A robust momentum management and attitude control system for the space station

A game theoretic controller is synthesized for momentum management and attitude control of the Space Station in the presence of uncertainties in the moments of inertia. Full state information is assumed since attitude rates are assumed to be very assurately measured. By an input-output decomposition of the uncertainty in the system matrices, the parameter uncertainties in the dynamic system are represented as an unknown gain associated with an internal feedback loop (IFL). The input and output matrices associated with the IFL form directions through which the uncertain parameters affect system response. If the quadratic form of the IFL output augments the cost criterion, then enhanced parameter robustness is anticipated. By considering the input and the input disturbance from the IFL as two noncooperative players, a linear-quadratic differential game is constructed. The solution in the form of a linear controller is used for synthesis. Inclusion of the external disturbance torques results in a dynamic feedback controller which consists of conventional PID (proportional integral derivative) control and cyclic disturbance rejection filters. It is shown that the game theoretic design allows large variations in the inertias in directions of importance

Tackling Arithmophobia : Teaching How to Read, Understand, and Analyze Financial Statements

This discussion presents different ideas on how to teach accounting and practical finance to law students

The Mass distribution of the Cluster 0957+561 from Gravitational Lensing

Multiply gravitationally lensed objects with known time delays can lead to direct determinations of H$_0$ independent of the distance ladder if the mass distribution of the lens is known. Currently, the double QSO 0957+561 is the only lensed object with a precisely known time delay. The largest remaining source of systematic error in the H$_0$ determination results from uncertainty in the mass distribution of the lens which is comprised of a massive galaxy (G1) and the cluster in which it resides. We have obtained V-band CCD images from CFHT in order to measure the mass distribution in the cluster from its gravitional distorting effect on the appearance of background galaxes. We use this data to constuct a two-dimensional mass map of the field. A mass peak is detected at the $4.5\sigma$ level, offset from, but consistent with, the position of G1. Simple tests reveal no significant substructure and the mass distribution is consistent with a spherical cluster. The peak in the number density map of bright galaxies is offset from G1 similarly to the mass peak. We constructed an azimuthally averaged mass profile centered on G1 out to 2 \arcmin ($400 h^{-1}$ kpc). It is consistent with an isothermal mass distribution with a small core (r_c \approx 5 \arcsec = 17 h^{-1} kpc). The inferred mass within 1 Mpc is consistent with the dynamical mass estimate but $2\sigma$ higher than the upper limits from a ROSAT X-ray study. We discuss implications for H$_0$ in a future paper.Comment: LaTeX, aas version 4 macros. Calibration error in original led to overestimate of cluster mass. Seven out of twelve figures included. Complete paper is available at: http://www.astro.lsa.umich.edu:80/users/philf

Incentivizing Credit Rating Agencies under the Issuer Pay Model Through a Mandatory Compensation Competition

Credit rating agencies are important institutions of the global capital markets. If they had performed properly, the financial crisis of 2008-2009 would not have occurred. This article offers the simplest fix proposed thus far, and it is contrarian. This Article accepts the central role of rating agencies in the regulation of bond investments, the realities of a duopoly, and the issuer-pay model of compensation. The status quo is the baseline. The role of regulation should be to create the conditions necessary to induce competition. This article proposes that a small, recurring portion of revenue earned by the largest rating agencies should be ceded to fund a pay-for-performance bonus, and that the agencies should compete for this bonus on a periodic winner-take-all basis. This modest, at-the-margin bonding mechanism would significantly affect incentives and outcomes: conflict of interest and implicit coordination would be minimized; competition would increase; the quality of ratings would improve. Since regulation would only be required to assess performance and would not change the fundamental industrial organization, this proposal has the advantage of simplicity and feasibility

The Terrorism Risk Insurance Act: Time to End the Corporate Welfare

The terrorist attacks of September 11, 2001, inflicted enormous losses on the insurance industry and businesses. In the wake of the disruptions occurring in the insurance market at the time, the government enacted the Terrorism Risk Insurance Act of 2002 to create a “temporary” federal backstop against catastrophic losses. This program subsidized private risk with public funds through a cost-sharing program for which the government does not receive any compensation. The compelling need for the program was unclear even in the smoldering aftermath of 9/11. Yet in response to effective lobbying by the insurance industry and business interests, Congress has twice extended the program. The program is now scheduled to sunset at the end of 2014, 12 years after this supposedly temporary program was instituted. If there was some ambiguity about the program’s need before, there is none now. Terrorism risk is not more severe than other insurable risks such as natural catastrophes, and a federal backstop stakes public money to protect the insurance industry, and subsidize the terrorism risk insurance premiums for commercial policyholders. The private market is capable of underwriting this risk. This policy analysis suggests that the program should sunset as scheduled in 2014, thus ending this form of corporate welfare