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.