ELL 808: Advanced Topics in Control Theory
Mode: Online lectures on MS-Teams and Impartus (MTh - 5-6:30pm).
Syllabus
Introduction To Geometric Viewpoint
Maps, Equivalence, Relations, Permutations
Vector Spaces, Linear Maps
Change Of Basis, Dual Space
Bilinear Forms
Flat Map, Sharp Map, Tensors
Tensors Basis Representation
Pullback Pushforward Maps
Topology
Differentiability, Taylor Series, Real Analyticity
Charts, Atlas, Differentiable Structure
Maps Between Spaces
Tangent Bundle
Tangent Bundle, Tangent Map
Lie Brackets, Examples, And Distributions
Involutivity, Accessibility, Strong Accessibility
Observability
Review
Reference books
Control Theory from the Geometric Viewpoint by A A Agrachev and Y L Sachkov
Non-linear Dynamical Control Systems by H. Nijmeijer and A. J. Van der Schaft
Geometric Control of Mechanical Systems by F. Bullo and A. D. Lewis
Geometric Control Theory by Velimir Jurjedvic
Some research papers to be specified later.
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