Midterm Information

The midterm will be held in class on Thursday, March 31. It will cover material from Lectures 1 to 13 (that is, from all lectures up to the date of before the spring break), with more emphasis on material that has been covered in problem sets. This includes (though this is not an exhaustive list):

  • The definition of fully-actuated and underactuated systems.
  • Linear systems and their stability and controllability.
  • Reasoning about nonlinear dynamics of "classical" underactuated systems, including the simple pendulum, the acrobot, the cart-pole, the quadrotor, etc.
  • The manipulator equations (as a useful and succint way of writing nonlinear rigid body dynamics).
  • Linearization, optimal control (including LQR).
  • Dynamic programming, value iteration, HJB equation.
  • Lyapunov functions for proving global stability (and LaSalle's Theorem).
  • Lyapunov analysis for linear systems as an SDP.
  • Lyapunov analysis with SOS for polynomial systems.
  • Estimating region of attraction with Lyapunov invariant sets and the S-procedure.
  • How to formulate trajectory optimization problems, e.g. how to write constraints, what would be the decision variables, and whether the resulting optimization is convex.
  • Trajectory stabilization with LQR, MPC and iLQR.

This roughly corresponds to textbook chapters 1, 2, 3, 7, 8, 9, 10 and some parts of appendices C and D.

Format and Allowed Resources

The midterm will be written (pencil-and-paper) -- see midterms from previous years, below. You are allowed to use 1 page of notes(front and back). The notesheet must be handwritten onto a piece of paper. Hand writing notes in electronic format and then printing out those notes is also not acceptable.

Additional Study Material

  • Here is the midterm from 2014, and here are solutions for it.
  • Here is 3/4 of the midterm from 2015, and here are solutions for it.