Covariance-Regulated Recursive Koopman Learning for Nonlinear Systems with Uncertain Time-Varying Dynamics
For autonomous robots operating under uncertain, time-varying dynamics, CR-RKL provides numerically stable online learning that maintains control performance where offline models fail.
CR-RKL prevents numerical instability (covariance windup, vanishing gain) in recursive Koopman learning for nonlinear systems with time-varying dynamics, achieving stable online modeling and reliable MPC tracking on a differential-drive robot and a flapping-wing micro aerial vehicle.
Offline models for autonomous robots often fail under time-varying dynamics outside their training distribution. Koopman operator theory offers a linear representation of nonlinear dynamics via lifting, but its transition to real-time recursive estimation may suffer numerical vulnerabilities: covariance windup under low excitation when using exponential forgetting, and vanishing gain without forgetting. This paper introduces a Covariance-Regulated Recursive Koopman Learning (CR-RKL) framework with two complementary strategies--error dead-zone gating and constant-trace normalization--each independently capable of preventing covariance explosion and parameter freezing, with the latter additionally preserving the geometric structure of uncertainty. Validated on a non-holonomic differential-drive robot with wheel slip and Stribeck friction and on a 26-gram butterfly-inspired flapping-wing micro aerial vehicle, CR-RKL achieves numerically stable and accurate online modeling, and when embedded in model predictive control, it maintains reliable tracking performance under uncertain, time-varying dynamics.