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A solution is presented to an optimization problem for time lag systems by the classical method of Lagrange multipliers in a Banach space. Following terminology and assumption definitions, the regularity and controllability of the Lagrange multipliers problem is discussed, and a set of necessary conditions for an optimal control is derived. In conclusion, the solution existence, uniqueness, and sufficiency are established.
Theoretical and experimental results are obtained in the investigation of a minimum energy control problem associated with a class of electrically driven vehicles. Analytical results are obtained by making several justifiable approximations in the dynamical equations of the plant, the performance index of which is related to the minimization of system energy consumption for any required control action. The control problem of interest is simplified and solved by using Bellman's invariant imbedding technique. The optimality of the resulting control law is compared with those of the bang-bang control law, which is the exact solution for the case of speed-setting control action, and the classical control laws under identical conditions. A stochastic optimization problem is then formulated and solved by using Bellman's dynamic programming technique. The resulting control law is mechanized for a particular vehicle configuration which is simulated in the laboratory.
The symbiotic co-evolution of plants and microbes leads to difficulties in understanding which of the two components is responsible for a given environmental response. Plant-microbe studies greatly benefit from the ability to grow plants in axenic (sterile) culture. Several studies have used axenic plant culture systems, but experimental procedures are often poorly documented, the plant growth environment is not optimal, and axenic conditions are not rigorously verified. We developed a unique axenic system using inert components that promotes plant health and can be kept sterile for at least 70 d. Crested wheatgrass (Agropyron cristatum cv. DII) plants were grown in sand within flow-through glass columns that were positively pressured with filtered air. Plant health was optimized by regulating temperature, light level, CO2 concentration, humidity, and nutrients. The design incorporates several novel aspects, such as pretreatment of the sand with Fe, graduated sand layers to optimize the air-water balance of the root zone, and modification of a laminar flow hood to serve as a plant growth chamber. Adaptations of several sterile techniques were necessary for maintenance of axenic conditions. Axenic conditions were verified by plating and staining leachates as well as rhizoplane stain. This system was designed to study nutrient and water stress effects on root exudates, but is useful for assessing a broad range of plant-microbe-environment interactions. Based on total organic C analysis, 74% of exudates was recovered in the leachate, 6% was recovered in the bulk sand, and 17% was recovered in the rhizosphere sand. Carbon in the leachate after 70 d reached 255 micro-g/d. Fumaric, malic, malonic, oxalic, and succinic acids were measured as components of the root exudates.
The Mapping Imaging Spectrometer for Europa (MISE) Instrument on the Europa Clipper mission has baselined a Lockheed Martin high-power Micro1-2 pulse tube cryocooler operating at 135 Hz with a 220 K heat rejection temperature. This paper describes the testing and results of two Lockheed Martin Micro1-2 coolers optimized for these conditions. The thermal performance of the microcoolers was measured in vacuum for heat reject temperatures between 220 and 230 K. The coolers were operated with input powers ranging from 5 W to 40 W and drive frequency between 125 Hz and 145 Hz. The optimal drive frequency was strongly dependent on heat reject temperature. In addition, the exported forces and torques of the coolers were measured at 300 K heat rejection for input powers ranging from 5 W to 60 W and drive frequency between 120 Hz and 160 Hz. The exported forces were dependent on both piston amplitude and drive frequency. Moreover, the following were measured on one of the coolers: DC and AC magnetic fields at various locations, the off-state conductance of the pulse tube, and the effect of inclination angle of the pulse tube relative to gravity on the performance of the cooler. Finally, one of the coolers was subjected to random vibration testing.
The theme for AbSciCon 2012 is "Exploring Life: Past and Present, Near and Far." The conference will address our current understanding of life - from processes at the molecular level to those which operate at planetary scales. Studying these aspects of life on Earth provides an essential platform from which to examine the potential for life on other worlds, both within our solar system and beyond. Mars exhibits a variety of extreme environments characterized by high UV and ionizing radiation flux, low pressure anoxic atmosphere, scarce or absent liquid water, extreme low temperatures, etc. The ability of terrestrial microorganisms to survive and adapt to the Mars environment has profound implications for astrobiology, planetary protection, and Mars life detection missions. At the NASA Ames Synthetic Biology Initiative, we believe that synthetic biology has the potential to revolutionize human space exploration. As such, the initiative is dedicated to applying the tools and techniques of synthetic biology to space exploration and astrobiology. Biological solutions will be invaluable for space exploration because they are not resource intensive, and they are versatile and self-renewing. An understanding of how to work with DNA in an unfavorable environment is paramount to utilizing biological tools on space missions. Furthermore, the ability to adjust life to the parameters of Mars is vital both to discovering what life on Mars might look like, and to using biological tools under such conditions. As a first step, we need an energy-efficient, low cost means of transporting, storing, and protecting genomic DNA, DNA parts, and whole microbial strains. Our goal is to develop and demonstrate viable and superior alternatives to standard DNA storage methods, which can be optimized to the conditions of space exploration, using synthetic biology as a tool. This includes protocols and kit designs for easy and repeatable DNA and strain recovery from protective storage conditions. We are constructing newly engineered genetic parts for different valuable host organisms, designed to increased long-term survival and functional retention. These methods should be applied for DNA and strain storage and transportation. In parallel, we seek inspiration from natural organisms that have developed means for survival in extreme environmental conditions. We are utilizing novel techniques for analysis of lipid biomarkers in the Antarctic Dry Valleys in order to identify resident microbes in the Antarctic soil and permafrost, as well as biomarker fossils of organisms that survived in the valleys in ages past. Through the identification of these life forms, we hope to understand and draw on new biological tools and strategies for synthetic biological applications on Mars.
The magnetoacoustic measurement technique has been used successfully for residual stress measurements in laboratory samples. However, when used to field test samples with complex geometries, such as railroad wheels, the sensitivity of the method declines dramatically. It has been suggested that the decrease in performance may be due, in part, to an insufficient or nonuniform magnetic induction in the test sample. The purpose of this paper is to optimize the test conditions by using finite element modeling to predict the distribution of the induced bulk magnetization of railroad wheels. The results suggest that it is possible to obtain a sufficiently large and uniform bulk magnetization by altering the shape of the electromagnet used in the tests. Consequently, problems associated with bulk magnetization can be overcome, and should not prohibit the magnetoacoustic technique from being used to make residual stress measurements in railroad wheels. We begin by giving a brief overview of the magnetoacoustic technique as it applies to residual stress measurements of railroad wheels. We then define the finite element model used to predict the behavior of the current test configuration along with the nonlinear constitutive relations which we obtained experimentally through measurements on materials typically used to construct both railroad wheels and electromagnets. Finally, we show that by modifying the pole of the electromagnet it is possible to obtain a significantly more uniform bulk magnetization in the region of interest.
Studies of biosignature formation in photosynthetic microbial mat communities offer potentially useful insights with regards to both solar and extrasolar astrobiology. Biosignature formation in such systems results from the chemical transformation of photosynthetically fixed carbon by accessory microorganisms. This fixed carbon represents a source not only of reducing power, but also energy, to these organisms, so that chemical and energy budgets should be coupled. We tested this hypothesis by applying an energy balance model to predict the fate of photosynthetic productivity under dark, anoxic conditions. Fermentation of photosynthetically fixed carbon is taken to be the only source of energy available to cyanobacteria in the absence of light and oxygen, and nitrogen fixation is the principal energy demand. The alternate fate for fixed carbon is to build cyanobacterial biomass with Redfield C:N ratio. The model predicts that, under completely nitrogen-limited conditions, growth is optimized when 78% of fixed carbon stores are directed into fermentative energy generation, with the remainder allocated to growth. These predictions were compared to measurements made on microbial mats that are known to be both nitrogen-limited and populated by actively nitrogen-fixing cyanobacteria. In these mats, under dark, anoxic conditions, 82% of fixed carbon stores were diverted into fermentation. The close agreement between these independent approaches suggests that energy balance models may provide a quantitative means of predicting chemical partitioning within such systems - an important step towards understanding how biological productivity is ultimately partitioned into biosignature compounds.
Introduction: Continuously evolving medical standards of care, limited crew training time, and the inherent constraints of space flight necessitate regular revisions of the mission medical support infrastructure and methodology. A three-day Operational and Research Musculoskeletal Summit was held to review NASA s current strategy for preflight health maintenance and injury screening, risk mitigation for musculoskeletal injuries or syndromes, treatment methods during flight, and research topics to mitigate risks to astronaut health. The Summit also undertook consideration of the best evidence-based terrestrial musculoskeletal practices to recommend their adaptation for use in space. Methods: The types and frequencies of musculoskeletal injuries sustained by short- and long-duration astronauts were obtained from the Longitudinal Study of Astronaut Health. The Summit panel was comprised of experts from the clinical and research communities, as well as representatives from NASA Headquarters, the Astronaut corps, and the offices of JSC Medical Operations, JSC Human Adaptation and Countermeasures, Glenn Research Center Human Research, and Astronaut Strength Conditioning and Rehabilitation. Before the summit, panelists participated in a Web-based review of NASA s Space Medical Conditions List (SMCL). Results: The Summit generated seventy-five operational and research recommendations to the NASA Office of Space Medicine, including changes to the SMCL and to the musculoskeletal section of the ISS debrief questionnaire. From these recommendations, seven were assigned highest value and priority, and could be immediately adopted for the exploration architecture. Discussion: Optimized exercise and conditioning to improve performance and forestall musculoskeletal damage on orbit were the primary area of focus. Special attention was paid to exercise timing and muscle group specificity. The panel s recommendations are currently in various stages of consideration or integration into the ISS and Exploration programs. This effort serves to enhance the on-orbit system so comprehensive treatment can be delivered in a more effective and standardized manner.
The concept of acceleration lines and their correlation with time-optimal paths of robotic manipulators is presented. The acceleration lines represent the directions of maximum tip acceleration from a point in the manipulator work-space, starting at a zero velocity. These lines can suggest the number and shapes of time-optimal paths for a class of manipulators. It is shown that nonsingular time-optimal paths are tangent to one of the acceleration lines near the end-points. A procedure for obtaining near-optimal paths, utilizing the acceleration lines, is developed. These paths are obtained by connecting the end-points with B splines tangent to the acceleration lines. The near-minimum paths are shown to yield better traveling times than the straight-line path between the same end-points. The near-minimum paths can be used as initial conditions in existing optimization methods to speed-up convergence and computation time. This method can be used for online robot path planning and for interactive designs of robotic-cell layouts. Examples of time-optimal paths of a two-link manipulator, obtained by other optimization procedures and their acceleration lines, are shown.
The optimal control of three-dimensional large angle maneuvers and vibrations of a Shuttle-mast-reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam subject to three-dimensional deformations. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem is then solved by using the quasilinearization algorithm and the method of particular solutions. The study of the large angle maneuvering of the Shuttle-beam-reflector spacecraft in the plane of a circular earth orbit is extended to consider the effects of the structural offset connection, the axial shortening, and the gravitational torque on the slewing motion. Finally the effect of additional design parameters (such as related to additional payload requirement) on the linear quadratic regulator based design of an orbiting control/structural system is examined.
In January 2004, President Bush gave the National Aeronautics and Space Administration (NASA) a vision for Space Exploration by setting our sight on a bold new path to go back to the Moon, then to Mars and beyond. In response to this vision, NASA started the Constellation Program, which is a new exploration launch vehicle program. The primary mission for the Constellation Program is to carry out a series of human expeditions ranging from Low Earth Orbit to the surface of Mars and beyond for the purposes of conducting human exploration of space, as specified by the Vision for Space Exploration (VSE). The intent is that the information and technology developed by this program will provide the foundation for broader exploration activities as our operational experience grows. The ARES I Crew Launch Vehicle (CLV) has been designated as the launch vehicle that will be developed as a "first step" to facilitate the aforementioned human expeditions. The CLV Project is broken into four major elements: First Stage, Upper Stage Engine, Upper Stage (US), and the Crew Exploration Vehicle (CEV). NASA's Marshall Space Flight Center (MSFC) is responsible for the design of the CLV and has the prime responsibility to design the upper stage of the vehicle. The US is the second propulsive stage of the CLV and provides CEV insertion into low Earth orbit (LEO) after separation from the First Stage of the Crew Launch Vehicle. The fully integrated Upper Stage is a mix of modified existing heritage hardware (J-2X Engine) and new development (primary structure, subsystems, and avionics). The Upper Stage assembly is a structurally stabilized cylindrical structure, which is powered by a single J-2X engine which is developed as a separate Element of the CLV. The primary structure includes the load bearing liquid hydrogen (LH2) and liquid oxygen (LOX) propellant tanks, a Forward Skirt, the Intertank structure, the Aft Skirt and the Thrust Structure. A Systems Tunnel, which carries fluid and electrical power functions to other Elements of the CLV, is included as secondary structure. The MSFC has an overall responsibility for the integrated US element as well as structural design an thermal control of the fuel tanks, intertank, interstage, avionics, main propulsion system, Reaction Control System (RCS) for both the Upper Stage and the First Stage. MSFC's Spacecraft and Vehicle Department, Structural and Analysis Design Division is developing a set of predicted mass of these elements. This paper details the methodology, criterion and tools used for the preliminary mass predictions of the upper stage structural assembly components. In general, weight of the cylindrical barrel sections are estimated using the commercial code Hypersizer, whereas, weight of the domes are developed using classical solutions. HyperSizer is software that performs automated structural analysis and sizing optimization based on aerospace methods for strength, stability, and stiffness. Analysis methods range from closed form, traditional hand calculations repeated every day in industry to more advanced panel buckling algorithms. Margin-of-safety reporting for every potential failure provides the engineer with a powerful insight into the structural problem. Optimization capabilities include finding minimum weight panel or beam concepts, material selections, cross sectional dimensions, thicknesses, and lay-ups from a library of 40 different stiffened and sandwich designs and a database of composite, metallic, honeycomb, and foam materials. Multiple different concepts (orthogrid, isogrid, and skin stiffener) were run for multiple loading combinations of ascent design load with and with out tank pressure as well as proof pressure condition. Subsequently, selected optimized concept obtained from Hypersizer runs was translated into a computer aid design (CAD) model to account for the wall thickness tolerance, weld land etc for developing the most probable weight of the components. The flow diram summarizes the analysis steps used in developing these predicted mass.
The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.
An investigation utilizing Reynolds-averaged simulations (RAS) was performed in order to find optimal designs for an interdigitated flushwall injector suitable for scramjet applications at hypervelocity conditions. The flight Mach number, duct height, spanwise width, and injection angle were the design variables selected to maximize two objective functions: the thrust potential and combustion efficiency. A Latin hypercube sampling design-of-experiments method was used to select design points for RAS. A methodology was developed that automated building geometries and generating grids for each design. The ensuing RAS analysis generated the performance database from which the two objective functions of interest were computed using a one-dimensional performance utility. The data were fitted using four surrogate models: an artificial neural network (ANN) model, a cubic polynomial, a quadratic polynomial, and a Kriging model. Variance-based decomposition showed that both objective functions were primarily driven by changes in the duct height. Multiobjective design optimization was performed for all four surrogate models via a genetic algorithm method. Optimal solutions were obtained at the upper and lower bounds of the flight Mach number range. The Kriging model obtained an optimal solution set that predicted high values for both objective functions. Additionally, three challenge points were selected to assess the designs on the Pareto fronts. Further sampling among the designs of the Pareto fronts are required in order to lower the errors and perform more accurate surrogate-based optimization. sed optimization.
Strong sufficient conditions are derived for the robustness of optimal linear-quadratic (LQ) regulators to large parameter perturbations. In particular, it is shown that under certain conditions LQ designs remain stable in the presence of actuator channel failures. The general results can be specialized to provide insight into the gain margin, gain reduction, and phase margin properties of optimal LQ regulators.
Problems involving functional differential equations with terminal conditions in function space are considered. Their application to mechanical and electrical systems is discussed. Investigations of controllability, existence of optimal controls, and necessary and sufficient conditions for optimality are reported.
We report initial data from a suspended rat model that quantitatively relates chronic partial weightbearing to bone loss. Chronic partial weightbearing is our simulation of the effect of limited artificial gravity aboard spacecraft or reduced planetary gravity. Preliminary analysis of bone by PQCT, histomorphometry, mechanical testing and biochemistry suggest that chronic exposure to half of Earth gravity is insufficient to prevent severe bone loss. The effect of episodic full weightbearing activity (Earth Gravity) on rats otherwise at 50% weightbearing was also explored. This has similarity to treatment by an Earth G-rated centrifuge on a spacecraft that normally maintained artificial gravity at half of Earth G. Our preliminary evidence, using the above techniques to analyze bone, indicate that 2 hours daily of full weightbearing was insufficient to prevent the bone loss observed in 50% weightbearing animals. The effectiveness of partial weightbearing and episodic full weightbearing as potential countermeasures to bone loss in spaceflight was compared with treatment by ibandronate. Ibandronate, a long-acting potent bisphosphonate proved more effective in preventing bone loss and associated functionality based upon structure than our first efforts at mechanical countermeasures. The effectiveness of ibandronate was notable by each of the testing methods we used to study bone from gross structure and strength to tissue and biochemistry. These results appear to be independent of generalized systemic stress imposed by the suspension paradigm. Preliminary evidence does not suggest that blood levels of vitamin D were affected by our countermeasures. Despite the modest theraputic benefit of mechanical countermeasures of partial weightbearing and episodic full weightbearing, we know that some appropriate mechanical signal maintains bone mass in Earth gravity. Moreover, the only mechanism that correctly assigns bone mass and strength to oppose regionally specific force applied to bone is mechanical, a process based upon bone strain. Substantial evidence indicates that the specifics of dynamic loading i.e. time-varying forces are critical. Bone strain history is a predictor of the effect that mechanical conditions have on bone structure mass and strength. Using servo-controlled force plates on suspended rats with implanted strain gauges we manipulated impact forces of ambulation in the frequency (Fourier) domain. Our results indicate that high frequency components of impact forces are particularly potent in producing bone strain independent of the magnitude of the peak force or peak energy applied to the leg. Because a servo-system responds to forces produced by the rat's own muscle activity during ambulation, the direction of ground-reaction loads act on bone through the rat's own musculature. This is in distinction to passive vibration of the floor where forces reach bone through the natural filters of soft tissue and joints. Passive vibration may also be effective, but it may or may not increase bone in the appropriate architectural pattern to oppose the forces of normal ambulatory activity. Effectiveness of high frequency mechanical stimulation in producing regional (muscle directed) bone response will be limited by 1. the sensitivity of bone to a particular range of frequencies and 2. the inertia of the muscles, limiting their response to external forces by increasing tension along insertions. We have begun mathematical modeling of normal ambulatory activity. Effectiveness of high frequency mechanical stimulation in producing regional (muscle directed) bone response will be limited by 1. the sensitivity of bone to a particular range of frequencies and 2. the inertia of the muscles, limiting their response to external forces by increasing tension along insertions. We have begun mathematical modeling of the rat forelimb as a transfer function between impact force and bone strain to predict optimal dynamic loading conditions for this system. We plan additional studies of mechanical counter-measures that incorporate improved dynamic loading, features relevant to anticipated evaluation of artificial gravity, exercise regimens and exposure to Martian gravity, The combination of mechanical countermeasures with ibandronate will also be investigated for signs of synergy.
In this paper, necessary conditions are obtained for optimal control problems containing equality constraints defined in terms of functions of the control and phase variables. The control system is assumed to be characterized by an ordinary differential equation, and more conventional constraints, including phase inequality constraints, are also assumed to be present. Because the first-mentioned equality constraint must be satisfied for all t (the independent variable of the differential equation) belonging to an arbitrary (prescribed) measurable set, this problem gives rise to infinite-dimensional equality constraints. To obtain the necessary conditions, which are in the form of a maximum principle, an implicit-function-type theorem in Banach spaces is derived.
Conditions under which optimal wave functions satisfy various time-dependent Hellmann-Feynman theorems