A robust optimization approach for magnetic spacecraft attitude stabilization

Attitude stabilization of spacecraft using magnetorquers can be achieved by a proportional–derivative-like control algorithm. The gains of this algorithm are usually determined by using a trial-and-error approach within the large search space of the possible values of the gains. However, when finding the gains in this manner, only a small portion of the search space is actually explored. We propose here an innovative and systematic approach for finding the gains: they should be those that minimize the settling time of the attitude error. However, the settling time depends also on initial conditions. Consequently, gains that minimize the settling time for specific initial conditions cannot guarantee the minimum settling time under different initial conditions. Initial conditions are not known in advance. We overcome this obstacle by formulating a min–max problem whose solution provides robust gains, which are gains that minimize the settling time under the worst initial conditions, thus producing good average behavior. An additional difficulty is that the settling time cannot be expressed in analytical form as a function of gains and initial conditions. Hence, our approach uses some derivative-free optimization algorithms as building blocks. These algorithms work without the need to write the objective function analytically: they only need to compute it at a number of points. Results obtained in a case study are very promising

Quasi-derivations and QD-algebroids

Axioms of Lie algebroid are discussed in order to review some known aspects for non-experts. In particular, it is shown that a Lie QD-algebroid (i.e. a Lie algebra bracket on the Functions(M)-module F of sections of a vector bundle E over a manifold M which satisfies [X,fY]=f[X,Y]+A(X,f)Y for all X,Y from F, all f from Functions(M), and for certain A(X,f) from Functions(M)) is a Lie algebroid if rank(E)>1, and is a local Lie algebra in the sense of Kirillov if E is a line bundle. Under a weak condition also the skew-symmetry of the bracket is relaxed.Comment: LaTeX, 6 pages. Minor corrections, also in the terminology. A few references added. The final version to be published in Rep. Math. Phy

Polynomial Linear Programming with Gaussian Belief Propagation

Interior-point methods are state-of-the-art algorithms for solving linear programming (LP) problems with polynomial complexity. Specifically, the Karmarkar algorithm typically solves LP problems in time O(n^{3.5}), where $n$ is the number of unknown variables. Karmarkar's celebrated algorithm is known to be an instance of the log-barrier method using the Newton iteration. The main computational overhead of this method is in inverting the Hessian matrix of the Newton iteration. In this contribution, we propose the application of the Gaussian belief propagation (GaBP) algorithm as part of an efficient and distributed LP solver that exploits the sparse and symmetric structure of the Hessian matrix and avoids the need for direct matrix inversion. This approach shifts the computation from realm of linear algebra to that of probabilistic inference on graphical models, thus applying GaBP as an efficient inference engine. Our construction is general and can be used for any interior-point algorithm which uses the Newton method, including non-linear program solvers.Comment: 7 pages, 1 figure, appeared in the 46th Annual Allerton Conference on Communication, Control and Computing, Allerton House, Illinois, Sept. 200

Characterizing partition functions of the vertex model

We characterize which graph parameters are partition functions of a vertex model over an algebraically closed field of characteristic 0 (in the sense of de la Harpe and Jones). We moreover characterize when the vertex model can be taken so that its moment matrix has finite rank

Institutions and Development: The Interaction between Trade Regime and Political System

This paper argues that openness to goods trade in combination with an unequal distribution of political power has been a major determinant of the comparatively slow development of resource- or land-abundant regions like South America and the Caribbean in the nineteenth century. We develop a two-sector general equilibrium model with a tax-financed public sector, and show that in a feudal society (dominated by landed elites) productivity-enhancing public investments like the provision of schooling are typically lower in an open than in a closed economy. Moreover, we find that, under openness to trade, development is faster in a democratic system. We also endogenize the trade regime and demonstrate that, in political equilibrium, a land-abundant and landowner-dominated economy supports openness to trade. Finally, we discuss empirical evidence which strongly supports our basic hypotheses.economic development, institutions, political system, public education, trade