On the convergence of successive Galerkin approximation for nonlinear output feedback H(infinity) control

Although the formulation of the nonlinear theory of H(infinity) control has been well developed, solving the Hamilton-Jacobi-Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H(infinity) control via output feedback are presented. An example is presented illustrating the application of the algorithm.

On state representations of nonlinear implicit systems

This work considers a semi-implicit system A, that is, a pair (S, y), where S is an explicit system described by a state representation (x)over dot(t) = f(t, x(t), u(t)), where x(t) is an element of R(n) and u(t) is an element of R(m), which is subject to a set of algebraic constraints y(t) = h(t, x(t), u(t)) = 0, where y(t) is an element of R(l). An input candidate is a set of functions v = (v(1),.... v(s)), which may depend on time t, on x, and on u and its derivatives up to a Finite order. The problem of finding a (local) proper state representation (z)over dot = g(t, z, v) with input v for the implicit system Delta is studied in this article. The main result shows necessary and sufficient conditions for the solution of this problem, under mild assumptions on the class of admissible state representations of Delta. These solvability conditions rely on an integrability test that is computed from the explicit system S. The approach of this article is the infinite-dimensional differential geometric setting of Fliess, Levine, Martin, and Rouchon (1999) (`A Lie-Backlund Approach to Equivalence and Flatness of Nonlinear Systems`, IEEE Transactions on Automatic Control, 44(5), (922-937)).

Fixed-point DSP implementation of nonlinear H(infinity) controller for large gap electromagnetic suspension system

Electromagnetic suspension systems are inherently nonlinear and often face hardware limitation when digitally controlled. The main contributions of this paper are: the design of a nonlinear H(infinity) controller. including dynamic weighting functions, applied to a large gap electromagnetic suspension system and the presentation of a procedure to implement this controller on a fixed-point DSP, through a methodology able to translate a floating-point algorithm into a fixed-point algorithm by using l(infinity) norm minimization due to conversion error. Experimental results are also presented, in which the performance of the nonlinear controller is evaluated specifically in the initial suspension phase. (C) 2009 Elsevier Ltd. All rights reserved.

Investigation of Normal Force and Moment Coefficients for an AUV at Nonlinear Angle of Attack and Sideslip Range

This paper presents a comparative study of computational fluid dynamics (CFD) and analytical and semiempirical (ASE) methods applied to the prediction of the normal force and moment coefficients of an autonomous underwater vehicle (AUV). Both methods are applied to the. bare hull of the vehicle and to the body-hydroplane combination. The results are validated through experiments in a towing tank. It is shown that the CFD approach allows for a good prediction of the coefficients over the range of angles of attack considered. In contrast with the traditional ASE formulations used in naval and aircraft fields, an improved methodology is introduced that takes advantage of the qualitative information obtained from CFD flow visualizations.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Interactions between the oscillations of piezoceramic transducer and the mechanism of as excitation-the generator of the electric current of limited power-supply-are analyzed in this paper In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power as that provided by a dc motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a nonideal problem. In this work, we present certain phenomena as Sommerfeld effect, jump, saturation, and stability, through the influences of the parameters of the governing equations motion. [DOI: 10.1115/1.3007909]

Methods for detection of anatoxin-a(s) by liquid chromatography coupled to electrospray ionization-tandem mass spectrometry

Anatoxin-a(s) is a potent irreversible inhibitor of the enzyme acetylcholinesterase with a unique N-hydroxyguanidine methylphosphate ester chemical structure. Determination of this toxin in environmental samples is hampered by the lack of specific methods for its detection. Using the toxic strain of Anabaena lemmermani PH-160 B as positive control, the fragmentation characteristics of anatoxin-a(s) under collision-induced dissociation conditions have been investigated and new LC-MS/MS methods proposed. Recommended ion transitions for correct detection of this toxin are 253 > 58, 253 > 159, 235 > 98 and 235 > 96. Chromatographic separation is better achieved under HILIC conditions employing a ZIC-HILIC column. This method was used to confirm for the first time the production of anatoxin-a(s) by strains of Anabaena oumiana ITEP-025 and ITEP-026. Considering no standard solutions are commercially available, our results will be of significant use for the correct identification of this toxin by LC-MS/MS. (C) 2009 Elsevier Ltd. All rights reserved.

Dissociation of deprotonated microcystin variants by collision-induced dissociation following electrospray ionization

Microcystins (MC) are a family of hepatotoxic cyclic heptapeptides produced by a number of different cyanobacterial species. Considering the recent advances in the characterization of deprotonated peptides by mass spectrometry, the fragmentation behavior of four structurally related microcystin compounds was investigated using collision-induced dissociation (CID) experiments on an orbitrap mass spectrometer. It is demonstrated in this study that significant structural information can be obtained from the CID spectra of deprotonated microcystins. A predominant ring-opening reaction at the isoMeAsp residue, as well as two major complementary fragmentation pathways, was observed, reducing the complexity of the product ion spectra in comparison with spectra observed from protonated species. This proposed fragmentation behavior was applied to characterize [Leu(1)]MC-LR from a cyanobacterial cell extract. In conclusion, CID spectra of microcystins in the negative ion mode provide rich structurally informative mass spectra which greatly enhance confidence in structural assignments, in particular when combined with complementary positive ion CID spectra. Copyright (C) 2011 John Wiley & Sons, Ltd.

Re-examination of the anion derivatives of isoflavones by radical fragmentation in negative electrospray ionization tandem mass spectrometry: experimental and computational studies

This paper reports theoretical and experimental studies of gas-phase fragmentation reactions of four naturally occurring isoflavones. The samples were analyzed in negative ion mode by direct infusion in ESI-QqQ, ESI-QqTOF and ESI-Orbitrap systems. The MS/MS and MS(n) spectra are in agreement with the fragmentation proposals and high-resolution analyses have confirmed the formulae for each ion observed. As expected, compounds with methoxyl aromatic substitution have showed a radical elimination of center dot CH(3) as the main fragmentation pathway. A second radical loss (center dot H) occurs as previously observed for compounds which exhibit a previous homolytic center dot CH(3) cleavage (radical anion) and involves radical resonance to stabilize the anion formed. However, in this study we suggest another mechanism for the formation of the main ions, on the basis of the enthalpies for each species. Compounds without methoxy substituent dissociate at the highest energies and exhibit the deprotonated molecule as the most intense ion. Finally, energy-resolved experiments were carried out to give more details about the gas-phase dissociation reaction of the isoflavones and the results are in agreement with the theoretical approaches. Copyright (C) 2011 John Wiley & Sons, Ltd.

Fragmentation studies and electrospray ionization mass spectrometry of lapachol: protonated, deprotonated and cationized species

Electrospray ionization mass spectrometric analysis of lapachol (2-hydroxy-3-(3-methy1-2-butenyl)-1,4-naphthoquinone) was accomplished in order to elucidate the gas-phase dissociation reactions of this important biologically active natural product. The occurrence of protonated and cationized species in the positive mode and of deprotonated species in the negative mode was explored by means of collision-induced dissociation (CID) experiments. For the protonated molecule, the H(2)O and C(4)H(8) losses occur by two competitive channels. For the deprotonated molecule, the even-electron rule is not conserved, and the radicalar species are eliminated by formation of distonic anions. The fragmentation mechanism for each ion was suggested on the basis of computational thermochemistry. Atomic charges, relative energies, and frontier orbitals were employed aiming at a better understanding of the gas-phase reactivity of lapachol. Potential energy surfaces for fragmentation reactions were obtained by the B3LYP/6-31+G(d,p) model. Copyright (C) 2010 John Wiley & Sons, Ltd.

Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.