Courses / control

CS-2 State-Space & Optimal Control

intermediate~15 hours15 lessonsEnvironment: pyodide

Prerequisites: cs1-classical-control

Start: From transfer functions to state space: the state vectorPractice questions

Modules

Module 1 — State-space modeling
  1. 1From transfer functions to state space: the state vector
  2. 2Linearization: taming nonlinear dynamics at an operating point
  3. 3The cart-pole and the 2-link arm: two canonical state-space models
Module 2 — Controllability/observability/pole placement
  1. 1Controllability: which states can the input reach?
  2. 2Observability: which states can the output reveal?
  3. 3Pole placement: choosing the closed-loop eigenvalues
Module 3 — LQR
  1. 1LQR I: pricing error against effort
  2. 2LQR II: solving Riccati, balancing the cart-pole
  3. 3LQR III: tuning Q and R — Bryson's rule and the angle-only shootout
Module 4 — Estimation
  1. 1The Luenberger observer: reconstructing the state
  2. 2From observer to Kalman: pricing noise
  3. 3LQG and the separation principle — and its fine print
Module 5 — MPC intro
  1. 1When constraints enter: saturation, capture regions, and the limits of clipping
  2. 2The receding horizon: plan, act, replan
  3. 3MPC as a quadratic program — and the road to walking

Textbooks

Video resources

  • Control Bootcamp — Steve Brunton