Distributed Solution of Constrained Optimal Control Problems Using the Alternating Direction Method of Multipliers

Many control problems in science and engineering can be formulated as optimal control problems (OCP) such as load changes in process control or point-to-point motion of industrial robots in a time-optimal or energy-optimal way while accounting for physical or security constraints. Hence, an efficient way to handle constrained OCPs is an important topic of research. A promising approach to address this issue is a transformation technique allowing to reformulate an inequality constrained OCP into an equality constrained counterpart. The reformulated OCP reveals to possess a particular structure that is favorable for a decomposition and the application of distributed optimization methods. Motivated by the Augmented Lagrangian approach, the structure of the reformulated OCP can be exploited to derive a decomposition method for splitting up the entire OCP into smaller subproblems. In addition, an algorithm is presented that follows the ideas of the Alternating Direction Method of Multipliers (ADMM) and solves the resulting subproblems in a distributed manner. The approach is applied to a mechatronic example system to demonstrate the performance of the presented method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chemische und cyclovoltammetrische Untersuchung der Redoxreaktionen der Decahalogendecaborate closo‐[B10X10]2– und hypercloso‐[B10X10]· – (X = Cl,Br). Kristallstrukturanalyse von Cs2[B10Br10] · 2 H2O

Chemical and Cyclovoltammetric Investigation of the Redoxreactions of the Decahalodecaborates closo ‐[B₁₀X₁₀]^2– and hypercloso ‐[B₁₀X₁₀]^{· –} (X = Cl, Br)¹⁾. Crystal Structure Analysis of Cs₂[B₁₀Br₁₀] · 2 H₂O The oxidation of the decachloro‐closo‐decaborates(2–) Cs₂[B₁₀Cl₁₀] or [Me₄N]₂[B₁₀Cl₁₀] with Tl(CF₃COO)₃ leads to the corresponding radical monoanion hypercloso‐[B₁₀Cl₁₀] ^{· –}, which was characterized by ESR and UV/Vis spectroscopy. [B₁₀Cl₁₀] ^{· –} does not dimerize like [B₁₀H₁₀] ^{· –} but it is reduced by acetonitrile to the dianion [B₁₀Cl₁₀]^2–. Cs₂[B₁₀Cl₁₀] reacts with stronger oxidation agents like CoF₃ (in dichloromethane) or XeF₂ (in perfluorhexane), respectively, to yield B₉Cl₉ and, in traces, B₈Cl₈. In opposite to this, the decabromoderivative Cs₂[B₁₀Br₁₀] does not show any reaction with Tl(CF₃COO)₃ in acetonitrile or with CoF₃ in CH₂Cl₂. The oxidation of the dianions [B₁₀X₁₀]^2– (X = Cl, Br) was studied by electroanalytical methods (cyclic voltammetry, chronoamperometry, chronocoulometry). Formal potentials were determined for the two steps of the reaction, which do not seem to be affected by structural rearrangements. The crystal structure of Cs₂[B₁₀Br₁₀] · 2 H₂O was analyzed by single‐crystal X‐ray diffraction. Cs₂[B₁₀Br₁₀] · 2 H₂O crystallizes monoclinic (space group I2/a, (no. 15), Z = 8, a = 1361.54(9) pm, b = 1215.89(5) pm, c = 3108.4(2) pm, α = 90°, β = 97.916(8)°, γ = 90°). The closo‐cluster B₁₀Br₁₀^2– has a bicapped square antiprismatic structure with idealized D_4d symmetry.     

Isomer-Specific Vibrational Spectroscopy of Microhydrated Lithium Dichloride Anions: Spectral Fingerprint of Solvent-Shared Ion Pairs

The vibrational spectroscopy of lithium dichloride anions microhydrated with one to three water molecules, [LiCl₂(H₂O)_1–3]⁻, is studied in the OH stretching region (3800–2800 cm⁻¹) using isomer-specific IR/IR double-resonance population labelling experiments. The spectroscopic fingerprints of individual isomers can only be unambiguously assigned after anharmonic effects are considered, but then yield molecular level insight into the onset of salt dissolution in these gas phase model systems. Based on the extent of the observed frequency shifts Δν^OH of the hydrogen-bonded OH stretching oscillators solvent-shared ion pair motifs (<3200 cm⁻¹) can be distinguished from intact-core structures (>3200 cm⁻¹). The characteristic fingerprint of a water molecule trapped directly in-between two ions of opposite charge provides an alternative route to evaluate the extent of ion pairing in aqueous electrolyte solutions.     

Formulation of Cannabidiol in Colloidal Lipid Carriers

In this study, the general processability of cannabidiol (CBD) in colloidal lipid carriers was investigated. Due to its many pharmacological effects, the pharmaceutical use of this poorly water-soluble drug is currently under intensive research and colloidal lipid emulsions are a well-established formulation option for such lipophilic substances. To obtain a better understanding of the formulability of CBD in lipid emulsions, different aspects of CBD loading and its interaction with the emulsion droplets were investigated. Very high drug loads (>40% related to lipid content) could be achieved in emulsions of medium chain triglycerides, rapeseed oil, soybean oil and trimyristin. The maximum CBD load depended on the type of lipid matrix. CBD loading increased the particle size and the density of the lipid matrix. The loading capacity of a trimyristin emulsion for CBD was superior to that of a suspension of solid lipid nanoparticles based on trimyristin (69% vs. 30% related to the lipid matrix). In addition to its localization within the lipid core of the emulsion droplets, cannabidiol was associated with the droplet interface to a remarkable extent. According to a stress test, CBD destabilized the emulsions, with phospholipid-stabilized emulsions being more stable than poloxamer-stabilized ones. Furthermore, it was possible to produce emulsions with pure CBD as the dispersed phase, since CBD demonstrated such a pronounced supercooling tendency that it did not recrystallize, even if cooled to −60 °C.     

Investigating the Disordered and Membrane-Active Peptide A-Cage-C Using Conformational Ensembles

The driving forces and conformational pathways leading to amphitropic protein-membrane binding and in some cases also to protein misfolding and aggregation is the subject of intensive research. In this study, a chimeric polypeptide, A-Cage-C, derived from α-Lactalbumin is investigated with the aim of elucidating conformational changes promoting interaction with bilayers. From previous studies, it is known that A-Cage-C causes membrane leakages associated with the sporadic formation of amorphous aggregates on solid-supported bilayers. Here we express and purify double-labelled A-Cage-C and prepare partially deuterated bicelles as a membrane mimicking system. We investigate A-Cage-C in the presence and absence of these bicelles at non-binding (pH 7.0) and binding (pH 4.5) conditions. Using in silico analyses, NMR, conformational clustering, and Molecular Dynamics, we provide tentative insights into the conformations of bound and unbound A-Cage-C. The conformation of each state is dynamic and samples a large amount of overlapping conformational space. We identify one of the clusters as likely representing the binding conformation and conclude tentatively that the unfolding around the central W23 segment and its reorientation may be necessary for full intercalation at binding conditions (pH 4.5). We also see evidence for an overall elongation of A-Cage-C in the presence of model bilayers.     

Thiourea- and Amino-Substituted Benzoxadiazole Dyes with Large Stokes Shifts as Red-Emitting Probe Monomers for Imprinted Polymer Layers Targeting Carboxylate-Containing Antibiotics

Bifunctional fluorescent molecular oxoanion probes based on the benzoxadiazole (BD) chromophore are described which integrate a thiourea binding motif and a polymerizable 2-aminoethyl methacrylate unit in the 4,7-positions of the BD core. Concerted charge transfer in this electron donor-acceptor-donor architecture endows the dyes with strongly Stokes shifted (up to >250 nm) absorption and fluorescence. Binding of electron-rich carboxylate guests at the thiourea receptor leads to further analyte-induced red-shifts of the emission, shifting the fluorescence maximum of the complexes to ≥700 nm. Association constants for acetate are ranging from 1–5×10⁵ M⁻¹ in acetonitrile. Integration of one of the fluorescent probes through its polymerizable moiety into molecularly imprinted polymers (MIPs) grafted from the surface of submicron silica cores yielded fluorescent MIP-coated particle probes for the selective detection of antibiotics containing aliphatic carboxylate groups such as enoxacin (ENOX) at micromolar concentrations in highly polar solvents like acetonitrile.     

Heterogeneous hydride generation in a packed membrane cell

Summary Volatilization of arsenic, selenium and antimony for sample introduction in atomic absorption spectrometry has been performed by pumping an acidic sample through an anion exchanger in the tetrahydroborate (III) form packed as a bed in the liquid channel of a gas-liquid separation membrane cell. The hydrides generated in the heterogeneous reaction between bound tetrahydroborate (III) ions and the analytes are rapidly transferred with the aid of the concomitantly generated hydrogen gas through the gas-permeable membrane into the gas phase and swept to the spectrometer by an additional hydrogen gas flow. This instant transfer of the hydrides to the gas phase kinetically discriminates the reaction of the hydride with metal borides and metal colloids, whose formation by reaction with tetra-hydroborate (III) is slower than the hydride reaction. The susceptibility to interference by transition metal ions is thus markedly reduced, as compared with both batch hydride generation methods and a previously presented heterogeneous reaction scheme. The detection limits for arsenic, selenium, and antimony were 1.2, 3.7, and 10 g/l, respectively. The calibration graphs were linear from the detection limit up to 125 g/l for arsenic, 150 g/l for selenium, and 250 g/l for antimony. The relative standard deviations at concentration levels of 10 and 100 g/l were 1.8 and 0.7% for arsenic and 2.3 and 1.2% for selenium. Corresponding figures for 50 and 100 g/l antimony were 2.5 and 1.6%.     

Integration of the 1,2,3‐Triazole “Click” Motif as a Potent Signalling Element in Metal Ion Responsive Fluorescent Probes

In a systematic approach we synthesized a new series of fluorescent probes incorporating donor–acceptor (D‐A) substituted 1,2,3‐triazoles as conjugative π‐linkers between the alkali metal ion receptor N‐phenylaza‐[18]crown‐6 and different fluorophoric groups with different electron‐acceptor properties (4‐naphthalimide, meso‐phenyl‐BODIPY and 9‐anthracene) and investigated their performance in organic and aqueous environments (physiological conditions). In the charge‐transfer (CT) type probes 1 , 2 and 7 , the fluorescence is almost completely quenched by intramolecular CT (ICT) processes involving charge‐separated states. In the presence of Na⁺ and K⁺ ICT is interrupted, which resulted in a lighting‐up of the fluorescence in acetonitrile. Among the investigated fluoroionophores, compound 7 , which contains a 9‐anthracenyl moiety as the electron‐accepting fluorophore, is the only probe which retains light‐up features in water and works as a highly K⁺/Na⁺‐selective probe under simulated physiological conditions. Virtually decoupled BODIPY‐based 6 and photoinduced electron transfer (PET) type probes 3 – 5 , where the 10‐substituted anthracen‐9‐yl fluorophores are connected to the 1,2,3‐triazole through a methylene spacer, show strong ion‐induced fluorescence enhancement in acetonitrile, but not under physiological conditions. Electrochemical studies and theoretical calculations were used to assess and support the underlying mechanisms for the new ICT and PET 1,2,3‐triazole fluoroionophores.