Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Monitoring and control technologies for bioregenerative life support systems/CELSS

The development of a controlled Ecological Life Support System (CELSS) will require NASA to develop innovative monitoring and control technologies to operate the different components of the system. Primary effort over the past three to four years has been directed toward the development of technologies to operate a biomass production module. Computer hardware and software required to operate, collect, and summarize environmental data for a large plant growth chamber facility were developed and refined. Sensors and controls required to collect information on such physical parameters as relative humidity, temperature, irradiance, pressure, and gases in the atmosphere; and PH, dissolved oxygen, fluid flow rates, and electrical conductivity in the nutrient solutions are being developed and tested. Technologies required to produce high artificial irradiance for plant growth and those required to collect and transport natural light into a plant growth chamber are also being evaluated. Significant effort was directed towards the development and testing of a membrane nutrient delivery system required to manipulate, seed, and harvest crops, and to determine plant health prior to stress impacting plant productivity are also being researched. Tissue culture technologies are being developed for use in management and propagation of crop plants. Though previous efforts have focussed on development of technologies required to operate a biomass production module for a CELSS, current efforts are expanding to include technologies required to operate modules such as food preparation, biomass processing, and resource (waste) recovery which are integral parts of the CELSS

Carbon dioxide and water exchange rates by a wheat crop in NASA's biomass production chamber: Results from an 86-day study (January to April 1989)

Gas exchange measurements were taken for a 20 sq m wheat stand grown from seed to harvest in NASA's Biomass Production Chamber. Respiration of the wheat stand caused the CO2 concentrations to rise an average of 440 ppm during the 4-h dark period each day, or 7.2 umol/sq m/sec. Dark period respiration was sensitive to temperature changes and could be increased 70 to 75 percent by raising the temperature from 16 C to 24 C. Stand photosynthesis (measured from the rate of CO2 drawdown immediately after the lights came on each day) peaked at 27 umol/sq m/sec at 25 days after planting and averaged 15 umol/sq m/sec throughout the study. By combining the average light period photosynthesis and average dark period respiration, a net of 860 g or 470 liters of CO2 were fixed per day. Stand photosynthetic rates showed a linear increase with increasing irradiance (750 umol/sq m/sec PPF the highest level tested), with an average light compensation point after day 30 of 190 umol/sq m/sec. Stand photosynthesis decreased slightly when CO2 levels were decreased from 2200 to 800 ppm, but dropped sharply when CO2 was decreased below 700 to 800 ppm. Water production from stand transpiration peaked at 120 L/day near 25 days and averaged about 90 L/day, or 4.5 L/sq m/day throughout the study

Hair today, gone tomorrow: the degradation and conservation of archaeological hair fibers

The research of this work describes the degradation and conservation of archaeological hair fibers. Chapter I will be a brief overview, with Chapter II following with a literary review and definition of terms. Chapter III focuses on research centered on the structure of hair fibers and their physical and chemical attributes. It will also focus on the archaeological and historical evidence of hair fiber use by humans. This research will help form the backbone of the paper and experiments performed. The next chapter focuses on the degradation of hair fibers in different environments. Hair fibers left in underwater, open air, burial, and arid environments are monitored for degree of degradation and brittleness. The hair fiber types used are four commonly found hair fibers types: coarse wool, fine wool, mohair, and human hair. After deposition, conservation using silicone oil treatment is tested on the degraded hair fibers. When silicone oil treatment proves to be a viable conservation method, the technique is then be applied to two artifacts. The two artifacts used are a Victorian era watch fob made from human hair and hair fibers mixed with tar from the excavation of Kittern in Bulgaria. Chapter VII deals with the conclusions of the experiments as a whole. The degradation of the fibers in different environmental conditions show that burial in acidic sandy clay is the most detrimental to hair fibers, while hair fibers from arid, dry environments are brittle, but well preserved aesthetically. The silicone oil treatments are shown to be viable treatment methods with positive results for all of the fibers tested, including two artifacts, a Victorian watch fob made from human hair fibers and hair fibers mixed with a tar-like substance from the shipwreck Kittern in Bulgaria

Proximate Composition of Seed and Biomass from Soybean Plants Grown at Different Carbon Dioxide (CO2) Concentrations

Soybean plants were grown for 90 days at 500, 1000, 2000, and 5000 ubar (ppm) carbon dioxide (CO2) and compared for proximate nutritional value. For both cultivars (MC and PX), seed protein levels were highest at 1000 (39.3 and 41.9 percent for MC and PX) and lowest at 2000 (34.7 and 38.9 percent for MC and PX). Seed fat (oil) levels were highest at 2000 (21.2 and 20.9 percent for MC and PX) and lowest at 5000 (13.6 and 16.6 percent for MC and PX). Seed carbohydrate levels were highest at 500 (31.5 and 28.4 percent for MC and PX) and lowest at 2000 (20.9 and 20.8 percent for MC and PX). When adjusted for total seed yield per unit growing area, the highest production of protein and carbohydrate occurred with MC at 1000, while equally high amounts of fat were produced with MC at 1000 and 2000. Seed set and pod development at 2000 were delayed in comparison to other CO2 treatments; thus the proportionately high fat and low protein at 2000 may have been a result of the delay in plant maturity rather than CO2 concentration. Stem crude fiber and carbohydrate levels for both cultivars increased with increased CO2. Leaf protein and crude fiber levels also tended to rise with increased CO2 but leaf carbohydrate levels decreased as CO2 was increased. The results suggest that CO2 effects on total seed yield out-weighed any potential advantages to changes in seed composition

Atmospheric leakage and condensate production in NASA's biomass production chamber. Effect of diurnal temperature cycles

A series of tests were conducted to monitor atmospheric leakage rate and condensate production in NASA's Biomass Production Chamber (BPC). Water was circulated through the 64 plant culture trays inside the chamber during the tests but no plants were present. Environmental conditions were set to a 12-hr photoperiod with either a matching 26 C (light)/20 C (dark) thermoperiod, or a constant 23 C temperature. Leakage, as determined by carbon dioxide decay rates, averaged about 9.8 percent for the 26 C/20 C regime and 7.3 percent for the constant 23 C regime. Increasing the temperature from 20 C to 26 C caused a temporary increase in pressure (up to 0.5 kPa) relative to ambient, while decreasing the temperature caused a temporary decrease in pressure of similar magnitude. Little pressure change was observed during transition between 23 C (light) and 23 C (dark). The lack of large pressure events under isothermal conditions may explain the lower leakage rate observed. When only the plant support inserts were placed in the culture trays, condensate production averaged about 37 liters per day. Placing acrylic germination covers over the tops of culture trays reduced condensate production to about 7 liters per day. During both tests, condensate production from the lower air handling system was 60 to 70 percent greater than from the upper system, suggesting imbalances exist in chilled and hot water flows for the two air handling systems. Results indicate that atmospheric leakage rates are sufficiently low to measure CO2 exchange rates by plants and the accumulation of certain volatile contaminants (e.g., ethylene). Control system changes are recommended in order to balance operational differences (e.g., humidity and temperature) between the two halves of the chamber

Effects of atmospheric CO2 on photosynthetic characteristics of soybean leaves

Soybean (Glycine max. cv. McCall) plants were grown at 500, 1000, and 2000 umol mol (exp -1) CO2 for 35 days with a photosynthetic photon flux of 300 umol m (exp -2) s (-1). Individual leaves were exposed to step changes of photosynthetic photon flux to study CO2 assimilation rates (CAR), i.e., leaf net photosynthesis. In general, CAR increased when CO2 increased from 500 to 1000 umol mol (exp -1), but not from 1000 to 2000 umol mol (exp -1). Regardless of the CO2 level, all leaves showed similar CAR at similar CO2 and PPF. This observation contrasts with reports that plants tend to become 'lazy' at elevated CO2 levels over time. Although leaf stomatal conductance (to water vapor) showed diurnal rhythms entrained to the photoperiod, leaf CAR did not show these rhythms and remained constant across the light period, indicating that stomatal conductance had little effect on CAR. Such measurements suggest that short-term changes in CO2 exchange dynamics for a controlled ecological life support system can be closely predicted for an actively growing soybean crop

MACRO- AND MICRO ELEMENT LEVELS IN CEREALS GROWN IN LOWER AUSTRIA

In order to study the effects of soil type and site conditions upon essential element levels in cereals, a pilot study of field and pot experiments were carried out on a Dystric cambisol, a Gleyic luvisol, a Calcareous phaeozem, and a Calcareous chernozem in 3 subsequent years. Based on the results of multiemelent analyses, it was evident that P and Zn were found mainly in the grains, and Ca, Fe, and Mn preferably in the straw. Concentrations in the grains were kept rather constant for Fe, Mn, S, and P, whereas the straw acted as a buffer to store excess mobile amounts. Apart from some differences due to cereal species and cultivars, additional supply of nutrient element fertilizer solution and shorter root length led to higher Cu, Fe, Mn, and Zn in cereals grown in pots, and a shift in the grain/straw ratios for Ca. Thus, the results obtained in pot experiments cannot be directly transferred to fi eld conditions. From at least 5 replicates of each setup, on the average, precision of analytical data obtained for whole grain samples was better than for straw samples, and precision obtained in pot experiments was less than those in fi eld experiments. In pot experiments, increase of the number of replicates from 5 to 10 or 20 did not improve analytical precision

Optimization as an analysis tool for human complex decision making

We present a problem class of mixed-integer nonlinear programs (MINLPs) with nonconvex continuous relaxations which stem from economic test scenarios that are used in the analysis of human complex problem solving. In a round-based scenario participants hold an executive function. A posteriori a performance indicator is calculated and correlated to personal measures such as intelligence, working memory, or emotion regulation. Altogether, we investigate 2088 optimization problems that differ in size and initial conditions, based on real-world experimental data from 12 rounds of 174 participants. The goals are twofold. First, from the optimal solutions we gain additional insight into a complex system, which facilitates the analysis of a participant’s performance in the test. Second, we propose a methodology to automatize this process by providing a new criterion based on the solution of a series of optimization problems. By providing a mathematical optimization model and this methodology, we disprove the assumption that the “fruit fly of complex problem solving,” the Tailorshop scenario that has been used for dozens of published studies, is not mathematically accessible—although it turns out to be extremely challenging even for advanced state-of-the-art global optimization algorithms and we were not able to solve all instances to global optimality in reasonable time in this study. The publicly available computational tool Tobago [TOBAGO web site https://sourceforge.net/projects/tobago] can be used to automatically generate problem instances of various complexity, contains interfaces to AMPL and GAMS, and is hence ideally suited as a testbed for different kinds of algorithms and solvers. Computational practice is reported with respect to the influence of integer variables, problem dimension, and local versus global optimization with different optimization codes