Linear Quadratic Regulator

Linear quadratic regulation (LQR) finds feedback policies that balance goals such as tracking and low control effort in systems modeled by linear dynamics and quadratic costs. Riccati equations provide the classical solution, while iterative LQR extends the approach to nonlinear trajectories and learning-based methods estimate controllers when system dynamics are unknown. Current work addresses safe and online learning, robustness to disturbances or intermittent communication, and faster computation through parallel algorithms and learned Riccati solvers. A central challenge is extending LQR’s efficient, well-understood guarantees to nonlinear or high-dimensional settings without sacrificing safety, stability, or computational practicality.