Control

Contraction Theory

Contraction theory is a framework for analyzing nonlinear system stability by studying whether trajectories converge toward each other exponentially, rather than toward a fixed equilibrium, formalized by Lohmiller and Slotine (1998) through the differential dynamics and a contraction metric. Contracting systems forget initial conditions and compose well under series, parallel, and feedback combinations, enabling modular stability certificates for observers, controllers, and learned dynamics.

Why it matters for physical AI

Contraction metrics provide tractable stability certificates for learned dynamics models and neural controllers, supporting certifiable learning-based control where trajectory-convergence guarantees are required for deployment.