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