Talks offered at Automation Robotics Research Institute, UTexas, Fort Worth

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Fall semester 2009:

(Coop. & Distrib. Control Research Group)

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October 14th 2009 Topics of Contraction Analysis

- Linear and Contraction maps

- Contractions in Operators Theory

- Topological vector spaces

- Tensor's contraction

- Lipzschitz continuity

- Metric spaces & Metric maps

 

October 21st 2009 Topics of Contraction Analysis

- Metric contractions

- Atractors

- Fixed points and limit cycles

- Fixed points in finite and infinite vector spaces

- Fixed point theorems in continuous and discrete Mathematics.

- Convergence of Fixed points

- Applications

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October 23th 2009 Topics on Computational methods

-Linear Matrix Inequalities,
-Interior Point Methods
-Convex minimization problem
-Newton-Raphson Method
-Quasi-Newton methods
-Wolfe conditions
-Secant Method
-Davidson Fletcher Formula
-Symmetric Rank Formula

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October 29th 2009 

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Stability  & Robust Analysis via Contraction Metrics

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- Manifolds, Topological spaces,

- Homeomorphisms,

- Topological Vector spaces

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November 9th 2009

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Introduction to differential Geometry

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Fieds, Vector fields, Algebras,

Vector spaces, Groups, Rings

Ck vector field, R-Module

Group Homomorphism, Ring Homomorphism

Topological Manifolds

Manifold Structure:  Charts, Atlals, smooth Structure

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November 25th 2009

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Differential Geometry topics

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Ck Atlases, Ck compatible charts, Ck differential Structure of a Manifold

Critical points, Non critical points, singular points of manifolds,

Differentiable and Orientable manifolds.

Smooth Manifolds and Lie Groups,

Riemanian Manifolds

Tangent vectors and directional derivatives

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December 2nd 2009

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Differential Geometry (Lie derivaties)

Inverse function theorems for manifolds

Einstein Notation

Vector representatons

Covariance and contravariance of Vectors

Lie derivatives

Lie Algebras