Optimal control and convex programming.
Optimal control for investment program, obtaining solution through convex programming
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Optimal control for investment program, obtaining solution through convex programming
Optimal control and convex programming, discussing problem of admissible investiment program control for production constraints
The capabilities and applications of the three-degree-of-freedom (3DOF) version and the six-degree-of-freedom (6DOF) version of the Program to Optimize Simulated Trajectories (POST) are summarized. The document supplements the detailed program manuals by providing additional information that motivates and clarifies basic capabilities, input procedures, applications and computer requirements of these programs. The information will enable prospective users to evaluate the programs, and to determine if they are applicable to their problems. Enough information is given to enable managerial personnel to evaluate the capabilities of the programs and describes the POST structure, formulation, input and output procedures, sample cases, and computer requirements. The report also provides answers to basic questions concerning planet and vehicle modeling, simulation accuracy, optimization capabilities, and general input rules. Several sample cases are presented.
As current and future NASA missions become increasingly more complex, the need to ensure requirements are met across the many phases of flight is more pertinent. Accurately modeling the individual phases of flight is difficult alone, but verifying that the overall mission is characterized properly presents additional challenges. In previous works, there have been successful demonstrations of interfacing multiple software applications to provide a more detailed end-to-end optimized simulation. The work herein will focus on leveraging two NASA built tools that have been successfully utilized on NASA missions: Copernicus and the Program to Optimize Simulated Trajectories II (POST2).
Optimum hat-stiffened compression panel designs are determined by a structural synthesis technique. The effects of simplifying assumptions made in the buckling analysis for the optimization program are investigated by a linked plate element program. Optimization results for hat-stiffened graphite-epoxy panels show a 50-percent weight savings over optimized aluminum panels. Composite panels are shown to possess a variety of proportions at nearly constant weight.
Programming Structural Synthesis System (PROSSS) provides structural synthesis capability by combining SPAR and CONMIN computer programs with set of interface procedures. SPAR is large general-purpose finite-element structural-analysis program, and CONMIN is large general-purpose optimization program. User supplies two small problem-dependent programs to define design variables, constraints, and objective function.
Documentation of the NBODY trajectory optimization program is presented in the form of a mathematical development plus a user's manual. Optimal multistage-launch ascent trajectories may be determined by variational thrust steering during the upper phase. Optimal low-thrust interplanetary spacecraft trajectories may also be calculated with solar power or constant power, all-propulsion or embedded coast arcs, fixed or optimal thrust angles, and a variety of terminal end conditions. A hybrid iteration scheme solves the boundary-value problem, while either transversality conditions or a univariate search scheme optimize vehicle or trajectory parameters.
Generalization of nonlinear programming problem - optimization problems
A significant energy and cost savings can be obtained by integrating various utility services (space heating and cooling, electrical power generation, solid waste disposal, potable water, and waste water treatment) into a single unit which provides buildings or groups of buildings with these services. This paper presents a description of a computer program, called the Energy Systems Optimization Program (ESOP). This program predicts the loads, energy requirements, equipment sizes, and life-cycle costs of alternative methods of meeting these utility requirements. The program has been used extensively for performing energy analyses of Modular Integrated Utility Systems (MIUS).
Optimization procedures are developed to systematically provide closely-spaced vibration frequencies. A general-purpose finite-element program for eigenvalue and sensitivity analyses is combined with formal mathematical programming techniques. Results are presented for three studies. The first study uses a simple model to obtain a design with two pairs of closely-spaced frequencies. Two formulations are developed: an objective function-based formulation and constraint-based formulation for the frequency spacing. It is found that conflicting goals are handled better by a constraint-based formulation. The second study uses a detailed model to obtain a design with one pair of closely-spaced frequencies while satisfying requirements on local member frequencies and manufacturing tolerances. Two formulations are developed. Both the constraint-based and the objective function-based formulations perform reasonably well and converge to the same results. However, no feasible design solution exists which satisfies all design requirements for the choices of design variables and the upper and lower design variable values used. More design freedom is needed to achieve a fully satisfactory design. The third study is part of a redesign activity in which a detailed model is used. The use of optimization in this activity allows investigation of numerous options (such as number of bays, material, minimum diagonal wall thicknesses) in a relatively short time. The procedure provides data for judgments on the effects of different options on the design.
Optimization procedures are developed to systematically provide closely-spaced vibration frequencies. A general purpose finite-element program for eigenvalue and sensitivity analyses is combined with formal mathematical programming techniques. Results are presented for three studies. The first study uses a simple model to obtain a design with two pairs of closely-spaced frequencies. Two formulations are developed: an objective function-based formulation and constraint-based formulation for the frequency spacing. It is found that conflicting goals are handled better by a constraint-based formulation. The second study uses a detailed model to obtain a design with one pair of closely-spaced frequencies while satisfying requirements on local member frequencies and manufacturing tolerances. Two formulations are developed. Both the constraint-based and the objective function-based formulations perform reasonably well and converge to the same results. However, no feasible design solution exists which satisfies all design requirements for the choices of design variables and the upper and lower design variable values used. More design freedom is needed to achieve a fully satisfactory design. The third study is part of a redesign activity in which a detailed model is used.
The Program to Optimize Simulated Trajectories II (POST2) has been continuously developed for over 40 years and has been used in many flight and research projects. Recently, there has been an effort to improve the POST2 architecture by promoting modularity, flexibility, and ability to support multiple simultaneous projects. The purpose of this paper is to provide insight into the development of trajectory simulation in POST2 by describing methods and examples of various improved models for a launch vehicle liftoff and ascent.
Optimal control method based on linear programming for satellite fuel consumption
Optimal transfer trajectories from earth parking orbit to various terminal conic constraints, and ROBOT computer program modifications
Search algorithms for computer programming of multivariate optimization techniques for nonlinear, parametrically defined systems
Development of the Program to Optimize Simulated Trajectories (POST) began in the 1970s. Since then, it has become widely utilized across NASA, industry, and academia to solve a variety of atmospheric ascent and entry problems. Its successor, POST2, has undergone many upgrades since its release in the 1990s. Recently, there has been an increasing desire to take advantage of the advances in parallel computing for both offline and online systems. Thus, modifications were made to allow POST2 to simulate multiple trajectories simultaneously without adversely affecting results. This capability is leveraged to calculate optimization solutions in parallel as opposed to sequentially. A demonstration of the benefits is presented using a small set of POST2 regression tests, as well as a project simulating a human-scale Lunar lander.
Development of the Program to Optimize Simulated Trajectories (POST) began in the 1970s. Since then, it has become widely utilized across NASA, industry, and academia to solve a variety of atmospheric ascent and entry problems. Its successor, POST2, has undergone many upgrades since its release in the 1990s. Recently, there has been an increasing desire to take advantage of the advances in parallel computing for both offline and online systems. Thus, modifications were made to allow POST2 to simulate multiple trajectories simultaneously without adversely affecting results. This capability is leveraged to calculate optimization solutions in parallel as opposed to sequentially. A demonstration of the benefits is presented using a small set of POST2 regression tests, as well as a project simulating a human-scale Lunar lander.
Optimization of time-temperature parameters for creep and stress rupture, with application to data from German cooperative long-time creep program