Kalman filter, LQR, LQG, and Separation Principle

by allenlu2007


From Andrew Ng lecture


Kalman filter is to estimate state

LQR is to obtain the optimal control policy

It turns out in Kalman filter case; estimate state is optimal for the optimal control policy,

namely LQG  – linear quadratic gaussian

This is also called the separation principle – estimation and control can separate independently.


LQR can ignore state noise

LQG can additionally ignore the observation noise

separation principle!!



From Princeton Stigel’s note


From MIT underactuated Robotics!! Excellent lecture by Russ Tedrake 

Very good in control.  Use a simple pendulum as a base example. 

Explore to different control algorithms for nonlinear dynamic 

–> nonlinear dynamics Chaos by Steve Strogatz

Simple pendulum

Lagrange: generalized force to model friction (damping)


— limit cycle


Optimal control 

— analytical OC

— numerical OC based on DP


Numerical OC based on policy search