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.

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.

Differential effects of dairy snacks on appetite, but not overall energy intake

Dietary regulation of appetite may contribute to the prevention and management of excess body weight. The present study examined the effect of consumption of individual dairy products as snacks on appetite and subsequent ad libitum lunch energy intake. In a randomised cross-over trial, forty overweight men (age 32 (sd 9) years; BMI 27 (sd 2) kg/m2) attended four sessions 1 week apart and received three isoenergetic (841 kJ) and isovolumetric (410 ml) servings of dairy snacks or water (control) 120 min after breakfast. Appetite profile was determined throughout the morning and ad libitum energy intake was assessed 90 min after the intake of snacks. Concentrations of amino acids, glucose, insulin, ghrelin and peptide tyrosine tyrosine were measured at baseline (0 min) and 80 min after the intake of snacks. Although the results showed that yogurt had the greatest suppressive effect on appetite, this could be confounded by the poor sensory ratings of yogurt. Hunger rating was 8, 10 and 24 % (P < 0·001) lower after the intake of yogurt than cheese, milk and water, respectively. Energy intake was 11, 9 and 12 % (P < 0·02) lower after the intake of yogurt, cheese and milk, respectively, compared with water (4312 (se 226) kJ). Although there was no difference in the postprandial responses of hormones, alanine and isoleucine concentrations were higher after the intake of yogurt than cheese and milk (P < 0·05). In conclusion, all dairy snacks reduced appetite and lunch intake compared with water. Yogurt had the greatest effect on suppressing subjective appetite ratings, but did not affect subsequent food intake compared with milk or cheese.

Differential effects of internal and external factors on the development of vocabulary, tense morphology and morpho-syntax in successive bilingual children

The present study investigates the effects of child internal (age/time) and child external/environmental factors on the development of a wide range of language domains in successive bilingual (L2) Turkish-English children of homogeneously low SES. Forty-three L2 children were tested on standardized assessments examining the acquisition of vocabulary and morpho-syntax. The L2 children exhibited a differential acquisition of the various domains: they were better on the general comprehension of grammar and tense morphology and less accurate on the acquisition of vocabulary and (complex) morpho-syntax. Profile effects were confirmed by the differential effects of internal and external factors on the language domains. The development of vocabulary and complex syntax were affected by internal and external factors, whereas external factors had no contribution to the development of tense morphology. These results are discussed in light of previous studies on the impact of internal and external factors in child L2 acquisition.

A novel satellite mission concept for upper air water vapour, aerosol and cloud observations using integrated path differential absorption LiDAR limb sounding

We propose a new satellite mission to deliver high quality measurements of upper air water vapour. The concept centres around a LiDAR in limb sounding by occultation geometry, designed to operate as a very long path system for differential absorption measurements. We present a preliminary performance analysis with a system sized to send 75 mJ pulses at 25 Hz at four wavelengths close to 935 nm, to up to 5 microsatellites in a counter-rotating orbit, carrying retroreflectors characterized by a reflected beam divergence of roughly twice the emitted laser beam divergence of 15 µrad. This provides water vapour profiles with a vertical sampling of 110 m; preliminary calculations suggest that the system could detect concentrations of less than 5 ppm. A secondary payload of a fairly conventional medium resolution multispectral radiometer allows wide-swath cloud and aerosol imaging. The total weight and power of the system are estimated at 3 tons and 2,700 W respectively. This novel concept presents significant challenges, including the performance of the lasers in space, the tracking between the main spacecraft and the retroreflectors, the refractive effects of turbulence, and the design of the telescopes to achieve a high signal-to-noise ratio for the high precision measurements. The mission concept was conceived at the Alpbach Summer School 2010.