Search NASA⌕ Search

SEARCH · Search NASA

Results for “rational”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Applications of different design methodologies in navigation systems and development at JPL

The NASA/JPL deep space navigation system consists of a complex array of measurement systems, data processing systems, and support facilities, with components located both on the ground and on-board interplanetary spacecraft. From its beginings nearly 30 years ago, this system has steadily evolved and grown to meet the demands for ever-increasing navigation accuracy placed on it by a succession of unmanned planetary missions. Principal characteristics of this system are its capabilities and great complexity. Three examples in the design and development of interplanetary space navigation systems are examined in order to make a brief assessment of the usefulness of three basic design theories, known as normative, rational, and heuristic. Evaluation of the examples indicates that a heuristic approach, coupled with rational-based mathematical and computational analysis methods, is used most often in problems such as orbit determination strategy development and mission navigation system design, while normative methods have seen only limited use is such applications as the development of large software systems and in the design of certain operational navigation subsystems.

Thurman, S. W.↗
NASA NTRS1991

l1-optimal control of multivariable systems with output norm constraints

This paper considers the l1-optimal control problem for general rational plants. It is shown that, for plants with no poles or zeros on the unit circle, an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs. Exactly or approximately, optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed-loop transfer function. No assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators. It is shown that constrained problems in which a set of outputs is regulated subject to l(infinity)-norm constraints on another set of outputs can be solved using a slight modification of the same algorithm.

Mcdonald, J. S.↗
NASA NTRS1992

Intelligent Processing Equipment Projects at DLA

The Defense Logistics Agency is successfully incorporating Intelligent Processing Equipment (IPE) into each of its Manufacturing Technology thrust areas. Several IPE applications are addressed in the manufacturing of two 'soldier support' items: combat rations and military apparel. In combat rations, in-line sensors for food processing are being developed or modified from other industries. In addition, many process controls are being automated to achieve better quality and to gain higher use (soldier) acceptance. IPE applications in military apparel include: in-process quality controls for identification of sewing defects, use of robots in the manufacture of shirt collars, and automated handling of garments for pressing.

Obrien, Donald F.↗
NASA NTRS1990

Efficient solution of parabolic equations by Krylov approximation methods

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Gallopoulos, E.↗
NASA NTRS1993

Undecidability in macroeconomics

In this paper we study the difficulty of solving problems in economics. For this purpose, we adopt the notion of undecidability from recursion theory. We show that certain problems in economics are undecidable, i.e., cannot be solved by a Turing Machine, a device that is at least as powerful as any computational device that can be constructed. In particular, we prove that even in finite closed economies subject to a variable initial condition, in which a social planner knows the behavior of every agent in the economy, certain important social planning problems are undecidable. Thus, it may be impossible to make effective policy decisions. Philosophically, this result formally brings into question the Rational Expectations Hypothesis which assumes that each agent is able to determine what it should do if it wishes to maximize its utility. We show that even when an optimal rational forecast exists for each agency (based on the information currently available to it), agents may lack the ability to make these forecasts. For example, Lucas describes economic models as 'mechanical, artificial world(s), populated by ... interacting robots'. Since any mechanical robot can be at most as computationally powerful as a Turing Machine, such economies are vulnerable to the phenomenon of undecidability.

Chandra, Siddharth↗
NASA NTRS1955

Aerodynamic Characteristics of Various Configurations of a Model of a 45 Degree Swept-wing Airplane at a Mach Number of 2.01

An investigation has been conducted at the Langley 4- by 4-foot supersonic pressure tunnel at a Mach nmber of 2.01 to determine the aerodynamic characteristics of several configurations of a model of a 45 deg swept-wing airplane. The basic configuratin had a wing with 45 deg sweepback at the quarter-chord line, aspect ration 3.2, taper ration 0.468, NACA 65A005.5 sections just outboard of the inlet and NACA 65A003.7 sections at the tip. The wing was mounted slightly above the body center line and an all-movable horizantal tail was located slightly below the extended chord line of the wing. Tre design incorporated twin wing-root supersonic inlets ducted to a single exit at the base of the fuselage. The configurations investigated included an extended nose length, a bumped-fuselage afterbody, an inlet droop, an lncreased wing aspect ratio, and a revised canopy shape. Configurations employing the wing of increased aspect ratio of 3.7, which constituted the bulk of the tests, produced about a 10-percent increase in lift and in longitudinal stability as compared with the basic wing of aspect ratio 3.2. There was a slight but masurable increase in minimum drag and maximum lift-drag ratio.

Spearman, Leroy M↗
NASA NTRS1993

Test results from a simple, low-cost, pressure-fed liquid hydrogen/liquid oxygen rocket combustor

A simple, low-cost rocket engine was designed, fabricated, and successfully hot fire tested over a wide range of interface conditions and operating parameters. The engine used low enthalpy hydrogen (45 to 70 R, 200 to 390 psia) and oxygen (139 to 163 R, 210 to 480 psia) propellants pressure-fed directly from facility cryogenic tanks. The engine demonstrated excellent performance, with 97% average combustion efficiency, and absence of combustion instabilities. Engine design chamber pressure was 300 psia, yielding about 16,500 pounds thrust at sea level with a 3:1 expansion ration test nozzle. The engine used a fixed-element injector based on TRW's unique coaxial pintle design, but was operated at 60%, 80%, and 100% thrust levels by throttling facility propellant valves. The engine was tested at propellant mixture ratios (O/F) from 5.8 to 8.4; design O/F was 6.6. To document combustion stability, in five tests RDX explosive pulse guns were detonated in radial and tangential directions across the combustion chamber during steady-state operation. The largest disturbance consisted of simultaneous detonation of a 20-grain radial gun and a 40-grain tangential gun. In no case was an instability, either feed system mode or chamber acoustic mode, excited. High-frequency piezoelectric pressure transducers documented stable recovery from disturbance overpressures within 40 milliseconds of peak pressure. A total of 67 firing tests, accumulating 149 seconds of firing time above 10% P(sub c), were performed. Since parametric testing required run durations of only 2 to 3 seconds, a heat sink combustion chamber was employed for most runs. To evaluate the feasibility of a low-cost ablative system for a flight engine design, one 20-second continuous firing was conducted with a silicone rubber chamber/throat/nozzle liner cast in one piece directly into the engine. The ablative engine operated at the equivalent of 309 seconds sea level specific impulse, when adjusted to a 98% efficient 6:1 expansion ration nozzle, and 430 seconds vacuum specific impulse, when adjusted to a 98% efficient 50:1 expansion ratio nozzle. This engine and test series represent an initial subscale demonstration of a new booster-class engine that eliminates the cost and complexity associated with regenerative cooling and typical engine cycles. This paper presents a description of the engine design and discussion and summary data plots of the performance measured during the parametric testing.

Dressler, G. A.↗
NASA NTRS1998

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

Belcastro, Christine M.↗
NASA NTRS2002

Effects of Thermomechanical History on the Tensile Behavior of Nitinol Ribbon

Shape memory alloys (SMAs) have enormous potential for a wide variety of applications. A large body of work exists on the characterization of the microstructure and stress-strain behavior of these alloys, Nitinol (NiTi) in particular. However, many attributes of these materials are yet to be fully understood. Previous work at NASA Langley Research Center (LaRC) has included fabrication of hybrid composite specimens with embedded Nitinol actuators and modeling of their thermomechanical behavior. An intensive characterization effort has been undertaken to facilitate fundamental understanding of this alloy and to promote implementation of Nitinol in aerospace applications. Previous work revealed attributes of the Nitinol ribbon that were not easily rationalized with existing data in the literature. In particular, tensile behavior at ambient temperature showed significant dependence on the thermomechanical history prior to testing. The present work is focused on characterizing differences in the microstructure of Nitinol ribbons exposed to four different thermomechanical histories and correlation of the microstructure with tensile properties. Differential scanning calorimetry (DSC) and x-ray diffraction (XRD) analysis were employed to rationalize the microstructures present after exposure to various thermomechanical histories. Three of the Nitinol ribbon conditions were reversible upon heating (in the DSC) through the reverse transformation temperature (A(sub f) to transform the microstructure to austenite. However, the prior thermomechanical conditioning for the Nitinol ribbon that reflected the entire fabrication procedure (4% thermal cycle condition) was found to have an irreversible effect on the microstructure, as it remained unchanged after repeated complete thermal cycles. Tensile tests were conducted to determine the effect of prior thermomechancal conditioning on both the tensile behavior of the Nitinol ribbons and the stress state of the microstructure. The stress-strain behavior of the Nitinol actuators appears to be governed by the interplay between two major variables: namely, microstructural constituents such as the R-phase and the martensite; and the stress state of these constituents (whether twinned with low residual stresses, or detwinned with high residual stresses). The most significant difference in the stress-strain behavior of the four conditions, the critical stress required to achieve an initial stress plateau, was found to depend on both the amount and stress state (twinned or detwinned) of R-phase present in the initial microstructure. Thus, the effect of prior thermomechanical processing is critical to the resulting tensile behavior of the Nitinol actuator. For numerical modeling inputs one must take into account the entire fabrication process on the Nitinol actuator.

Lach, Cynthia L.↗
NASA NTRS2004

Adaptive Multi-Agent Systems for Constrained Optimization

Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.

Macready, William↗
NASA NTRS2004

Adaptive, Distributed Control of Constrained Multi-Agent Systems

Product Distribution (PO) theory was recently developed as a broad framework for analyzing and optimizing distributed systems. Here we demonstrate its use for adaptive distributed control of Multi-Agent Systems (MASS), i.e., for distributed stochastic optimization using MAS s. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (Probability dist&&on on the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. One common way to find that equilibrium is to have each agent run a Reinforcement Learning (E) algorithm. PD theory reveals this to be a particular type of search algorithm for minimizing the Lagrangian. Typically that algorithm i s quite inefficient. A more principled alternative is to use a variant of Newton's method to minimize the Lagrangian. Here we compare this alternative to RL-based search in three sets of computer experiments. These are the N Queen s problem and bin-packing problem from the optimization literature, and the Bar problem from the distributed RL literature. Our results confirm that the PD-theory-based approach outperforms the RL-based scheme in all three domains.

Bieniawski, Stefan↗
NASA NTRS2004

Product Distribution Theory for Control of Multi-Agent Systems

Product Distribution (PD) theory is a new framework for controlling Multi-Agent Systems (MAS's). First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint stare of the agents. Accordingly we can consider a team game in which the shared utility is a performance measure of the behavior of the MAS. For such a scenario the game is at equilibrium - the Lagrangian is optimized - when the joint distribution of the agents optimizes the system's expected performance. One common way to find that equilibrium is to have each agent run a reinforcement learning algorithm. Here we investigate the alternative of exploiting PD theory to run gradient descent on the Lagrangian. We present computer experiments validating some of the predictions of PD theory for how best to do that gradient descent. We also demonstrate how PD theory can improve performance even when we are not allowed to rerun the MAS from different initial conditions, a requirement implicit in some previous work.

Lee, Chia Fan↗
NASA NTRS2005

Distributed Optimization

We demonstrate a new framework for analyzing and controlling distributed systems, by solving constrained optimization problems with an algorithm based on that framework. The framework is ar. information-theoretic extension of conventional full-rationality game theory to allow bounded rational agents. The associated optimization algorithm is a game in which agents control the variables of the optimization problem. They do this by jointly minimizing a Lagrangian of (the probability distribution of) their joint state. The updating of the Lagrange parameters in that Lagrangian is a form of automated annealing, one that focuses the multi-agent system on the optimal pure strategy. We present computer experiments for the k-sat constraint satisfaction problem and for unconstrained minimization of NK functions.

Macready, William↗
NASA NTRS2006

Distributed Constrained Optimization with Semicoordinate Transformations

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve constrained optimization problems. This is done by translating the problem into an iterated game, where each agent controls a different variable of the problem, so that the joint probability distribution across the agents moves gives an expected value of the objective function. The dynamics of the agents is designed to minimize a Lagrangian function of that joint distribution. Here we illustrate how the updating of the Lagrange parameters in the Lagrangian is a form of automated annealing, which focuses the joint distribution more and more tightly about the joint moves that optimize the objective function. We then investigate the use of "semicoordinate" variable transformations. These separate the joint state of the agents from the variables of the optimization problem, with the two connected by an onto mapping. We present experiments illustrating the ability of such transformations to facilitate optimization. We focus on the special kind of transformation in which the statistically independent states of the agents induces a mixture distribution over the optimization variables. Computer experiment illustrate this for &sat constraint satisfaction problems and for unconstrained minimization of NK functions.

Macready, William↗
NASA NTRS2005

Predictive Game Theory

Probability theory governs the outcome of a game; there is a distribution over mixed strat.'s, not a single "equilibrium". To predict a single mixed strategy must use our loss function (external to the game's players. Provides a quantification of any strategy's rationality. Prove rationality falls as cost of computation rises (for players who have not previously interacted). All extends to games with varying numbers of players.

Wolpert, David H.↗
NASA NTRS2007

On the Relationality of the Composition Product: A Survey

When two bilinear state space systems are interconnected in a cascade fashion, the resulting input-output map may not have a bilinear realization. So in 1972, Brockett asked under what conditions is bilinearity preserved under composition. In 1979, Ferfera produced the least restrictive sufficient condition which is presently known using formal power series representations of the input-output maps. The primary intent of this paper is to supply a self-contained proof of Ferfera's sufficient condition for preserving rationality under composition, or equivalently, preserving bilinearity under composition. The proof provided here, which in the large follows the original, is somewhat less complicated as it employs different tools from the theory of rational transductions.

DuffautEspinosa, Luis A.↗
NASA NTRS2008

Stable Calibration of Raman Lidar Water-Vapor Measurements

A method has been devised to ensure stable, long-term calibration of Raman lidar measurements that are used to determine the altitude-dependent mixing ratio of water vapor in the upper troposphere and lower stratosphere. Because the lidar measurements yield a quantity proportional to the mixing ratio, rather than the mixing ratio itself, calibration is necessary to obtain the factor of proportionality. The present method involves the use of calibration data from two sources: (1) absolute calibration data from in situ radiosonde measurements made during occasional campaigns and (2) partial calibration data obtained by use, on a regular schedule, of a lamp that emits in a known spectrum determined in laboratory calibration measurements. In this method, data from the first radiosonde campaign are used to calculate a campaign-averaged absolute lidar calibration factor (t(sub 1)) and the corresponding campaign-averaged ration (L(sub 1)) between lamp irradiances at the water-vapor and nitrogen wavelengths. Depending on the scenario considered, this ratio can be assumed to be either constant over a long time (L=L(sub 1)) or drifting slowly with time. The absolutely calibrated water-vapor mixing ratio (q) obtained from the ith routine off-campaign lidar measurement is given by q(sub 1)=P(sub 1)/t(sub 1)=LP(sub 1)/P(sup prime)(sub 1) where P(sub 1) is water-vapor/nitrogen measurement signal ration, t(sub 1) is the unknown and unneeded overall efficiency ratio of the lidar receiver during the ith routine off-campaign measurement run, and P(sup prime)(sub 1) is the water-vapor/nitrogen signal ratio obtained during the lamp run associated with the ith routine off-campaign measurement run. If L is assumed constant, then the lidar calibration is routinely obtained without the need for new radiosonde data. In this case, one uses L=L(sub 1) = P(sup prime)(sub 1)/t(sub 1), where P(sub 1)(sup prime) is the water-vapor/nitrogen signal ratio obtained during the lamp run associated with the first radiosonde campaign. If L is assumed to drift slowly, then it is necessary to postpone calculation of a(sub 1) until after a second radiosonde campaign. In this case, one obtains a new value, L(sub 2), from the second radiosonde campaign, and for the ith routine off-campaign measurement run, one uses an intermediate value of L obtained by simple linear time interpolation between L(sub 1) and L(sub 2).

Leblanc, Thierry↗
NASA NTRS2006

Aspect-Oriented Subprogram Synthesizes UML Sequence Diagrams

The Rational Sequence computer program described elsewhere includes a subprogram that utilizes the capability for aspect-oriented programming when that capability is present. This subprogram is denoted the Rational Sequence (AspectJ) component because it uses AspectJ, which is an extension of the Java programming language that introduces aspect-oriented programming techniques into the language

Barry, Matthew R.↗