Latent Linear Quadratic Regulator for Robotic Control Tasks

Model predictive control (MPC) offers high-performance control but remains computationally expensive for nonlinear dynamics, hindering its real-time deployment in robotic tasks. Inspired by the Koopman operator, we propose the $\textbf{la}$tent $\textbf{l}$inear $\textbf{q}$uadratic $\textbf{r}$egulator (LaLQR) framework, which learns an alternative latent linear-quadratic structure enabling efficient LQR-based control for nonlinear systems. LaLQR enforces the fixed Brunovsky canonical form on the latent linear dynamics to ensure controllability and numerical stability, while jointly learning a nonlinear embedding and cost function under latent state and cost prediction objectives. Experiments on diverse MuJoCo simulated robotic tasks show that LaLQR achieves comparable control quality to expensive gradient-based optimization methods while offering superior computational efficiency and superior generalization over learning-based baselines.