Linear Quadratic Regulator (LQR)

LQR is a Control method used to design a controller for linear systems, which seeks to optimize a quadratic cost function based on the system’s state and control inputs.

Brian Machado & Friends used LQR on the BracketBot, so cool.

Wow this is what is used to build the autonomous Helicopter.

The LQR setting assumes a linear dynamical system: where

  • is the state at time
  • is the input at time

It assumes a quadratic cost function , are symmetric with , .

What happens when Q and R are not symmetric? Peter abbeel derives in class for lecture 5, we only care about the symmetric part anyways.