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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.
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Discontinuous integrands in calculus of variations formulations of trajectory optimization and maximum payload problems with discontinuous state variables
New method for treating optimal trajectories
Optimal final value control theory, applying variational calculus and functional analysis to control function selection for dynamic systems
Lagrange multiplier technique for determining stationary points /of functions/ or stationary functions /of integrals/ of expected value of random functions with certain random constraints
Optimal design of RC lines distributed parameter systems using gradient technique and variational calculus
A description is given of the optimization of solar-sail interplanetary trajectories. The optimization procedure is based on the calculus of variations. Attention is given to aspects of thrust optimization, optimization criteria, a terrestrial planet rendezvous, the Venus and Mars rendezvous, the Mercury rendezvous, and an asteroid roundtrip mission. The investigation shows that a solar-sail spacecraft represents a viable option for the exploration of the solar system in the future.
Accelerated gradient method for numerical solution of parameter optimization problems with nonlinear constraints
Determining sign of second variation in optimal control theory
Solution of trajectory optimization problems by calculus of variations, dynamic programming, and Pontryagin's Principle
The true optimal transfers, including the effects of the inclination and eccentricity of the planets' orbits, between earth and Venus are presented as functions of the corresponding idealized Hohmann transfers. The method of determining the optimal transfers using the calculus of variations is presented. For every possible Hohmann window, specified as a continuous function of the longitude of perihelion of the Hohmann trajectory, the corresponding numerically exact optimal two-impulse transfers are given in graphical form. The cases for which the optimal two-impulse transfer is the absolute optimal, and those for which a three-impulse transfer provides the absolute optimal transfer are indicated. This information furnishes everything necessary for quick and accurate orbit calculations for preliminary Venus mission analysis. This makes it possible to use the actual optimal transfers for advanced planning in place of the standard Hohmann transfers.
Second variation method for computation of optimal control problem with terminal constraint
An implementation of the Sequential Gradient/Restoration Algorithm, SeGRAm, is presented along with selected examples. This spacecraft trajectory optimization and simulation program uses variational calculus to solve problems of spacecraft flying under the influence of one or more gravitational bodies. It produces a series of feasible solutions to problems involving a wide range of vehicles, environments and optimization functions, until an optimal solution is found. The examples included highlight the various capabilities of the program and emphasize in particular its versatility over a wide spectrum of applications from ascent to interplanetary trajectories.
Discontinuous variational problems & optimal flight of multistage rockets
Bolza problem of calculus of variations in terms of control coding applied to trajectories
Simulation of pursuit-evasion differential game using variational method, comparing performance of human pilot to optimal pursuer
In this work, a direct force control numerical predictor-corrector guidance architecture is developed to enable Neptune aerocapture using flight-heritage blunt body aeroshells. A linear aerodynamics model is formulated for a Mars Science Laboratory-derived aeroshell. The application of calculus of variations shows that the optimal angle of attack and side-slip angle control laws are bang-bang. A closed-loop numerical predictor-corrector direct force control guidance algorithm is developed and numerically simulated using the Program to Optimize Simulated Trajectories II. The Monte Carlo simulated trajectories are demonstrated to be robust to the modeled dispersions in aerodynamics, atmospheric density, and entry state. An aerocapture technology trade study demonstrates that blunt body direct force control aerocapture enables similar performance as slender body bank angle control but halves the peak g-loading.
Basic similarities in calculus of variations and optimum control theory for rocket flight between two points
Impulsive solution used to solve optimum trajectory problems with bounded thrust magnitude