Researchers prove stability of MPPI control with explicit error bounds

Model Predictive Path Integral (MPPI) control is a powerful technique for nonlinear systems because it only requires forward rollouts of dynamics—no gradients, linearizations, or convex optimizations. Until now, however, it lacked a closed-loop stability guarantee. In a new arXiv paper, researchers Hyung-Jin Yoon and Hunmin Kim close that gap by proving that MPPI can inherit stability from a deterministic nonlinear MPC policy that uses a Control Lyapunov Function terminal cost and a contraction metric.

Their key insight: if the sampling-based MPPI update approximates this reference policy closely enough, the closed-loop system remains locally stable with high probability. The approximation error splits into a finite-temperature bias floor and a Monte Carlo term that shrinks at an inverse square-root rate as sample count increases. The paper also provides an ISS (Input-to-State Stability) restatement and a practical design procedure for choosing the localization set, temperature, and number of samples—making MPPI much more predictable for real-world robotics and autonomous systems.