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At least 145 records · Page 8

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

Collectives for Multiple Resource Job Scheduling Across Heterogeneous Servers

Efficient management of large-scale, distributed data storage and processing systems is a major challenge for many computational applications. Many of these systems are characterized by multi-resource tasks processed across a heterogeneous network. Conventional approaches, such as load balancing, work well for centralized, single resource problems, but breakdown in the more general case. In addition, most approaches are often based on heuristics which do not directly attempt to optimize the world utility. In this paper, we propose an agent based control system using the theory of collectives. We configure the servers of our network with agents who make local job scheduling decisions. These decisions are based on local goals which are constructed to be aligned with the objective of optimizing the overall efficiency of the system. We demonstrate that multi-agent systems in which all the agents attempt to optimize the same global utility function (team game) only marginally outperform conventional load balancing. On the other hand, agents configured using collectives outperform both team games and load balancing (by up to four times for the latter), despite their distributed nature and their limited access to information.

Tumer, K.↗

Hybrid Power Management Program Evaluated Fuel Cell/Ultracapacitor Combinations and Developed Other New Applications

In fiscal year 2003, the continuation of the Hybrid Power Management (HPM) Program through NASA Glenn Research Center's Commercial Technology Office resulted in several new successful applications of this pioneering technology. HPM is the innovative integration of diverse, state-of-the-art power devices in an optimal configuration for space and terrestrial applications. The appropriate application and control of the various power devices significantly improves overall system performance and efficiency. The advanced power devices include ultracapacitors, fuel cells, and photovoltaics. HPM has extremely wide potential, with applications from nanowatts to megawatts--including power generation, transportation systems, biotechnology systems, and space power systems. HPM has the potential to significantly alleviate global energy concerns, improve the environment, and stimulate the economy. Fuel cells provide excellent efficiency and energy density, but do not have good power density. In contrast, ultracapacitors have excellent power density and virtually unlimited cycle life. To improve the power density of the fuel cell, the combination of fuel cells and ultracapacitors was evaluated.

Eichenberg, Dennis J.↗

Performance Optimization Methods for a Memory-Bound, Unstructured-Grid CFD Application on Massively Parallel GPU Platforms

Computational performance of the FUN3D unstructured-grid computational fluid dynamics (CFD) application on massively parallel GPU environments is memory-bound and highly dependent upon efficient reads from and atomic updates to the irregular cell-, edge-, and node-based data structures. In this talk, we present recent efforts into optimizing select performance-critical kernels on NVIDIA Tesla V100 and A100 GPUs and AMD CDNA MI100 GPUs. A novel use of L2 cache residency controls and asynchronous loads into on-chip shared memory are explored on the A100 GPU for the sparse iterative solver, which is dominated by mixed-precision, sparse matrix vector multiplication. Demonstrations show that these methods improve global memory bandwidth utilization by 13.5% on the A100 GPU. Several techniques are also presented that use registers and/or shared memory to facilitate array transposition and aggregation which combine to reduce the frequency and increase the cache efficiency of floating-point atomic updates to the irregular data structures. These methods are demonstrated to improve the kernel throughput by nearly 500% on select kernels on the AMD MI100 over atomic updates directly to global memory. Overall, both V100 and A100 GPUs outperformed the MI100 GPU on kernels dominated by double-precision atomic updates; however, the techniques demonstrated here reduced the performance gap and improved the MI100 performance.

GPU CPU unstructured CFD memory↗

Hybrid Power Management (HPM) Program Resulted in Several New Applications

Hybrid Power Management (HPM) is the innovative integration of diverse, state-of-the-art power devices in an optimal configuration for space and terrestrial applications. The appropriate application and control of the various power devices significantly improves overall system performance and efficiency. The advanced power devices include ultracapacitors, fuel cells, and photovoltaics. HPM has extremely wide potential with applications from nanowatts to megawatts. Applications include power generation, transportation systems, biotechnology systems, and space power systems. HPM has the potential to significantly alleviate global energy concerns, improve the environment, and stimulate the economy.

Eichenberg, Dennis J.↗

Global Radius of Curvature Estimation and Control for the Hobby-Eberly Telescope

A system, which estimates the global radius of curvature (GroC) and corrects for changes in GroC on a segmented primary mirror has been developed for and verified on McDonald Observatory's Hobby Eberly Telescope (HET). The GroC estimation and control system utilizes HET's primary mirror control (PMC) system and the Segment Alignment Maintenance System (SAMS), an inductive edge sensor system. A special set of boundary conditions is applied to the derivation of the optimal edge match control. The special boundary conditions allow the further derivation of an observer, which enables estimation and control of the Groc mode to within HET's specification. The magnitude of the GroC mode can then be controlled despite the inability of the SAMS edge sensor system, by itself, to observe or control the GroC mode. The observer can be extended to any segmented mirror telescope. It will be shown that the observer improves with accuracy as the number of segments increases. This paper presents the mathematical theory of the observer. Simulation results will demonstrate the inherent accuracy and robustness of the system. Performance verification data from the HET will be presented.

Rakoczy, John↗

Research in Satellite-Fiber Network Interoperability

This four part report evaluated the performance of high data rate transmission links using the ACTS satellite, and to provide a preparatory test framework for two of the space science applications that have been approved for tests and demonstrations as part of the overall ACTS program. The test plan will provide guidance and information necessary to find the optimal values of the transmission parameters and then apply these parameters to specific applications. The first part will focus on the satellite-to-earth link. The second part is a set of tests to study the performance of ATM on the ACTS channel. The third and fourth parts of the test plan will cover the space science applications, Global Climate Modeling and Keck Telescope Acquisition Modeling and Control.

Edelson, Burt↗

A Novel Multi-Spacecraft Interplanetary Global Trajectory Optimization Transcription

As the frontier of space exploration continues to advance, so does the design complexity of future interplanetary missions. One avenue of this increasing complexity includes a class of designs known as ``Distributed Spacecraft Missions"; missions where multiple spacecraft coordinate to perform shared objectives. Current approaches for the global trajectory optimization of these Multi-Vehicle Missions (MVMs) are prone to shortcomings including laborious iterative design, considerable human-in-the-loop effort, treatment of the multi-vehicle problem as multiple separate trajectory optimization subproblems (resulting in suboptimal solutions where the whole is less than the sum of its parts), and poor handling of coordination objectives and constraints. There are only a handful of software platforms in existence capable of fully-automated, rapid, interplanetary mission and systems global optimization including the Parallel Global Multiobjective Optimizer (PaGMO), the Gravity Assisted Low-thrust Local Optimization Program (GALLOP), and the Evolutionary Mission Trajectory Generator (EMTG). However, none of these tools is capable of performing such tasks for MVM designs. The work outlined in this paper lays the groundwork for a technique to begin addressing these shortcomings. We present a fully-automated technique which frames interplanetary MVMs as Multi-Objective, Multi-Agent Hybrid Optimal Control Problems (MOMA HOCP). First, the basic functionality of this technique is validated on the single-vehicle problem of reproducing the Cassini interplanetary cruise.

Napier, Sean W.↗

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

Nelson, Andrea↗

Developing a Fundamental Model for an Integrated GPS/INS State Estimation System with Kalman Filtering

This work will demonstrate the integration of sensor and system dynamic data and their appropriate models using an optimal filter to create a robust, adaptable, easily reconfigurable state (motion) estimation system. This state estimation system will clearly show the application of fundamental modeling and filtering techniques. These techniques are presented at a general, first principles level, that can easily be adapted to specific applications. An example of such an application is demonstrated through the development of an integrated GPS/INS navigation system. This system acquires both global position data and inertial body data, to provide optimal estimates of current position and attitude states. The optimal states are estimated using a Kalman filter. The state estimation system will include appropriate error models for the measurement hardware. The results of this work will lead to the development of a "black-box" state estimation system that supplies current motion information (position and attitude states) that can be used to carry out guidance and control strategies. This black-box state estimation system is developed independent of the vehicle dynamics and therefore is directly applicable to a variety of vehicles. Issues in system modeling and application of Kalman filtering techniques are investigated and presented. These issues include linearized models of equations of state, models of the measurement sensors, and appropriate application and parameter setting (tuning) of the Kalman filter. The general model and subsequent algorithm is developed in Matlab for numerical testing. The results of this system are demonstrated through application to data from the X-33 Michael's 9A8 mission and are presented in plots and simple animations.

Canfield, Stephen↗

A random search algorithm for laboratory computers

The small laboratory computer is ideal for experimental control and data acquisition. Postexperimental data processing is often performed on large computers because of the availability of sophisticated programs, but costs and data compatibility are negative factors. Parameter optimization can be accomplished on the small computer, offering ease of programming, data compatibility, and low cost. A previously proposed random-search algorithm ('random creep') was found to be very slow in convergence. A method is proposed (the 'random leap' algorithm) which starts in a global search mode and automatically adjusts step size to speed convergence. A FORTRAN executive program for the random-leap algorithm is presented which calls a user-supplied function subroutine. An example of a function subroutine is given which calculates maximum-likelihood estimates of receiver operating-characteristic parameters from binary response data. Other applications in parameter estimation, generalized least squares, and matrix inversion are discussed.

Curry, R. E.↗

Receiver Would Control Phasing of a Phased-Array Antenna

In a proposed digital signal-processing technique, a radio receiver would control the phasing of a phased-array antenna to aim the peaks of the antenna radiation pattern toward desired signal sources while aiming the nulls of the pattern toward interfering signal sources. The technique was conceived for use in a Global Positioning System (GPS) receiver, for which the desired signal sources would be GPS satellites and typical interference sources would be terrestrial objects that cause multipath propagation. The technique could also be used to optimize reception in spread-spectrum cellular-telephone and military communication systems. During reception of radio signals in a conventional phased-array antenna system, received signals at their original carrier frequencies are phase-shifted, then combined by analog circuitry. The combination signal is then subjected to down-conversion and demodulation. In a system according to the proposed technique (see figure), the signal received by each antenna would be subjected to down-conversion, spread-spectrum demodulation, and correlation; this processing would be performed separately from, and simultaneously with, similar processing of signals received by the other antenna elements. Following analog down-conversion to baseband, the signals would be digitized, and all subsequent processing would be digital. In the digital process, residual carriers would be removed and each signal would be correlated with a locally generated model pseudorandum-noise code, all following normal GPS procedure. As part of this procedure, accumulated values would be added in software and the resulting signals would be phase-shifted in software by the amounts necessary to synthesize the desired antenna directional gain pattern of peaks and nulls. The principal advantage of this technique over the conventional radio-frequency-combining technique is that the parallel digital baseband processing of the signals from the various antenna elements would be a relatively inexpensive and flexible means for exploiting the inherent multiple-peak/multiple-null aiming capability of a phased-array antenna. In the original intended GPS application, the peaks and nulls could be directed independently for each GPS signal being tracked by the GPS receiver. The technique could also be applied to other code-division multiple-access communication systems.

Dunn, Charles E.↗

Implementation of Autonomous GPS Guidance and Control for Spacecraft Formation Flying

This paper presents the general relative orbit dynamics equations and GPS (Global Positioning System) orbit observational equations that have been developed for on-board control of spacecraft flying in formation. The approach to the implementation of the autonomous control for orbit acquisition and maintenance of spacecraft formation using GPS code pseudoranges are presented. As a practical application of the models and method provided in this paper, the orbit control of the Earth-Orbiter 1(EO-1) / Landsat 7 system has been designed, using the discrete-time linear optimal output feedback control. For the actuator of the on/off type reaction jets, the implementation problem of the pulse-amplitude modulation is also studied. Simulation results of autonomous orbit control and maintenance, for 3-dimensional initial orbit error, using optimal output feedback control are shown. These simulation results certified the feasibility of the implementation of the autonomous maintenance control for EO-1/Landsat 7 formation flying by means of the discrete-time linear optimal output feedback control.

Xing, Guang Q.↗

Hesperian-Amazonian Transition Mid-Latitude Valleys: Markers of a Late Martian Climate Optima?

Recently the inventory of fluvial features that have been dated to the late Hesperian to early Amazonian epoch has increased dramatically, including a reassessment of the ages of the large alluvial fans and deltas (e.g., Eberswalde) to this time period. Mid-latitude Valleys (MLVs) are distinct from the older, more integrated Noachian-Hesperian Valley Networks which are deeply dissected, are generally of much larger spatial extent, and are more degraded. Although some MLVs involve rejuvenation of older Valley Networks, many MLVs are carved into smooth or rolling slopes and intercrater terrain. The MLVs range from a few meters to < 300 m in width, with nearly parallel valley walls and planforms that are locally sinuous. Although the MLVs in Newton and Gorgonum basins extend from the basin rims up to 75 km into the basin interior, most MLVs are shorter and often discontinuous. The occurrence of widespread MLVs suggest the possibility of their formation during one or perhaps more regional to global climatic episodes, possibly due to melting of seasonal to long-term accumulations of snow and ice. Temperatures warm enough to cause extensive melting may have occurred during optimal orbital and obliquity configurations, perhaps in conjunction with intensive volcanism releasing moisture and greenhouse gasses, or as a result of a brief episode of warming from a large impact. The concentration of MLVs to the northern and western basin slopes of Newton and Gorgonum basins suggests a possible aspect control to ice accumulation or melting. MLV activity occurred about at the same time as formation of the major outflow channels. A possible scenario is that delivery of water to the northern lowlands provided, through evaporation and sublimation, water that temporarily accumulated in the mid-southern latitudes as widespread ice deposits whose partial melting formed the MLVs and small, dominantly ice-covered lakes.

Moore, Jeffrey↗

Optimization of composite box-beam structures including effects of subcomponent interactions

Minimum mass designs are obtained for a simple box beam structure subject to bending, torque and combined bending/torque load cases. These designs are obtained subject to point strain and linear buckling constraints. The present work differs from previous efforts in that special attention is payed to including the effects of subcomponent panel interaction in the optimal design process. Two different approaches are used to impose the buckling constraints. When the global approach is used, buckling constraints are imposed on the global structure via a linear eigenvalue analysis. This approach allows the subcomponent panels to interact in a realistic manner. The results obtained using this approach are compared to results obtained using a traditional, less expensive approach, called the local approach. When the local approach is used, in-plane loads are extracted from the global model and used to impose buckling constraints on each subcomponent panel individually. In the global cases, it is found that there can be significant interaction between skin, spar, and rib design variables. This coupling is weak or nonexistent in the local designs. It is determined that weight savings of up to 7% may be obtained by using the global approach instead of the local approach to design these structures. Several of the designs obtained using the linear buckling analysis are subjected to a geometrically nonlinear analysis. For the designs which were subjected to bending loads, the innermost rib panel begins to collapse at less than half the intended design load and in a mode different from that predicted by linear analysis. The discrepancy between the predicted linear and nonlinear responses is attributed to the effects of the nonlinear rib crushing load, and the parameter which controls this rib collapse failure mode is shown to be the rib thickness. The rib collapse failure mode may be avoided by increasing the rib thickness above the value obtained from the (linear analysis based) optimizer. It is concluded that it would be necessary to include geometric nonlinearities in the design optimization process if the true optimum in this case were to be found.

Ragon, Scott A.↗

An algorithm for a general class of routing problems derived from Huygens' principle

If a set of N points or nodes with a nonnegative cost associated with each ordered pair is known, it is desired to find a path from one given node to another given node which minimizes the cost sum. An algorithm is presented which yields a global minimum solution after at most N - 1 iterations or on a typical large third-generation computer, after 1 hour of computation time for a 10,000-node problem. The rapid-access data storage capacity demanded by the algorithm is approximately 3N words for costs read in from slow-access storage or 2N words for calculable costs. The time-storage requirements of the algorithm known to the authors. When the problem is viewed as a discretized optimal control problem, after N-1 iterations, an optimal control or node transition is established for each of the N nodes or states; thus, the algorithm can be applied to situations were there may be errors in the control that necessitate a closed loop control that necessitate a closed loop control philosophy.

Avis, L. M.↗

Robust Path Planning and Feedback Design Under Stochastic Uncertainty

Autonomous vehicles require optimal path planning algorithms to achieve mission goals while avoiding obstacles and being robust to uncertainties. The uncertainties arise from exogenous disturbances, modeling errors, and sensor noise, which can be characterized via stochastic models. Previous work defined a notion of robustness in a stochastic setting by using the concept of chance constraints. This requires that mission constraint violation can occur with a probability less than a prescribed value.In this paper we describe a novel method for optimal chance constrained path planning with feedback design. The approach optimizes both the reference trajectory to be followed and the feedback controller used to reject uncertainty. Our method extends recent results in constrained control synthesis based on convex optimization to solve control problems with nonconvex constraints. This extension is essential for path planning problems, which inherently have nonconvex obstacle avoidance constraints. Unlike previous approaches to chance constrained path planning, the new approach optimizes the feedback gain as wellas the reference trajectory.The key idea is to couple a fast, nonconvex solver that does not take into account uncertainty, with existing robust approaches that apply only to convex feasible regions. By alternating between robust and nonrobust solutions, the new algorithm guarantees convergence to a global optimum. We apply the new method to an unmanned aircraft and show simulation results that demonstrate the efficacy of the approach.

autonomuys vehicles↗