Control

LQR

LQR (linear quadratic regulator) is an optimal control method that, for linear dynamics and a quadratic cost on state error and control effort, yields the optimal linear state-feedback law u = -Kx, with the gain computed by solving an algebraic Riccati equation. Nonlinear robots use LQR on local linearizations, in gain scheduling, for trajectory stabilization via time-varying LQR, and inside iterative variants such as iLQR for trajectory optimization.

Why it matters for physical AI

Principled feedback synthesis with provable properties remains indispensable for stabilizing balancing robots and tracking planned trajectories, and iLQR-style solvers power the model-based planning layers beneath many learned systems.