and foreground cloud contributing to the [C II] emission. From this analysis we estimate the extinction due to the foreground cloud to be ~9.9 mag, which is slightly less than the reddening estimated towards S1. Since some of the hot gas in the PDR is not traced by low J CO emission, this result appears quite plausible. Using a plane parallel PDR model with the observed [OI(145)]/[C II] brightness ratio and an estimated FUV intensity of 3100-5000 G0 suggests that the density of the [C II] emitting gas is ~3-4x10^3 cm^-3.Comment: Accepted for publication in Astronomy & Astrophysic

Robustness results in LQG based multivariable control designs

The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, the LQ and LQG robustness results are discussed

Opening the Treasure Chest in Carina

We have mapped the G287.84-0.82 cometary globule (with the Treasure Chest cluster embedded in it) in the South Pillars region of Carina (i) in [CII], 63micron [OI], and CO(11-10) using upGREAT on SOFIA and (ii) in J=2-1 transitions of CO, 13CO, C18O and J=3-2 transitions of H2CO using the APEX telescope in Chile. We probe the morphology, kinematics, and physical conditions of the molecular gas and the photon dominated regions (PDRs) in G287.84-0.82. The [CII] and [OI] emission suggest that the overall structure of the pillar (with red-shifted photo evaporating tails) is consistent with the effect of FUV radiation and winds from eta-Car and O stars in Trumpler 16. The gas in the head of the pillar is strongly influenced by the embedded cluster, whose brightest member is an O9.5V star, CPD-59 2661. The emission of the [CII] and [OI] lines peak at a position close to the embedded star, while all other tracers peak at another position lying to the north-east consistent with gas being compressed by the expanding PDR created by the embedded cluster. The molecular gas inside the globule is probed with the J=2-1 transitions of CO and isotopologues as well as H2CO, and analyzed using a non-LTE model (escape-probability approach), while we use PDR models to derive the physical conditions of the PDR. We identify at least two PDR gas components; the diffuse part (~10^4 cm^-3) is traced by [CII], while the dense (n~ 2-8x10^5 cm^-3) part is traced by [CII], [OI], CO(11-10). Using the F=2-1 transition of [13CII] detected at 50 positions in the region, we derive optical depths (0.9-5), excitation temperatures of [CII] (80-255 K), and N(C+) of 0.3-1x10^19 cm^-2. The total mass of the globule is ~1000 Msun, about half of which is traced by [CII]. The dense PDR gas has a thermal pressure of 10^7-10^8 K cm^-3, which is similar to the values observed in other regions.Comment: Accepted for publication in Astronomy and Astrophysics (abstract slightly abridged

Control of Finite-State, Finite Memory Stochastic Systems

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems

The structure of protostellar envelopes derived from submillimeter continuum images

High dynamic range imaging of submillimeter dust emission from the envelopes of eight young protostars in the Taurus and Perseus star-forming regions has been carried out using the SCUBA submillimeter camera on the James Clerk Maxwell Telescope. Good correspondence between the spectral classifications of the protostars and the spatial distributions of their dust emission is observed, in the sense that those with cooler spectral energy distributions also have a larger fraction of the submillimeter flux originating in an extended envelope compared with a disk. This results from the cool sources having more massive envelopes rather than warm sources having larger disks. Azimuthally-averaged radial profiles of the dust emission are used to derive the power-law index of the envelope density distributions, p (defined by rho proportional to r^-p), and most of the sources are found to have values of p consistent with those predicted by models of cloud collapse. However, the youngest protostars in our sample, L1527 and HH211-mm, deviate significantly from the theoretical predictions, exhibiting values of p somewhat lower than can be accounted for by existing models. For L1527 heating of the envelope by shocks where the outflow impinges on the surrounding medium may explain our result. For HH211-mm another explanation is needed, and one possibility is that a shallow density profile is being maintained in the outer envelope by magnetic fields and/or turbulence. If this is the case star formation must be determined by the rate at which the support is lost from the cloud, rather than the hydrodynamical properties of the envelope, such as the sound speed.Comment: Accepted for publication in the Astrophysical Journa

A Submillimeter Study of the Star-Forming Region NGC7129

New molecular (13CO J=3-2) and dust continuum (450 and 850 micron) SCUBA maps of the NGC7129 star forming region are presented, complemented by C18O J=3-2 spectra at several positions within the mapped region. The maps include the Herbig Ae/Be star LkHalpha 234, the far-infrared source NGC 7129 FIRS2 and several other pre-stellar sources embedded within the molecular ridge. The SCUBA maps help us understand the nature of the pre-main sequence stars in this actively star forming region. A deeply embedded submillimeter source, SMM2, not clearly seen in any earlier data set, is shown to be a pre-stellar core or possibly a protostar. The highest continuum peak emission is identified with the deeply embedded source IRS6, a few arcseconds away from LkHalpha 234, and also responsible for both the optical jet and the molecular outflow. The gas and dust masses are found to be consistent, suggesting little or no CO depletion onto grains. The dust emissivity index is lower towards the dense compact sources, beta ~1 - 1.6, and higher, beta ~ 2.0, in the surrounding cloud, implying small size grains in the PDR ridge, whose mantles have been evaporated by the intense UV radiation.Comment: Accepted by Ap

High Spectral and Spatial Resolution Observations of the PDR Emission in the NGC2023 Reflection Nebula with SOFIA and APEX

We have mapped the NGC 2023 reflection nebula in [CII] and CO(11--10) with the heterodyne receiver GREAT on SOFIA and obtained slightly smaller maps in 13CO(3--2), CO(3--2), CO(4--3), CO(6--5), and CO(7--6) with APEX in Chile. We use these data to probe the morphology, kinematics, and physical conditions of the C II region, which is ionized by FUV radiation from the B2 star HD37903. The [CII] emission traces an ellipsoidal shell-like region at a position angle of ~ -50 deg, and is surrounded by a hot molecular shell. In the southeast, where the C II region expands into a dense, clumpy molecular cloud ridge, we see narrow and strong line emission from high-J CO lines, which comes from a thin, hot molecular shell surrounding the [CII] emission. The [CII] lines are broader and show photo evaporating gas flowing into the C II region. Based on the strength of the [13CII] F=2--1 line, the [CII] line appears to be somewhat optically thick over most of the nebula with an optical depth of a few. We model the physical conditions of the surrounding molecular cloud and the PDR emission using both RADEX and simple PDR models. The temperature of the CO emitting PDR shell is ~ 90 -- 120 K, with densities of 10^5 -- 10^6 cm^-3, as deduced from RADEX modeling. Our PDR modeling indicates that the PDR layer where [CII] emission dominates has somewhat lower densities, 10^4 to a few times 10^5 cm^-3Comment: Accepted by A&