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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

New high performance algorithmic solution for diagnosis problem

In this paper we address the problem of generating the minimal diagnosis from the conflicts. This problem can be formulated as the well-known Hitting Set Problem. Our approach starts by mapping the Hitting Set problem into the Integer Programming Problem that enables us, for the first time, a priori determination of the lower and upper bounds on the size for the solution. Based on these bounds, we introduce a new concept of solution window for the problem. We also propose a new branch-and-bound technique that not only is faster than the current techniques in terms of number of operations (by exploiting the structure of the problem) but also, using the concept of window, allows a massive reduction (pruning) in the number of branches. Furthermore, as the branch-and-bound proceeds, the solution window is dynamically updated and narrowed to enable further pruning.

diagnosis problems↗
NASA NTRS2006

Hard and Soft Constraints in Reliability-Based Design Optimization

This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

Crespo, L.uis G.↗
NASA NTRS2007

Exposed Ice in the Northern Mid-Latitudes of Mars

Ice-Rich Layer: Polygonal features with dimensions of approximately 100 meters, bounded by cracks, are commonly observed on the martian northern plains. These features are generally attributed to thermal cracking of ice-rich sediments, in direct analogy to polygons in terrestrial polar regions. We mapped polygons in the northern mid-latitudes (30 to 65 N) using MOC and HiRISE images. Polygons are scattered across the northern plains, with a particular concentration in western Utopia Planitia. This region largely overlaps the Late Amazonian Astapus Colles unit, characterized by polygonal terrain and nested pits consistent with periglacial and thermokarst origins. Bright and Dark Polygonal Cracks: An examination of all MOC images (1997 through 2003) covering the study area demonstrated that, at latitudes of 55 to 65 N, most of the imaged polygons show bright bounding cracks. We interpret these bright cracks as exposed ice. Between 40 and 55 N, most of the imaged polygons show dark bounding cracks. These are interpreted as polygons from which the exposed ice has been removed by sublimation. The long-term stability limit for exposed ice, even in deep cracks, apparently lies near 55 N. Bright and Dark Spots: Many HiRISE and MOC frames showing polygons in the northern plains also show small numbers of bright and dark spots, particularly in western Utopia Planitia. Many of the spots are closely associated with collapse features suggestive of thermokarst. The spots range from tens to approximately 100 meters in diameter. The bright spots are interpreted as exposed ice, due to their prevalence on terrain mapped as ice rich. The dark spots are interpreted as former bright spots, which have darkened as the exposed ice is lost by sublimation. The bright spots may be the martian equivalents of pingos, ice-cored mounds found in periglacial regions on Earth. Terrestrial pingos from which the ice core has melted often collapse to form depressions similar to the martian dark spots. Future Observations: The SHARAD radar should be able to confirm the presence and measure the depth of the interpreted ice-rich layer that forms the Astapus Colles unit. If this layer is confirmed it will strengthen the interpretation of bright polygon cracks and bright spots as exposed ice. HiRISE images of the northern plains are showing unprecedented details of the polygonal cracks. Future HiRISE images that include bright spots, compared to MOC images taken years earlier, will illustrate the temporal stability of the spots. The CRISM spectrometer, with multiple spectral bands and a spatial resolution around 20 meters, should allow mineralogical identification of the material exposed in the polygonal bounding cracks and in the bright spots.

Allen, Carlton C.↗
NASA NTRS1994

Continuous hierarchical slope-aspect color display for parametric surfaces

A method for generating an image of a parametric surface, such as the aspect of terrain which maximizes color contrast to permit easy discrimination of the magnitude, ranges, intervals or classes of a surface parameter while making it easy for the user to visualize the form of the surface, such as a landscape. The four pole colors of the opponent process color theory are utilized to represent intervals or classes at 90 degree angles. The color perceived as having maximum measured luminance is selected to portray the color having an azimuth of an assumed light source and the color showing minimum measured luminance portrays the diametrically opposite azimuth. The 90 degree intermediate azimuths are portrayed by unique colors of intermediate measured luminance, such as red and green. Colors between these four pole colors are used which are perceived as mixtures or combinations of their bounding colors and are arranged progressively between their bounding colors to have perceived proportional mixtures of the bounding colors which are proportional to the interval's angular distance from its bounding colors.

Moellering, Harold J.↗
NASA NTRS1991

Slope-aspect color shading for parametric surfaces

The invention is a method for generating an image of a parametric surface, such as the compass direction toward which each surface element of terrain faces, commonly called the slope-aspect azimuth of the surface element. The method maximizes color contrast to permit easy discrimination of the magnitude, ranges, intervals or classes of a surface parameter while making it easy for the user to visualize the form of the surface, such as a landscape. The four pole colors of the opponent process color theory are utilized to represent intervals or classes at 90 degree angles. The color perceived as having maximum measured luminance is selected to portray the color having an azimuth of an assumed light source and the color showing minimum measured luminance portrays the diametrically opposite azimuth. The 90 degree intermediate azimuths are portrayed by unique colors of intermediate measured luminance, such as red and green. Colors between these four pole colors are used which are perceived as mixtures or combinations of their bounding colors and are arranged progressively between their bounding colors to have perceived proportional mixtures of the bounding colors which are proportional to the interval's angular distance from its bounding colors.

Moellering, Harold J.↗
NASA NTRS2010

Orion Entry Performance-Based Center-of-Gravity Box

The Orion capsule is designed both for Low Earth Orbit missions to the ISS and for missions to the moon. For ISS class missions, the capsule will use an Apollo-style direct entry. For lunar return missions, depending on the timing of the mission, the capsule could perform a direct entry or a skip entry of up to 4800 n.mi. in order to land in the coastal waters of California. The physics of atmospheric re-entry determine the capability of the Orion vehicle. For a given vehicle mass and shape, physics tells us that the driving parameters for an entry vehicle are the hypersonic lift-to-drag ratio (L/D) and the flight path angle at entry interface (gamma(sub EI)). The design of the Orion atmospheric re-entry must meet constraints during both nominal and dispersed flight conditions on landing accuracy, heating rate, total heat load, sensed acceleration, and proper disposal of the Service Module. These constraints define an entry corridor in the space of L/D-gamma(sub EI); if the vehicle falls within this corridor, then all constraints are met. The gamma(sub EI) dimension of the corridor can be further constrained by the gloads experienced during emergency entries. Thus, the entry performance for the Orion vehicle can be described completely by the L/D. Bounds on the hypersonic L/D necessary to achieve all the mission requirements can be defined for the given entry corridor. Landing accuracy performance drives the lower limit on L/D. In order to achieve the desired landing accuracy, a minimum L/D must be ensured. The design of the Thermal Protection System (TPS) drives the upper limit on L/D. A higher L/D can drive mass into the design of the TPS. Conversely, once the TPS is designed, the L/D must be ensured to stay below a certain limit in order for the TPS to stay within its design envelop. The L/D must stay within its upper and lower bounds during dispersed flight conditions. L/D is a function of both the aerodynamics and the center-of-gravity (CG) of the vehicle. The aerodynamics of the vehicle are determined by Computational Fluid Mechanics (CFD) and wind tunnel tests. However, the aerodynamics are not known precisely. Instead, an aerodynamic database has been developed where the aerodynamic coefficients are known to fall within a probabilistic band defined by upper and lower bounds. It is expected that the probabilistic band will shrink after the first missions are flown and real-world data is collected. Until that time, the Orion must be designed to the current aerodynamic database. Thus, for a given aerodynamic database with given uncertainties, the allowable range in L/D can be mapped to an allowable box for the CG location. The CG box is used to set requirements on the dispersions allowed for vehicle packaging and cargo storage. As the aerodynamic uncertainties decrease, the size of the CG box can increase. This paper discusses the technique used to map the minimum and maximum L/D bounds set by the entry performance requirements to the allowable dispersions in CG while accounting for aerodynamic uncertainties. The L/D is defined as the ratio of the lift force to the drag force. It is equivalent to the ratio of lift coefficient (C(sub L)) over drag coefficient (C(sub D)). C(sub L) and C(sub D) are functions of Mach number (M) and angle of attack (alpha). A Mach number of 25 is used as a measuring point of the hypersonic L/D. Variations in C(sub L), C(sub D) and alpha cause variations in L/D. Equation (1) shows the three contributions to the variation in L/D.

Rea, Jeremy R.↗
NASA NTRS2010

Analytical Dimensional Reduction of a Fuel Optimal Powered Descent Subproblem

Current renewed interest in exploration of the moon, Mars, and other planetary objects is driving technology development in many fields of space system design. In particular, there is a desire to land both robotic and human missions on the moon and elsewhere. The landing guidance system must be able to deliver the vehicle to a desired soft landing while meeting several constraints necessary for the safety of the vehicle. Due to performance limitations of current launch vehicles, it is desired to minimize the amount of fuel used. In addition, the landing site may change in real-time in order to avoid previously undetected hazards which become apparent during the landing maneuver. This complicated maneuver can be broken into simpler subproblems that bound the full problem. One such subproblem is to find a minimum-fuel landing solution that meets constraints on the initial state, final state, and bounded thrust acceleration magnitude. With the assumptions of constant gravity and negligible atmosphere, the form of the optimal steering law is known, and the equations of motion can be integrated analytically, resulting in a system of five equations in five unknowns. It is shown that this system of equations can be reduced analytically to two equations in two unknowns. With an additional assumption of constant thrust acceleration magnitude, this system can be reduced further to one equation in one unknown. It is shown that these unknowns can be bounded analytically. An algorithm is developed to quickly and reliably solve the resulting one-dimensional bounded search, and it is used as a real-time guidance applied to a lunar landing test case.

Rea, Jeremy R.↗
NASA NTRS2011

On Time Delay Margin Estimation for Adaptive Control and Optimal Control Modification

This paper presents methods for estimating time delay margin for adaptive control of input delay systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent an adaptive law by a locally bounded linear approximation within a small time window. The time delay margin of this input delay system represents a local stability measure and is computed analytically by three methods: Pade approximation, Lyapunov-Krasovskii method, and the matrix measure method. These methods are applied to the standard model-reference adaptive control, s-modification adaptive law, and optimal control modification adaptive law. The windowing analysis results in non-unique estimates of the time delay margin since it is dependent on the length of a time window and parameters which vary from one time window to the next. The optimal control modification adaptive law overcomes this limitation in that, as the adaptive gain tends to infinity and if the matched uncertainty is linear, then the closed-loop input delay system tends to a LTI system. A lower bound of the time delay margin of this system can then be estimated uniquely without the need for the windowing analysis. Simulation results demonstrates the feasibility of the bounded linear stability method for time delay margin estimation.

Nguyen, Nhan T.↗
NASA NTRS2014

Improving Coverage of Test Cases Generated by Symbolic PathFinder for Programs with Loops

Symbolic execution is a program analysis technique that is used for many purposes, one of which is test-case generation. For loop-free programs, this generates a test-set that achieves path coverage. Program loops, however, imply exponential growth of the number of paths in the best case and non-termination in the worst case. In practice, the number of loop unwindings needs to be bounded for analysis. We consider symbolic execution in the context of the tool Symbolic Pathfinder. This tool extends the model-checker Java Pathfinder and relies on its bounded state-space exploration for termination. We present an implementation of k-bounded loop unwinding, which increases the amount of user-control over the symbolic execution of loops. Bounded unwinding can be viewed as a naive way to prune paths through loops. When using symbolic execution for test-case generation, naively pruning paths is likely at the cost of coverage. In order to improve coverage of branches within a loop body, we present a technique that semi-automatically concretizes variables used in a loop. The basic technique is limited and we therefore present annotations to manually steer symbolic execution towards certain branches, as well as ideas on how the technique can be extended to be more widely applicable.

Programs With Loops↗
NASA NTRS2019

Challenges in Qualification of Thermal Protection Systems in Extreme Entry Environments

Planetary entry vehicles employ ablative TPS materials to shield the aeroshell from entry aeroheating environments. To ensure mission success, it must be demonstrated that the heat shield system, including local features such as seams, does not fail at conditions that are suitably margined beyond those expected in flight. Furthermore, its thermal response must be predictable, with acceptable fidelity, by computational tools used in heat shield design. Mission assurance is accomplished through a combination of ground testing and material response modelling. A material's robustness to failure is verified through arcjet testing while its thermal response is predicted by analytical tools that are verified against experimental data. Due to limitations in flight-like ground testing capability and lack of validated high-fidelity computational models, qualification of heat shield materials is often achieved by piecing together evidence from multiple ground tests and analytical simulations, none of which fully bound the flight conditions and vehicle configuration. Extreme heating environments (>2000 W/sq. cm heat flux and >2 atm pressure), experienced during entries at Venus, Saturn and Ice Giants, further stretch the current testing and modelling capabilities for applicable TPS materials. Fully-dense Carbon Phenolic was the material of choice for these applications; however, since heritage raw materials are no longer available, future uses of re-created Carbon Phenolic will require re-qualification. To address this sustainability challenge, NASA is developing a new dual-layer material based on 3D weaving technology called Heat shield for Extreme Entry Environments (HEEET). Regardless of TPS material, extreme environments pose additional certification challenges beyond what has been typical in recent NASA missions. Scope of this presentation: This presentation will give an overview of challenges faced in verifying TPS performance at extreme heating conditions. Examples include: (1) Bounding aeroheating parameters (heat flux, pressure, shear and enthalpy) in ground facilities. How to certify TPS if environments can't be bounded or aeroheating parameters can't be simultaneously achieved. (2) Higher uncertainties in ground test environments (facility calibration and analytical predictions) at extreme conditions. (3) Testing in flows similar to planetary atmosphere composition (H2/He for Gas and Ice Giants). (4) Test sample size limitations for qualifying seam designs. (5) Lack of computational tools capable of simulating all significant aspects of TPS performance (including initiation and propagation of failures). This presentation will provide recommendations on how the EDL community can address these challenges and mitigate some of the risks involved in flying TPS materials at extreme conditions. Examples include: (1) Dedicated activity to understanding TPS failure modes. Develop computational tools capable of modelling fluid interaction with material's thermostructural response. Validate these tools through failure testing. A better understanding of failure mechanisms may eliminate the need to fully bound all aeroheating parameters in ground testing. (2) Enhancements to current testing facilities to simulate flight-like ablation mechanism (ex. testing in Nitrogen at Ames Interaction Heating Facility to limit oxidation in favor of more sublimation). (3) Improved characterization of test conditions with new diagnostic methods and determination of environment uncertainty through rigorous statistical analysis of available data. (4) Design margin policies that are directly tied to uncertainties in ground test environments and modelling fidelity

Mahzari, Milad↗
NASA NTRS2021

A lingering local exopshere created by a gas plume of a lunar lander

We model the expected local exosphere created by outgassing from a lunar lander plume water deposit located adjacent to a lunar lander. We assume the landing is near dawn within Lacus Mortis at 45oN. We consider a set of water desorption scenarios especially focusing on the water-surface desorption activation energy that can possess a distribution of energy states. Our initial simulation starts with a deposition surface having 1020 water molecules per square meter in a 2 km × 2 km region where 90% of the water is retained by weak water-water sorption interactions and 10% are bound by water-regolith sorption interactions. We find that the loosely bound water molecules in water-water interactions quickly desorb within hours after landing. However, water molecules bound to surface sites having a desorption activation greater than 0.7 eV were found to be retained until the source region rotated to later local times (i.e., surface temperature becomes relatively high). We found such time-delayed desorption leads to a tenuous but lingering exosphere emitted from the lander plume deposit region for many 10's of hours after landing. We also adjusted the initial condition by considering different landing local times and considered a case where 100% of the water is bound by water-regolith interactions (mimicking a porous regolith).

W.M. Farrell↗
NASA NTRS2022

Constraints on Axions from Cosmic Distance Measurements

Axion couplings to photons could induce photon-axion conversion in the presence of magnetic fields in the Universe. This conversion could impact various cosmic distance measurements, such as luminosity distances to type Ia supernovae and angular distances to galaxy clusters, in different ways. In this paper we consider different combinations of the most up-to-date distance measurements to constrain the axion-photon coupling. Employing the conservative cell magnetic field model for the magnetic fields in the intergalactic medium (IGM) and ignoring the conversion in the intracluster medium (ICM), we find the upper bounds on axion-photon couplings to be around 5 × 10^(−12) (nG/B) √(Mpc/s) Ge/V for axion masses m(a) below 10^(−13) eV, where B is the strength of the IGM magnetic field, and s is the comoving size of the magnetic domains. When including the conversion in the ICM, the upper bound is lowered and could reach 5 × 10^(−13) Ge/V for m(a) < 5 × 10^(−12) eV. While this stronger bound depends on the ICM modeling, it is independent of the strength of the IGM magnetic field, for which there is no direct evidence yet. These constraints could be placed on firmer footing with an enhanced understanding and control of the astrophysical uncertainties associated with the IGM and ICM. All the bounds are determined by the shape of the Hubble rate as a function of redshift reconstructable from various distance measurements, and insensitive to today’s Hubble rate, of which there is a tension between early and late cosmological measurements. As an appendix, we discuss the model building challenges of the use of photon-axion conversion to make type Ia supernovae brighter to alleviate the Hubble problem/crisis.

Cosmology of Theories beyond the SM↗
NASA NTRSDate not supplied

Effect of salinity on the preservation of biomarkers in hypersaline microbial mat kerogens

Kerogen is the residue that remains after the minerals and organic compounds have been extracted from a rock using acid and organic solvents, respectively [1]. It is not only the largest organic carbon sink in the geological record but the best-preserved fraction due to its recalcitrance and ability to retain syngenetic source information during deposition [2]. Due to the complex, macromolecular, cross-linked polymeric structure of kerogen, it is difficult to analyse intact, often requiring breakdown into smaller subunits through thermal (pyrolysis) or chemical treatment (chemolysis) [3]. Saline and hypersaline environments host diverse microbial communities, which can trap and bind organic matrices such as cellular components (e.g., extracellular polymeric substances, cell wall, peptidoglycan, sheath material, etc.) with sediments, forming layered, laminated structures called microbial mats. Here we present depth profiles of two hypersaline cores through a microbial mat with differing total salinities. We looked at the composition of organic compounds released from kerogen during high temperature, hydrogen-assisted, pyrolysis to understand the effect of salinity on the composition and timing of their incorporation [4]. Field Site: The Exportadora del Sal S. A. (ESSA) saltern of Guerrero Negro (Baja California Sur, Mexico) lies within a typical sabhka environment adjacent to Laguna Ojo de Liebre. Note the spatial extent of the 13 major ponds of the ESSA system. The GN ponds thrive under well-monitored and stable conditions with steady state accretion and degradation of mat layers (around 0.5–1.4 cm per year). Organic mats typically attain up to 10 cm in thickness, depending on the location, which represents about 60 years of growth since these ponds were established. Sedimentation rate is rapid in these non-lithifying and non-mineralising mats, 1–1.5 cm per year. This environment is ideal for investigating in situ lipid preservation and diagenesis without the influence of constantly changing physical parameters. Methods: P4n5 and P5AB cores were collected as ~9 cm and 6.5 cm fresh cores, respectively, in June 2001 and September 2010, respectively from the ESSA saltern. The P4n5 core (9-9.1% salinity) was taken from Pond 4 near 5 and sub-divided into 10 layers. The P5AB core (11.2% salinity) was taken from Pond 5A near 5B and sub-divided into 8 layers. Lyophilised microbial mat powders were solvent-extracted using a modified Bligh-Dyer method and analysed by gas chromatography-mass spectrometry (GC-MS). Additionally, a subset of layers—layer 4 and layer 7—which represented active biomass and sediment-processed, respectively, were subjected to mild-acid methanolysis. The respective residues from conventional solvent extraction and acid methanolysis were loaded with a molybdenum sulfide catalyst and placed into a stainless-steel reactor. Samples were run on the hydropyrolysis set up (heated to 500 °C with 13-15 MPa of H2 pressure), extracted, and analysed by GC-MS. Results: Molecular profiles from the two ponds were significantly different and reflect the contributions of different photosynthetic and respiratory microbial communities to preserved organic matter. For example, the higher salinity P5AB core showed evidence of greater archaeal inputs (similarly observed in lab culture experiments [5]) as well as potential kerogen-bound carotenoids/carotenoid rearranged products or fragments. A hydrophobic emulsion formed during the acid methanolysis processing of layer 4 from both P4n5 and P5AB and layer 7 of P5AB. Hydropyrolysis of this hydrophobic residues released a greater abundance of polycyclic lipids relative to the pre-extracted control. Implications and Future Work: Catalytic hydropyrolysis of kerogen can rapidly generate abundant saturated pyrolysate products from the bound biomarker pool without altering the structures or stereochemistries of the products [6]. Chemical processing of solvent-extractable residues indicated that cellular matrices such as extracellular polymeric substances (EPS) may play a role in the sequestration of polycyclic lipid biomarkers such as steranes and hopanes. Their higher relative abundance compared to the pre-extracted control in the higher salinity layers and cores preliminarily aligns with this hypothesis, although further experiments are required to confirm this. It has been well-documented that EPS plays an important role in mineralisation, specifically carbonate formation, in microbial ecosystems. EPS can enhance calcium carbonate precipitation by providing diffusion-limited sites that create alkalinity gradients in response to microbial processes [7]. It has been experimentally demonstrated that salinity influences the total amount of EPS (both loosely- and tightly-bound) which increases with increasing salinity [8]. The higher salinity at Guerrero Negro switches the microbial population from filamentous Microcoleus to being dominated by Phormidium, Oscillatoria, and unicellular cyanobacteria. We demonstrated that lipid binding into kerogen via strong covalent linkages occurs at the very earliest stages of sedimentary diagenesis. We are currently investigating the influence of salinity on organic preservation through experimental and modelling approaches. Understanding how key biomarkers transform into preserved organic matter (i.e., from precursor biolipids to bound geolipids) in brine ecosystems will aid the search for organic biosignatures on other planetary bodies, especially Icy Moons and modern Mars.

hypersaline↗
NASA NTRS2021

Safe Tracking Control of an Uncertain Euler-Lagrange System with Full-State Constraints using Barrier Functions

This paper presents a novel, safe tracking control design method that learns the parameters of an uncertain Euler-Lagrange (EL) system online using adaptive learning laws. A barrier function (BF) is first used to transform the full-state constrained EL-dynamics into an equivalent unconstrained dynamics. An adaptive tracking controller is then developed along with the parameter update law in the transformed state space such that the states remain bounded for all time within a prescribed bound. A stability analysis is developed that considers the EL-dynamics’ uncertainty, yielding a semi-globally uniformly ultimately bounded (SGUUB) tracking error and the parameter estimation error. The controller design is validated in simulations using a two-link planar manipulator. The results show the proposed method’s ability to track the reference trajectory while remaining inside each of the predefined state bounds.

Robots↗
NASA NTRS1972

Temperature effects on the strainrange partitioning approach for creep-fatigue analysis

Examination is made of the influence of temperature on the strainrange partitioning approach to creep-fatigue. Results for Cr-Mo steel and Type 316 stainless steel show the four partitioned strainrange-life relationships to be temperature insensitive to within a factor of two on cyclic life. Monotonic creep and tensile ductilities were also found to be temperature insensitive to within a factor of two. The approach provides bounds on cyclic life that can be readily established for any type of inelastic strain cycle. Continuous strain cycling results obtained over a broad range of high temperatures and frequencies are in excellent agreement with bounds provided by the approach. The observed transition from one bound to the other is also in good agreement with the approach.

Halford, G. R.↗
NASA NTRS1970

Minimax control of a system with process uncertainty in substate space

The control of a single input-single output plant with parameter uncertainty was approached using a minimax technique. A linear time invariant controller results which requires only partial state feedback and is optimal in the sense that it minimizes a quadratic criterion involving tracking error, control, and parameter uncertainty. Bounded input-bounded output stability is guaranteed provided the transfer function has only left half plane zeros. If uncertainties are bounded, it is always possible to stabilize the system when sufficient control amplitude is available. The number of states required to generate the control is equal to the system order less the number of zeros.

Basuthakur, S.↗
NASA NTRS1971

Synthesis of feedback systems with large plant ignorance for prescribed time domain tolerances

There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values. The plant is imbedded in a two-degree-of freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor noise at the input to the plant. This report presents a design procedure for this purpose, based on frequency response concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop transmission function in the form of continuous curves on the Nichols chart. The properties of the loop transmission function which satisfy these bounds with minimum effect of sensor noise, are derived.

Horowitz, I. M.↗
NASA NTRS1973

Topologies for neutral functional differential equations.

Bounded topologies are considered for functional differential equations of the neutral type in which present dynamics of the system are influenced by its past behavior. A special bounded topology is generated on a collection of absolutely continuous functions with essentially bounded derivatives, and an application to a class of nonlinear neutral functional differential equations due to Driver (1965) is presented.

Melvin, W. R.↗