Optimal guidance law development for an advanced launch system

A regular perturbation analysis is presented. Closed-loop simulations were performed with a first order correction including all of the atmospheric terms. In addition, a method was developed for independently checking the accuracy of the analysis and the rather extensive programming required to implement the complete first order correction with all of the aerodynamic effects included. This amounted to developing an equivalent Hamiltonian computed from the first order analysis. A second order correction was also completed for the neglected spherical Earth and back-pressure effects. Finally, an analysis was begun on a method for dealing with control inequality constraints. The results on including higher order corrections do show some improvement for this application; however, it is not known at this stage if significant improvement will result when the aerodynamic forces are included. The weak formulation for solving optimal problems was extended in order to account for state inequality constraints. The formulation was tested on three example problems and numerical results were compared to the exact solutions. Development of a general purpose computational environment for the solution of a large class of optimal control problems is under way. An example, along with the necessary input and the output, is given

Singular perturbation analysis of AOTV-related trajectory optimization problems

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model

The Effects of Acute Stress Exposure on Neural Correlates of Pavlovian Conditioning with Monetary Gains and Losses

Pavlovian conditioning involves the association of an inherently neutral stimulus with an appetitive or aversive outcome, such that the neutral stimulus itself acquires reinforcing properties. Across species, this type of learning has been shown to involve subcortical brain regions such as the striatum and the amygdala. It is less clear, however, how the neural circuitry involved in the acquisition of Pavlovian contingencies in humans, particularly in the striatum, is affected by acute stress. In the current study, we investigate the effect of acute stress exposure on Pavlovian conditioning using monetary reinforcers. Participants underwent a partial reinforcement conditioning procedure in which neutral stimuli were paired with high and low magnitude monetary gains and losses. A between-subjects design was used, such that half of the participants were exposed to cold stress while the remaining participants were exposed to a no stress control procedure. Cortisol measurements and subjective ratings were used as measures of stress. We observed an interaction between stress, valence, and magnitude in the ventral striatum, with the peak in the putamen. More specifically, the stress group exhibited an increased sensitivity to magnitude in the gain domain. This effect was driven by those participants who experienced a larger increase in circulating cortisol levels in response to the stress manipulation. Taken together, these results suggest that acute stress can lead to individual differences in circulating cortisol levels which influence the striatum during Pavlovian conditioning with monetary reinforcers

A Test of Photometric Redshifts for X-ray Selected Sources

We test the effectiveness of photometric redshifts based upon galaxy spectral template fitting for X-ray luminous objects, using a sample of 65 sources detected by Chandra in the field of the Caltech Faint Galaxy Redshift Survey (CFGRS). We find that sources with quasar-dominated spectra (for which galaxy spectral templates are not appropriate) are easily identified, and that photometric redshifts are robust for the rest of the sources in our sample. Specifically, for the 59 sources that are not quasar-dominated at optical wavelengths, we find that the photometric redshift estimates have scatter comparable to the field galaxy population in this region. There is no evidence for a trend of increasing dispersion with X-ray luminosity over the range L_X = 10^39 - 5x10^43 erg/s, nor is there a trend with the ratio of X-ray to optical flux, f_X/f_R. The practical implication of this work is that photometric redshifts should be robust for the majority (~90%) of the X-ray sources down to f_X ~ 10^-16 erg/s/cm^2 that have optical counterparts brighter than R ~ 24. Furthermore, the same photometry can be easily used to identify the sources for which the photometric redshifts are likely to fail. Photometric redshift estimation can thus be utilized as an efficient tool in analyzing the statistical properties of upcoming large Chandra and XMM-Newton data sets and identifying interesting subsamples for further study.Comment: To appear in ApJ (6 pages, 6 figures). Replaced with accepted versio

Distant Galaxy Clusters Identified From Optical Background Fluctuations

We present the first high redshift (0.3 < z < 1.1) galaxy clusters found by systematically identifying optical low surface brightness fluctuations in the background sky. Using spectra obtained with the Keck telescope and I-band images from the Palomar 1.5m telescope, we conclude that at least eight of the ten candidates examined are high redshift galaxy clusters. The identification of such clusters from low surface brightness fluctuations provides a complementary alternative to classic selection methods based on overdensities of resolved galaxies, and enables us to search efficiently for rich high redshift clusters over large areas of the sky. The detections described here are the first in a survey that covers a total of nearly 140 sq. degrees of the sky and should yield, if these preliminary results are representative, over 300 such clusters.Comment: Submitted to ApJ

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