Optimal control of nonlinear systems represented by differential algebraic equations

An iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified simplified model based problem with parameter updating in such a manner that the correct solution of the original nonlinear problem is achieved.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Optimal control of nonlinear differential algebraic equation systems

A novel iterative procedure is described for solving nonlinear optimal control problems subject to differential algebraic equations. The procedure iterates on an integrated modified linear quadratic model based problem with parameter updating in such a manner that the correct solution of the original non-linear problem is achieved. The resulting algorithm has a particular advantage in that the solution is achieved without the need to solve the differential algebraic equations . Convergence aspects are discussed and a simulation example is described which illustrates the performance of the technique. 1. Introduction When modelling industrial processes often the resulting equations consist of coupled differential and algebraic equations (DAEs). In many situations these equations are nonlinear and cannot readily be directly reduced to ordinary differential equations.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Radiative efficiencies and global warming potentials using theoretically determined absorption cross-sections for several hydrofluoroethers (HFEs) and hydrofluoropolyethers (HFPEs)

Integrated infrared cross-sections and wavenumber positions for the vibrational modes of a range of hydrofluoroethers (HFEs) and hydrofluoropolyethers (HFPEs) have been calculated. Spectra were determined using a density functional method with an empirically derived correction for the wavenumbers of band positions. Radiative efficiencies (REs) were determined using the Pinnock et al. method and were used with atmospheric lifetimes from the literature to determine global warming potentials (GWPs). For the HFEs and the majority of the molecules in the HG series HFPEs, theoretically determined absorption cross-sections and REs lie within ca. 10% of those determined using measured spectra. For the larger molecules in the HG series and the HG′ series of HFPEs, agreement is less good, with theoretical values for the integrated cross-sections being up to 35% higher than the experimental values; REs are up to 45% higher. Our method gives better results than previous theoretical approaches, because of the level of theory chosen and, for REs, because an empirical wavenumber correction derived for perfluorocarbons is effective in predicting the positions of C–F stretching frequencies at around 1250 cm−1 for the molecules considered here.

Water vapour continuum absorption in near-infrared windows derived from laboratory measurements

In most near-infrared atmospheric windows, absorption of solar radiation is dominated by the water vapor self-continuum and yet there is a paucity of measurements in these windows. We report new laboratory measurements of the self-continuum absorption at temperatures between 293 and 472 K and pressures from 0.015 to 5 atm in four near-infrared windows between 1 and 4 m (10000-2500 cm-1); the measurements are made over a wider range of wavenumber, temperatures and pressures than any previous measurements. They show that the self-continuum in these windows is typically one order of magnitude stronger than given in representations of the continuum widely used in climate and weather prediction models. These results are also not consistent with current theories attributing the self continuum within windows to the far-wings of strong spectral lines in the nearby water vapor absorption bands; we suggest that they are more consistent with water dimers being the major contributor to the continuum. The calculated global-average clear-sky atmospheric absorption of solar radiation is increased by 0.75 W/m2 (which is about 1% of the total clear-sky absorption) by using these new measurements as compared to calculations with the MT_CKD-2.5 self-continuum model.

Inverting recurrent neural networks for internal model control of nonlinear systems

In this paper, we show how a set of recently derived theoretical results for recurrent neural networks can be applied to the production of an internal model control system for a nonlinear plant. The results include determination of the relative order of a recurrent neural network and invertibility of such a network. A closed loop controller is produced without the need to retrain the neural network plant model. Stability of the closed-loop controller is also demonstrated.

Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Identification of nonlinear systems with a dynamic recurrent neural network

Two approaches are presented to calculate the weights for a Dynamic Recurrent Neural Network (DRNN) in order to identify the input-output dynamics of a class of nonlinear systems. The number of states of the identified network is constrained to be the same as the number of states of the plant.

Origin of electronic absorption spectra of MLCT-excited and one-electron reduced 2,2′-bipyridine and 1,10-phenanthroline complexes

UV–Vis absorption spectra of one-electron reduction products and 3MLCT excited states of [ReICl(CO)3- (N,N)] (N,N = 2,20-bipyridine, bpy; 1,10-phenanthroline, phen) have been measured by low-temperature spectroelectrochemistry and UV–Vis transient absorption spectroscopy, respectively, and assigned by open-shell TD-DFT calculations. The characters of the electronic transitions are visualized and analyzed using electron density redistribution maps. It follows that reduced and excited states can be approximately formulated as [ReICl(CO)3(N,Nÿ)]ÿ and ⁄[ReIICl(CO)3(N,Nÿ)], respectively. UV–Vis spectra of the reduced complexes are dominated by IL transitions, plus weaker MLCT contributions. Excited-state spectra show an intense band in the UV region of 50% IL origin mixed with LMCT (bpy, 373 nm) or MLCT (phen, 307 nm) excitations. Because of the significant IL contribution, this spectral feature is akin to the principal IL band of the anions. In contrast, the excited-state visible spectral pattern arises from predominantly LMCT transitions, any resemblance with the reduced-state visible spectra being coincidental. The Re complexes studied herein are representatives of a broad class of metal a-diimines, for which similar spectroscopic behavior can be expected.

Nonlinear data assimilation in geosciences: an extremely efficient particle filter

Almost all research fields in geosciences use numerical models and observations and combine these using data-assimilation techniques. With ever-increasing resolution and complexity, the numerical models tend to be highly nonlinear and also observations become more complicated and their relation to the models more nonlinear. Standard data-assimilation techniques like (ensemble) Kalman filters and variational methods like 4D-Var rely on linearizations and are likely to fail in one way or another. Nonlinear data-assimilation techniques are available, but are only efficient for small-dimensional problems, hampered by the so-called ‘curse of dimensionality’. Here we present a fully nonlinear particle filter that can be applied to higher dimensional problems by exploiting the freedom of the proposal density inherent in particle filtering. The method is illustrated for the three-dimensional Lorenz model using three particles and the much more complex 40-dimensional Lorenz model using 20 particles. By also applying the method to the 1000-dimensional Lorenz model, again using only 20 particles, we demonstrate the strong scale-invariance of the method, leading to the optimistic conjecture that the method is applicable to realistic geophysical problems. Copyright c 2010 Royal Meteorological Society

A preliminary investigation of the impact of catechol-O-methyltransferase genotype on the absorption and metabolism of green tea catechins

Purpose Green tea is thought to possess many beneficial effects on human health. However, the extent of green tea polyphenol biotransformation may affect its proposed therapeutic effects. Catechol-O-methyltransferase (COMT), the enzyme responsible for polyphenolic methylation, has a common polymorphism in the genetic code at position 158 reported to result in a 40% reduction in enzyme activity in in vitro studies. The current preliminary study was designed to investigate the impact of COMT genotype on green tea catechin absorption and metabolism in humans. Methods Twenty participants (10 of each homozygous COMT genotype) were recruited, and plasma concentration profiles were produced for epigallocatechin gallate (EGCG), epigallocatechin (EGC), epicatechin gallate (ECG), epicatechin (EC) and 4′-O-methyl EGCG after 1.1 g of Sunphenon decaffeinated green tea extract (836 mg green tea catechins), with a meal given after 60 min. Results For the entire group, EGCG, EGC, EC, ECG and 4′-O-methyl EGCG reached maximum concentrations of 1.09, 0.41, 0.33, 0.16 and 0.08 μM at 81.5, 98.5, 99.0, 85.5 and 96.5 min, respectively. Bimodal curves were observed for the non-gallated green tea catechins EGC and EC as opposed to single-peaked curves for the gallated green tea catechins EGCG and ECG. No significant parametric differences between COMT genotype groups were found. Conclusions In conclusion, the COMT Val(158/108)Met does not appear to have a dramatic influence on EGCG absorption and elimination. However, further pharmacokinetic research is needed to substantiate these findings.