K–R Adaptive Flight Control: Physics-Informed Nonlinear Residual Correction for Robust Trajectory Tracking Under Model Uncertainty

This paper presents a physics-informed adaptive control framework, termed K–R control, that combines a linear model-based controller (K-step) with an online nonlinear residual correction (R-step) for robust flight trajectory tracking. The R-step employs recursive least squares with ridge regularization to learn a nonlinear feature-based correction that compensates for model mismatch, aerodynamic nonlinearities, and external disturbances without requiring offline training data. The method is validated on a nonlinear F-16 aircraft model using Stevens & Lewis aerodynamic lookup tables and MIL-F-8785C Dryden turbulence. Seven scenarios are tested including extreme turbulence with 40% mass mismatch, near-stall flight, sensor failure, parameter drift, adversarial disturbances, computational latency, and multi-axis coupled control. K–R is compared against PID, LQR, MPC, L1 adaptive, and ablated variants across 100-run Monte Carlo campaigns with statistical significance testing. Results show K–R achieves the lowest RMSE in 5 of 7 scenarios, with 73% improvement over LQR under parameter drift and 42% improvement in disturbance estimation quality, while maintaining bounded weights and real-time feasibility at 34 µs per update.