Dual-Sampling-Rate Moving-Horizon Control of a Class of Linear Systems with Input Saturation and Plant Uncertainty

Moving-horizon control is a type of sampled-data feedback control in which the control over each sampling interval is determined by the solution of an open-loop optimal control problem. We develop a dual-sampling-rate moving-horizon control scheme for a class of linear, continuous-time plants with strict input saturation constraints in the presence of plant uncertainty and input disturbances. Our control scheme has two components: a slow-sampling moving-horizon controller for a nominal plant and a fast-sampling state-feedback controller whose function is to force the actual plant to emulate the nominal plant. The design of the moving-horizon controller takes into account the nonnegligible computation time required to compute the optimal control trajectory.We prove the local stability of the resulting feedback system and illustrate its performance with simulations. In these simulations, our dual-sampling-rate controller exhibits performance that is considerably superior to its single-sampling-rate moving-horizon controller counterpart.     

A second-order method for unconstrained optimization

This paper presents a quadratically converging algorithm for unconstrained minimization. All the accumulation points that it constructs satisfy second-order necessary conditions of optimality. Thus, it avoids second-order saddle andinflection points, an essential feature for a method to be used in minimizing the modified Lagrangians in multiplier methods.The work of the first author was supported by NSF RANN AEN 73-07732-A02 and JSEP Contract No. F44620-71-C-0087; the work of the second author was supported by NSF Grant No. GK-37672 and the ARO Contract No. DAHCO4-730C-0025.     

Initial stages of soot formation in thermal pyrolysis of acetylene. I. Mechanism for homogeneous pyrolysis of acetylene

A probable mechanism for the homogeneous pyrolysis of acetylene, using carbene reactions, is considered. Analysis of the energetics for the probable mechanism of the initiation reactions shows the rearrangement C₂H₂CCH₂ to be the most probable. Using the energetic barriers for simple carbene reactions and formation enthalpies for more complicated carbenes, we evaluated the activation energies for the reactions mechanism. The vibrational excitation of the products of carbene reactions is taken into account. Calculations of the acetylene conversion kinetics and yields of the main gas-phase pyrolysis products, based on the carbene molecular mechanism, show significantly better agreement with available experimental data as compared to those based on traditional radical mechanisms. The calculated time for the appearance of aromatic products is close to the measured induction times for the appearance of soot particles.     

Silicagele mit engen und weiten Poren als Trockenmittel

Ohne Zusammenfassung     

Two-quanta progressive saturation: pulsed NMR of 23Na in single crystal sodium nitrate

Progressive saturation effects due to induction of two-quanta transitions in the quadrupolar-split levels of a spit, 3/2, (²³Na) nucleus were studied by monitoring changes occuring in the 1/2 → ? 1/2 magnetization after applying trains of identical pulses at various radiofrequencies and repetition rates. The variety of single- and double-quantum (DO) interconnected population effects observed in the experiments is explained by incorporating solutions of the ordinary two-level Bloch equations with those of the two-quanta, three-level Bloch-like equations (including off-resonance conditions) derived recently by Gold and Hahn. Small displacements of nuclear levels under DQ irradiation (analogous to the optical ac Stark shift) the cause rf power-dependent DQ frequency shifts are predicted for all spins I> 1, and explicit expressions are derived. Additional effects due to state mixing and to population transfer by satellite excitation are presented, and the relevance of DQ saturation to the recently developed double-resonance interferometric spectroscopy is discussed.     

Semiempirical SCF theory with “Scaled” slater orbitals

A new method is presented for the calculation of molecular properties in which the one center integrals are evaluated within their environment (scaled in the molecule) rather than carried over from atomic structures.The procedure can be incorporated into any SCF scheme using a minimal basis set of atomic orbitals. In this paper an INDO framework was chosen to illustrate the results. Both heats of formation and bond distances for various types of molecules were found in satisfactory agreement with experiment.

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Zusammenfassung Es wird eine neue Methode für die Berechnung von Moleküleigenschaften vorgeschlagen, in welcher die Einzentrenintegrale innerhalb ihrer Umgebung im Molekül bestimmt werden, statt sie von freien Atomen zu übernehmen.Diese Methode kann bei jedem SCF Verfahren angewandt werden, das auf einer minimalen Basis von Atomorbitalen aufbaut. Zur Illustration der Ergebnisse in dieser Arbeit wird das INDO-Verfahren gewählt. Sowohl Bildungswärmen als auch Bindungsabstände von verschiedenen Molekülarten sind in guter Übereinstimmung mit den experimentellen Daten.

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Résumé Une nouvelle méthode pour le calcul des propriétés moléculaires est présentée, dans laquelle les intégrales monocentriques sont évaluées dans leur environnement (ajustées à la molécule), au lieu d'être transférées du calcul atomique.Le procédé peut être incorporé dans n'importe quel schema SCF qui utilise un «basis set» minimal.Dans cet article, le procédé est illustré par l'utilisation d'un schema INDO.Les chaleurs de formation et les distances de liaison pour plusieurs types de molécules sont trouvées en accord satisfaisant avec l'experience.

     

New nonbinary code bounds based on divisibility arguments

For \(q,n,d \in \mathbb {N}\), let \(A_q(n,d)\) be the maximum size of a code \(C \subseteq [q]^n\) with minimum distance at least d. We give a divisibility argument resulting in the new upper bounds \(A_5(8,6) \le 65\), \(A_4(11,8)\le 60\) and \(A_3(16,11) \le 29\). These in turn imply the new upper bounds \(A_5(9,6) \le 325\), \(A_5(10,6) \le 1625\), \(A_5(11,6) \le 8125\) and \(A_4(12,8) \le 240\). Furthermore, we prove that for \(\mu ,q \in \mathbb {N}\), there is a 1–1-correspondence between symmetric \((\mu ,q)\)-nets (which are certain designs) and codes \(C \subseteq [q]^{\mu q}\) of size \(\mu q^2\) with minimum distance at least \(\mu q - \mu \). We derive the new upper bounds \(A_4(9,6) \le 120\) and \(A_4(10,6) \le 480\) from these ‘symmetric net’ codes.     

On the Perpetual Collision-Free RHC of Fleets of Vehicles

Receding horizon control is emerging as a very promising technique for the centralized control of fleets of vehicles on land, sea, and in the air. We present a sufficient condition for collision avoidance within a fleet under receding horizon control, over an indefinite period of operation.     

Histochemical and Phytochemical Analysis of Lamium album subsp. album L. Corolla: Essential Oil,Triterpenes, and Iridoids

The aim of this study was to conduct a histochemical analysis to localize lipids, terpenes, essential oil, and iridoids in the trichomes of the L. album subsp. album corolla. Morphometric examinations of individual trichome types were performed. Light and scanning electron microscopy techniques were used to show the micromorphology and localization of lipophilic compounds and iridoids in secretory trichomes with the use of histochemical tests. Additionally, the content of essential oil and its components were determined using gas chromatography-mass spectrometry (GC-MS). Qualitative analyses of triterpenes carried out using high-performance thin-layer chromatography (HPTLC) coupled with densitometric detection, and the iridoid content expressed as aucubin was examined with spectrophotometric techniques. We showed the presence of iridoids and different lipophilic compounds in papillae and glandular and non-glandular trichomes. On average, the flowers of L. album subsp. album yielded 0.04 mL/kg of essential oil, which was dominated by aldehydes, sesquiterpenes, and alkanes. The extract of the L. album subsp. album corolla contained 1.5 × 10⁻³ ± 4.3 × 10⁻⁴ mg/mL of iridoid aucubin and three triterpenes: oleanolic acid, β-amyrin, and β-amyrin acetate. Aucubin and β-amyrin acetate were detected for the first time. We suggest the use of L. album subsp. album flowers as supplements in human nutrition.