Schedule

* Each day 2 lectures of 90 minutes duration each and a tutorial of 60 minutes to conclude the day.

* Timings Europe (CET):

Lecture 1 - 1430 to 1600 hrs IST (1100 to 1230 CET)

Lecture 2 - 1830 to 2000 hrs IST (1500 to 1630hrs CET)

Tutorial - 2030 to 2130 hrs IST (1700 to 1800 hrs CET)

Day 1:

• Introduction to submanifolds (as subsets of \R^n); tangent space and the cotangent space

• Groups, Lie groups, Lie algebras, group actions, the exponential map

• The infinitesimal generator, the adjoint and coadjoint actions

• Tutorial by Ashutosh and Siddhartha working out details on the SO(3) and SE(3) groups

Day 2:

• A short introduction to the Euler-Lagrange (EL) equations and variational calculus

• The discrete action functional and the derivation of the discrete EL (DEL) equations

• The Hamiltonian side of the DEL equations; DEL equations for systems on Lie groups

• Tutorial by Ashutosh and Siddhartha deriving the DEL equations for a few simple mechanical systems

Day 3:

• Basic ideas of convexity, cones and dual cones

• Tents

• Discrete optimal control

• Tutorial by Siddhartha and Pradyumna on basic discrete optimal control

Day 4:

• Introduction to the discrete PMP

• A quick derivation on Euclidean spaces

• Tutorial by Pradyumna

• Quick recap of discrete optimal control on Lie groups

• Introduction to the discrete PMP on Lie groups

Day 5:

• A quick derivation of the PMP on Lie groups

• Tutorial by Pradyumna

• Numerical aspects with emphasis on the shooting method

• Guest lecture: Karmvir Singh Phogat on his numerics (CANCELLED --- speaker indisposed)