Robustness of minimax controllers to nonlinear perturbations

We study the robustness of minimax controllers, originally designed for nominal linear or nonlinear systems, to unknown static nonlinear perturbations in the state dynamics, measurement equation, and performance index. When the nominal system is linear, we consider both perfect state measurements and general imperfect state measurements; in the case of nominally nonlinear systems, we consider perfect state measurements only. Using a differential game theoretic approach, we show for the former class that, as the perturbation parameter (say, >0) approaches zero, the optimal disturbance attenuation level for the overall system converges to the optimal disturbance attenuation level for the nominal system if the nonlinear structural uncertainties satisfy certain prescribed growth conditions. We also show that anH -controller, designed based on a chosen performance level for the nominal linear system, achieves the same performance level when the parameter is smaller than a computable threshold, except for the finite-horizon imperfect state measurements case. For that case, we show that the design of the nominal controller must be based on a decreased confidence level of the initial data, and a controller thus designed again achieves a desired performance level in the face of nonlinear perturbations satisfying a computable norm bound. In the case of nominally nonlinear systems, and assuming that the nominal system is solvable, we obtain sufficient conditions such that the nominal controller achieves a desired performance in the face of perturbations satisfying computable norm bounds. In this way, we provide a characterization of the class of uncertainties that are tolerable for a controller designed based on the nominal system. The paper also presents two numerical examples; in one of these, the nominal system is linear; in the other one, it is nonlinear.This research was supported in part by the US Department of Energy, Grant DE-FG-02-88-ER-13939 and in part by the National Science Foundation, Grant ECS-91-13153.An abridged version was presented at the 32nd IEEE Conference on Decision and Control, San Antonio, Texas, December 15–17, 1993, and it appeared in the Conference Proceedings.     

Mononuclear nitrogen/sulfur-ligated cobalt(II) methoxide complexes: structural, EPR, paramagnetic 1H NMR, and electrochemical investigations

The first examples of mononuclear nitrogen/sulfur-ligated Co(II) alkoxide complexes, species of relevance to a reactive intermediate observed for Co(II)-substituted liver alcohol dehydrogenase, have been isolated and characterized by multiple methods including X-ray crystallography, EPR, paramagnetic (1)H NMR, and cyclic voltammetry.     

Determination of iron and nickel by flame atomic absorption spectrophotometry after preconcentration on Saccharomyces cerevisiae immobilized sepiolite

Iron and nickel have been preconcentrated on Saccharomyces cerevisiae immobilized sepiolite and determined by flame atomic absorption spectrophotometry (FAAS). Preconcentration studies were conducted by the column method. Effect of pH, amount of adsorbent, elution solution, flow rate and interfering ions on the recovery of the analytes have been investigated. Recoveries of Fe and Ni were 95+/-1 and 99.5+/-0.1%, respectively, at 95% confidence level. The breakthrough capacities of analytes were also investigated and found to be 0.042 mmol g(-1) for Fe and 0.055 mmol g(-1) for Ni. The proposed method was applied to the determination of iron and nickel in brass (NBS SRM 37e). The detection limit of iron and nickel were found as 0.065 and 0.087 mug ml(-1), respectively. The direct determination of trace metals by flame atomic absorption spectrometry (FAAS) is limited and difficult because of low concentration and/or matrix interferences. The proposed method is excellent for the determination of trace metal in matrixes, such as metal alloys.     

Synthesis and structure of the edge-bridged open zirconocene, Zr(6,6-dmch)2(PMe3)2 (dmch=dimethylcyclohexadienyl), and its imine coupling product

The reaction of ZrCl₄ with four equivalents of the 6,6-dimethylcyclohexadienyl anion (6,6-dmch⁻) in the presence of PMe₃ leads to the 18 electron Zr(6,6-dmch)₂(PMe₃)₂. This complex was found to undergo a coupling reaction with two equivalents of PhCHNPh, such that the couplings involved the two termini of the same dienyl ligand, yielding a formal Zr(η⁵-dienyl)(η³-allyl)(π-amide)₂ complex. Both metal complexes have been structurally characterized.     

Preconcentration of trace elements by aluminium hydroxide

Summary Coprecipitation of traces of cobalt, zinc, chromium, ruthenium and mercury with freshly precipitated aluminium hydroxide has been investigated by a radiotracer method. Investigations were performed over a wide range of pH. The results indicate that traces of cobalt, zinc and chromium could be almost completely coprecipitated between pH 6 and 10. On the other hand coprecipitation yield for ruthenium in this pH range do not exceed 95%, which is believed to be the consequence of the various physicochemical states of ruthenium. The coprecipitation yields for mercury are very low as a consequence of the presence of non-ionized HgCl₂.

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Zusammenfassung Die Mitfällung von Spuren Kobalt, Zink, Chrom, Ruthenium und Quecksilber mit frisch gefälltem Aluminiumhydroxid wurde radiochemisch untersucht. Die dazu nötigen Experimente erstreckten sich über ein weites pH-Gebiet. Die Ergebnisse zeigen, daß Spuren Kobalt, Zink und Chrom zwischen pH 6 und 10 fast vollständig mitgefällt werden konnten. Andrerseits sind die Mitfällungsausbeuten für Ruthenium in diesem pH-Gebiet nicht größer als 95%, was vermutlich die Folge der verschiedenen physikalischchemischen Zustände des Rutheniums ist. Die Mitfällungsausbeuten für Queckilber sind infolge der nur geringen Dissoziation des HgCl₂ sehr gering.

     

Preparation and optical characterization of catalyst free SiO<Subscript>2</Subscript> sonogel hybrid materials

The synthesis of sol-gel materials induced by ultrasonic irradiation (sonolysis) is implemented as an alternative method for the fabrication of highly pure organic-inorganic composites with good monolithic, mechanical and optical properties. Ultrasonic irradiation, instead of commonly used basic- or acidic-catalyst was used to produce acoustical cavitation within the liquid H₂O/tetraethyl-ortosilicate (TEOS) reactants. This procedure forms a hydrolyzed-TEOS colloidal dispersion (sol) which produces, after drying, a highly pure SiO₂ network. The resulting SiO₂ glass exhibits high porosity and allows the inclusion of several organic compounds in the colloidal sol-state. Novel, optical active synthesized liquid crystalline (LC)-azo-compounds, bent shaped mesogens, cis- and trans-poly(1-ethynylpyrene)s, as well as fullerene (C₆₀) spheres and classical organic dyes were successfully incorporated as dopant agents within the novel catalyst free (CF) SiO₂-sonogel host matrix. Absorption and fluorescence spectroscopy studies were carried out in order to characterize the optical performance of both the CF-sonogel and several hybrid composites The pulsed laser photoacoustic technique (LPAT) was implemented to determine thermodynamic phase transitions of LC-based hybrids and laser induced damage (photo-degradation) in dye-based composites. Finally, comparative morphology studies between undoped reference samples and some doped composites were performed by Atomic Force Microscopy (AFM), where an optimal TEOS/dopant concentration ratio, to obtain good mechanical properties among the studied samples, has been found.     

Manganese(II) chemistry of a new N3O-donor chelate ligand: synthesis, X-ray structures, and magnetic properties of solvent- and oxalate-bound complexes

The synthesis and characterization of a new N3O donor ligand N-benzyl-N-((6-pivaloylamido-2-pyridyl)methyl)-N-(2-pyridylmethyl)amine (bpppa) is reported. Treatment of bpppa with Mn(II)(ClO4)2.6H2O in acetonitrile solution yielded the mononuclear [(bpppa)Mn(CH3CN)(H2O)](ClO4)2 (1) which was characterized by X-ray crystallography, elemental analysis, IR spectroscopy, mass spectrometry, and a solution magnetic moment measurement. Admixture of equimolar equivalents of bpppa and Mn(II)(ClO4)2.6H2O in methanol solution, followed by addition of 0.5 or 1 equivalents of sodium oxalate, yielded the binuclear complex [{(bpppa)Mn}2([mu]-C2O4)](ClO4)2 (2), which was characterized by X-ray crystallography, elemental analysis, IR spectroscopy, mass spectrometry, and solid-state magnetic measurements. While 1 is mononuclear, the formation of the binuclear oxalate derivative indicates that use of the bpppa ligand does not enable isolation of a complex that is structurally relevant to a proposed 1:1 Mn(II)-oxalate adduct in the catalytic cycle of the oxalate degrading enzyme oxalate decarboxylase.     

Design, synthesis, and crystallographic studies of neutral platinum-based macrocycles formed via self-assembly

A series of neutral, platinum-based macrocycles was synthesized from rigid oxygen donor building blocks via self-assembly. The combination of a platinum-based 60 degrees acceptor unit 1 with several linear and angular dicarboxylate bridging ligands afforded hitherto unknown neutral platinum-based supramolecular triangles and rhomboids. In addition, a similar reaction of the diplatinum molecular clip 6 and three different linear dicarboxylates led to the formation of neutral molecular rectangles. Most of the macrocycles were characterized by X-ray single-crystal structure analysis, and, in all cases, NMR spectra were consistent with the formation of single highly symmetrical species.