The midterm will be held in class on Tuesday, March 20. It will cover material from Lectures 1-9 (that is, from all lectures up to the date of the midterm), 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), PFL, and energy shaping.
- Optimization: LPs, QPs, SDPs (and how they're distinct and special with respect to more general nonlinear programs)
- 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.
Format and Allowed ResourcesThe midterm will be written (pencil-and-paper) -- see midterms from previous years, below. You're allowed to bring any written reference material you would like, including printed resources. However, we recommend you prioritize and refine the material you bring, so that you don't spend the entire exam trying to find the right reference.
Additional Study Material
- Here's the midterm from 2014, and here are solutions for it.
- Here's 3/4ths of the midterm from 2015, and here are solutions for it.