A weak Hamiltonian finite element method for optimal control problems

A temporal finite element method based on a mixed form of the Hamiltonian weak principle is developed for dynamics and optimal control problems. The mixed form of Hamilton's weak principle contains both displacements and momenta as primary variables that are expanded in terms of nodal values and simple polynomial shape functions. Unlike other forms of Hamilton's principle, however, time derivatives of the momenta and displacements do not appear therein; instead, only the virtual momenta and virtual displacements are differentiated with respect to time. Based on the duality that is observed to exist between the mixed form of Hamilton's weak principle and variational principles governing classical optimal control problems, a temporal finite element formulation of the latter can be developed in a rather straightforward manner. Several well-known problems in dynamics and optimal control are illustrated. The example dynamics problem involves a time-marching problem. As optimal control examples, elementary trajectory optimization problems are treated

A finite element based method for solution of optimal control problems

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution

More thought - more framing effects? : Framing effects as a function of elaboration

Three studies investigate the impact of the amount of elaboration on framing effects. In all three studies, participants were exposed to decision scenarios similar to the 'Asian disease' problem (Tversky & Kahneman, 1981). The results replicated previous findings: Participants avoided the risky option when the scenario was framed in terms of gains, but preferred the risky option when the scenario was framed in terms of losses. Most importantly, these effects were most pronounced when participants spent more time working on the decision, because of either increased elaboration time (Study 1 and 2) or increased processing motivation (Study 3). Moreover, increased elaboration increased framing effects only when the situation required the scenario to be enriched with additional information. The discussion focuses on the possibility that increased elaboration may not necessarily result in less bias in social judgment and decision making

X-Ray Tomography To Measure Size Of Fragments From Penetration Of High-Velocity Tungsten Rods

Behind-armor debris that results from tungsten rods penetrating armor steel at 2 km/s was studied by analysis of recovered fragments. Fragment recovery was by means of particle board. Individual fragments were analyzed by x-ray tomography, which provides information for fragment identification, mass, shape, and penetration down to masses of a few milligrams. The experiments were complemented by AUTODYN and EPIC calculations. Fragments were steel or tungsten generated from the channel or from the breakout through the target rear surface. Channel fragment motions were well described by Tate theory. Breakout fragments had velocities from the projectile remnant to the channel velocity, apparently depending on where in the projectile a fragment originated. The fragment size distribution was extremely broad and did not correlate well with simple uniform-fragment-size models.Mechanical Engineerin

Optimal guidance law development for an advanced launch system

The proposed investigation on a Matched Asymptotic Expansion (MAE) method was carried out. It was concluded that the method of MAE is not applicable to launch vehicle ascent trajectory optimization due to a lack of a suitable stretched variable. More work was done on the earlier regular perturbation approach using a piecewise analytic zeroth order solution to generate a more accurate approximation. In the meantime, a singular perturbation approach using manifold theory is also under current investigation. Work on a general computational environment based on the use of MACSYMA and the weak Hamiltonian finite element method continued during this period. This methodology is capable of the solution of a large class of optimal control problems

Variational Trajectory Optimization Tool Set: Technical description and user's manual

The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included

The Hubble Space Telescope high speed photometer

The Hubble Space Telescope will provide the opportunity to perform precise astronomical photometry above the disturbing effects of the atmosphere. The High Speed Photometer is designed to provide the observatory with a stable, precise photometer with wide dynamic range, broad wavelenth coverage, time resolution in the microsecond region, and polarimetric capability. Here, the scientific requirements for the instrument are examined, the unique design features of the photometer are explored, and the improvements to be expected over the performance of ground-based instruments are projected

Guiding Trustful Behavior: The Role of Accessible Content and Accessibility Experiences

Trust has been identified as a key ingredient to the prosperity of close relationships, organizations, and societies. While research mainly focused on the antecedents and consequences of trust, much less is known about how individuals assess whether there are enough reasons to warrant trustful action. Two experiments explored the how and when of this assessment, suggesting that antecedents may not only be integrated as content information per se (as generally assumed), but in a feeling-based summary form. Specifically, our results show that the ease or difficulty associated with the identification of antecedents to trust may guide trustful behavior. Furthermore, it is shown that such a feeling-based influence is particularly likely to occur in conditions of personal certainty. Together these results extend prior research in the domains of trust and economic games, and further attest to the fundamental role cognitive feelings play in social life