Koopman-lifted dual-mode predictive control for intrusion detection system (IDS)-based multi-UAV formation

Abstract

This paper presents an integrated Koopman-lifted dual-mode Model Predictive Control (MPC) framework combined with an Intrusion Detection System (IDS) for secure and resilient multi-UAV formation flight. The horizontal translational dynamics of each quadrotor are abstracted, via an inner attitude loop, as a disturbed double-integrator, and the proposed architecture exploits the Koopman operator to approximately linearize the tracking dynamics in a high-dimensional lifted observable space, enabling computationally tractable predictive control with formal stability guarantees of the input-to-state type that explicitly account for the finite-dimensional Koopman approximation error and bounded process disturbances. The dual-mode structure combines an online Koopman-MPC for nominal tracking with a terminal linear quadratic regulator (LQR) activated upon anomaly detection, ensuring recursive feasibility and closed-loop stability. The integrated IDS employs a Mahalanobis distance metric computed on temporal Koopman observable residuals to detect False Data Injection Attacks (FDIA) within approximately one sampling period of the first corrupted measurement. Comprehensive simulations, including a robustness study over attack magnitudes, noise levels, attack durations, and multiple simultaneously compromised vehicles, demonstrate that the tracking error of all UAVs converges to a small bounded neighbourhood of the origin, with bounded transient errors during the attack window, the IDS-enabled framework reduces the compromised UAV’s mean tracking error by 75.5% relative to the unprotected baseline. The Lyapunov function remains bounded during the attack and decreases geometrically after recovery-mode activation.