Laboratory for Analysis and Architecture of Systems

About: Laboratory for Analysis and Architecture of Systems is a facility organization based out in Toulouse, France. It is known for research contribution in the topics: Semidefinite programming & Polynomial. The organization has 379 authors who have published 407 publications receiving 10115 citations. The organization is also known as: LAAS-CNRS & LAAS.

Global Optimization with Polynomials and the Problem of Moments

Abstract: We consider the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): {\mathbb{R}}^n\to {\mathbb{R}}$, as well as the global minimum of p(x), in a compact set K defined by polynomial inequalities. It is shown that this problem reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems. A notion of Karush--Kuhn--Tucker polynomials is introduced in a global optimality condition. Some illustrative examples are provided.

Moments, Positive Polynomials And Their Applications

Abstract: . From a theoretical viewpoint, the GPM has developments and impact in var-ious area of Mathematics like algebra, Fourier analysis, functional analysis, operator theory, probabilityand statistics, to cite a few. In addition, and despite its rather simple and short formulation, the GPMhas a large number of important applications in various fields like optimization, probability, mathematicalfinance, optimal control, control and signal processing, chemistry, cristallography, tomography, quantumcomputing, etc.In its full generality, the GPM is untractable numerically. However when K is a compact basic semi-algebraic set, and the functions involved are polynomials (and in some cases piecewise polynomials orrational functions), then the situation is much nicer. Indeed, one can define a systematic numerical schemebased on a hierarchy of semidefinite programs, which provides a monotone sequence that converges tothe optimal value of the GPM. (A semidefinite program is a convex optimization problem which up toarbitrary fixed precision, can be solved in polynomial time.) Sometimes finite convergence may evenocccur.In the talk, we will present the semidefinite programming methodology to solve the GPM and describein detail several applications of the GPM (notably in optimization, probability, optimal control andmathematical finance).R´ef´erences[1] J.B. Lasserre, Moments, Positive Polynomials and their Applications, Imperial College Press, inpress.[2] J.B. Lasserre, A Semidefinite programming approach to the generalized problem of moments,Math. Prog. 112 (2008), pp. 65–92.

Fundamental Concepts of Dependability

Abstract: 1 Origins and Integration of the Concepts Critical Applications was held in 1989 This and the six working conferences that followed fostered the interaction of the dependability and security communities, and advanced the integration of security (confidentiality, integrity and availability) into the framework of dependable computing [22] A summary of [22] is presented next The concept of dependable computing first appears in the 1830’s in the context of Babbage’s Calculating Engine [1,2] The first generation of electronic computers (late 1940’s to mid-50’s) used rather unreliable components, therefore practical techniques were employed to improve their reliability, such as error control codes, duplexing with comparison, triplication with voting, diagnostics to locate failed components, etc [3-5] 2 The Principal Concepts: a Summary

Complementary filter design on the special orthogonal group SO(3)

Abstract: This paper considers the problem of obtaining high quality attitude extraction and gyros bias estimation from typical low cost intertial measurement units for applications in control of unmanned aerial vehiccles. Two different non-linear complementary filters are proposed: Direct complementary filter and Passive non-linear complementary filter. Both filters evolve explicity on the special orthogonal group SO(3) and can be expressed in quaternion form for easy implementation. An extension to the passive ocmplementary filter is proposed to provide adaptive gyro bias estimation.