EasyDeepLearn

LQR — Linear Quadratic Regulator and where it's still used.

medium

Answer

  • For linear dynamics xt+1  =  Ax_{t + 1}\; = \;A xt  +  Bx_{t}\; + \;B ut  +  noiseu_{t}\; + \;\mathrm{noise} and quadratic cost x'Qx + u'Ru, optimal policy is linear in state: u = -K x.
  • Solve via discrete-time Riccati equation.
  • Closed-form + fast + optimal for LQ systems.
  • Basis of iLQR (linearize around trajectory + LQR iteratively) — used in robotics locomotion + humanoid control.
  • Modern MBRL uses iLQR / LQR inside planning loops.
Check yourself — multiple choice
  • Same as MPC
  • Linear dynamics xt+1=Ax+Bu+noise  +  quadraticx_{t + 1} = \mathrm{Ax} + \mathrm{Bu} + \mathrm{noise}\; + \;\mathrm{quadratic} cost → optimal u=-Kx via Riccati; closed-form + fast; iLQR linearizes around trajectory for nonlinear systems; robotics staple
  • Random
  • Not real

LQR: linear-quadratic optimal control; iLQR generalization; robotics.

#planning#theory

Practise Reinforcement Learning

214 interview questions in this topic.

Read the lessonFlashcardsTake the quiz

Related questions