A modified Newton's method for solving trajectory optimization problems.
Modified Newton method for solution of simultaneous nonlinear equations applied to variational two point boundary value problems in trajectory optimization
Lastman, G. J.↗
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Results for “Nonlinear optimization”
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Optimal control of satellite attitude acquisition by a random search algorithm on a hybrid computer.
Random search algorithm for nonlinear orbital transfer problems applied to optimal control of satellite attitude acquisition
Brocker, D. H.↗
A trajectory planning scheme for spacecraft in the space station environment
Simulated annealing is used to solve a minimum fuel trajectory problem in the space station environment. The environment is special because the space station will define a multivehicle environment in space. The optimization surface is a complex nonlinear function of the initial conditions of the chase and target crafts. Small permutations in the input conditions can result in abrupt changes to the optimization surface. Since no prior knowledge about the number or location of local minima on the surface is available, the optimization must be capable of functioning on a multimodal surface. It was reported in the literature that the simulated annealing algorithm is more effective on such surfaces than descent techniques using random starting points. The simulated annealing optimization was found to be capable of identifying a minimum fuel, two-burn trajectory subject to four constraints which are integrated into the optimization using a barrier method. The computations required to solve the optimization are fast enough that missions could be planned on board the space station. Potential applications for on board planning of missions are numerous. Future research topics may include optimal planning of multi-waypoint maneuvers using a knowledge base to guide the optimization, and a study aimed at developing robust annealing schedules for potential on board missions.
Soller, Jeffrey Alan↗
Optimization of transformer ratio and beam loading in a plasma wakefield accelerator with a structure-exploiting algorithm
Plasma-based acceleration has emerged as a promising candidate as an accelerator technology for a future linear collider or a next-generation light source. We consider the plasma wakefield accelerator (PWFA) concept where a plasma wave wake is excited by a particle beam and a trailing beam surfs on the wake. For a linear collider, the energy transfer efficiency from the drive beam to the wake and from the wake to the trailing beam must be large, while the emittance and energy spread of the trailing bunch must be preserved. One way to simultaneously achieve this when accelerating electrons is to use longitudinally shaped bunches and nonlinear wakes. In the linear regime, there is an analytical formalism to obtain the optimal shapes. In the nonlinear regime, however, the optimal shape of the driver to maximize the energy transfer efficiency cannot be precisely obtained because currently no theory describes the wake structure and excitation process for all degrees of nonlinearity. In addition, the ion channel radius is not well defined at the front of the wake where the plasma electrons are not fully blown out by the drive beam. We present results using a novel optimization method to effectively determine a current profile for the drive and trailing beam in PWFA that provides low energy spread, low emittance, and high acceleration efficiency. We parameterize the longitudinal beam current profile as a piecewise-linear function and define optimization objectives. For the trailing beam, the algorithm converges quickly to a nearly inverse trapezoidal trailing beam current profile similar to that predicted by the ultrarelativistic limit of the nonlinear wakefield theory. For the drive beam, the beam profile found by the optimization in the nonlinear regime that maximizes the transformer ratio also resembles that predicted by linear theory. Furthermore, the current profiles found from the optimization method provide higher transformer ratios compared with the linear ramp predicted by the relativistic limit of the nonlinear theory.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Iteration procedures for indirect trajectory optimization methods.
Numerical method solution of nonlinear two point boundary value problem associated with optimum transfer of spacecraft
Lewallen, J. M.↗
Supersonic second order analysis and optimization program user's manual
Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance theory was utilized to meet this objective. Numerical codes were developed for analysis and design of relatively general three dimensional geometries. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes. Case computational time of one minute on a CDC 176 are typical for practical aircraft arrangement.
Clever, W. C.↗
General Methodology for Designing Spacecraft Trajectories
A methodology for designing spacecraft trajectories in any gravitational environment within the solar system has been developed. The methodology facilitates modeling and optimization for problems ranging from that of a single spacecraft orbiting a single celestial body to that of a mission involving multiple spacecraft and multiple propulsion systems operating in gravitational fields of multiple celestial bodies. The methodology consolidates almost all spacecraft trajectory design and optimization problems into a single conceptual framework requiring solution of either a system of nonlinear equations or a parameter-optimization problem with equality and/or inequality constraints.
Condon, Gerald↗
An algorithm for Liapunov stability analysis of complex nonlinear systems with application to the Orbiting Astronomical Observatory
Optimal quadratic Liapunov function generating algorithm for estimating domain of equilibrium attraction of nonlinear star tracker attitude control systems for OAO stability
Chomas, A.↗
Simultaneous analysis and design
Optimization techniques are increasingly being used for performing nonlinear structural analysis. The development of element by element (EBE) preconditioned conjugate gradient (CG) techniques is expected to extend this trend to linear analysis. Under these circumstances the structural design problem can be viewed as a nested optimization problem. There are computational benefits to treating this nested problem as a large single optimization problem. The response variables (such as displacements) and the structural parameters are all treated as design variables in a unified formulation which performs simultaneously the design and analysis. Two examples are used for demonstration. A seventy-two bar truss is optimized subject to linear stress constraints and a wing box structure is optimized subject to nonlinear collapse constraints. Both examples show substantial computational savings with the unified approach as compared to the traditional nested approach.
Haftka, R. T.↗
Simultaneous analysis and design
Optimization techniques are increasingly being used for performing nonlinear structural analysis. The development of element by element (EBE) preconditioned conjugate gradient (CG) techniques is expected to extend this trend to linear analysis. Under these circumstances the structural design problem can be viewed as a nested optimization problem. There are computational benefits to treating this nested problem as a large single optimization problem. The response variables (such as displacements) and the structural parameters are all treated as design variables in a unified formulation which performs simultaneously the design and analysis. Two examples are used for demonstration. A seventy-two bar truss is optimized subject to linear stress constraints and a wing box structure is optimized subject to nonlinear collapse constraints. Both examples show substantial computational savings with the unified approach as compared to the traditional nested approach.
Haftka, R. T.↗
Supersonic airfoil optimization
A procedure for the optimization of supersonic airfoils is presented. A nonlinear, full-potential solver (NCOREL) is coupled with a numerical optimizer (CONMIN). The NCOREL code is a three-dimensional supersonic marching method, however, only two-dimensional (conical) results are used for the airfoil problem. Each airfoil evaluated in the NCOREL aerodynamic code is composed of a linear combination of user-specified basis airfoils. The weighting factors of the basis airfoils plus the angle of attack form the design variable vector. The inviscid drag coefficient is minimized subject to lift and crossflow Mach number gradient constraints. The optimization strategy is found to be extremely important for the efficient determination of an optimum airfoil.
Pittman, J. L.↗
Flat nonlinear optics with intersubband polaritonic metasurfaces
Nonlinear intersubband polaritonic metasurfaces produce some of the strongest second- and third-order nonlinear optical responses reported for condensed matter systems at infrared frequencies. These metasurfaces are fabricated as two-dimensional arrays of nanoresonators from multi-quantum-well semiconductor heterostructures, designed to produce strong nonlinear responses associated with intersubband transitions. By optimally coupling the optical modes of the nanoresonators to vertically polarized intersubband transitions in semiconductor heterostructures, one can boost the nonlinear response associated with intersubband transitions, make intersubband transitions interact with free-space radiation at normal incidence, and hence produce optically thin flat nonlinear optical elements compatible with free-space optical setups. As a result of the strong nonlinear response in these systems, significant nonlinear conversion efficiencies (>0.1 %) can be attained in deeply subwavelength optical films using modest pumping intensities of only 10–100 kW/cm 2 . Subwavelength metasurface thickness relaxes phase-matching constraints limiting the operation of bulk nonlinear crystals. Furthermore, the amplitude and phase of the nonlinear optical response in intersubband polaritonic metasurfaces can be tailored for a specific pump wavelength and a nonlinear process of interest through the co-optimization of quantum engineering of electron states in semiconductor heterostructures and photonic engineering of the metasurface nanoresonators design. Additionally, an applied voltage can dynamically control the amplitude and phase of the nonlinear optical response at a nanoresonator level. Here, we review the current state of the art in this rapidly expanding field, focusing on nonlinear processes supporting second-harmonic generation, saturable absorption, and optical power limiting.
flat optics↗
Optimal control of saturating systems with stochastic inputs.
Wiener filtering theory for stationary ergodic inputs with known spectral densities and optimal control transfer functions of random-input nonlinear saturating systems with random unwanted disturbances
RANDOM VARIABLE↗
Automated design and optimization of flexible booster autopilots via linear programming, volume 1
A nonlinear programming technique was developed for the automated design and optimization of autopilots for large flexible launch vehicles. This technique, which resulted in the COEBRA program, uses the iterative application of linear programming. The method deals directly with the three main requirements of booster autopilot design: to provide (1) good response to guidance commands; (2) response to external disturbances (e.g. wind) to minimize structural bending moment loads and trajectory dispersions; and (3) stability with specified tolerances on the vehicle and flight control system parameters. The method is applicable to very high order systems (30th and greater per flight condition). Examples are provided that demonstrate the successful application of the employed algorithm to the design of autopilots for both single and multiple flight conditions.
Hauser, F. D.↗
A technique for locating function roots and for satisfying equality constraints in optimization
A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.
Sobieszczanski-Sobieski, Jaroslaw↗
A technique for locating function roots and for satisfying equality constraints in optimization
A new technique for locating simultaneous roots of a set of functions is described. The technique is based on the property of the Kreisselmeier-Steinhauser function which descends to a minimum at each root location. It is shown that the ensuing algorithm may be merged into any nonlinear programming method for solving optimization problems with equality constraints.
Sobieszczanski-Sobieski, J.↗
Exploring Optimization and Robust Control Techniques for use in Control Design of Nonlinear Dynamic Systems.
Abstract not provided.
Wilbanks, James↗
Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting
This paper is focused on the aspects of limiting in residual distribution (RD) schemes for high-order finite element approximations to advection problems. Both continuous and discontinuous Galerkin methods are considered in this work. Discrete maximum principles are enforced using algebraic manipulations of element contributions to the global nonlinear system. The required modifications can be carried out without calculating the element matrices and assembling their global counterparts. The components of element vectors associated with the standard Galerkin discretization are manipulated directly using localized subcell weights to achieve optimal accuracy. Low-order nonlinear RD schemes of this kind were originally developed to calculate local extremum diminishing predictors for flux-corrected transport (FCT) algorithms. In the present paper, we incorporate limiters directly into the residual distribution procedure, which makes it applicable to stationary problems and leads to well-posed nonlinear discrete problems. To circumvent the second-order accuracy barrier, the correction factors of monolithic limiting approaches and FCT schemes are adjusted using smoothness sensors based on second derivatives. Finally, the convergence behavior of presented methods is illustrated by numerical studies for two-dimensional test problems.
97 MATHEMATICS AND COMPUTING↗