Koopman-Based Hybrid Modeling and Zonotopic Tube Robust MPC for Motion Control of Automated Vehicles

Strong nonlinearities under extreme conditions pose intractable challenges for the motion control of Automated Vehicles (AVs). Incapable or inaccurate modeling of nonlinearities, coupled with enormous cost of nonlinear controls, severely limit stability and performance enhancements in these scenarios. This paper proposes a novel modeling and robust control framework to address these issues. First, a novel hybrid modeling approach for trajectory tracking of AVs, combining a prior nominal model and a data-driven uncertain model based on Koopman theory, is proposed to enhance model predictive ability effectively. The finite approximation of Koopman operators captures the intrinsic characteristics of the nonlinear AV system via linear evolution in lifted observable space. Second, a Koopman-based Tube Robust MPC (K-TRMPC) is developed based on the hybrid model and zonotopic set theory. Koopman modeling error raised by the finite operators is considered a disturbance of the perturbed system. Tube-based design for constraint-tightening is developed for the nominal and lifted systems to guarantee closed-loop robustness. A reachability analysis on the future evolution of the perturbed system proves its convergence. Finally, the proposed framework is validated on real-time experiments and simulations, confirming the improved tracking performance on various surface conditions and vehicle stability in combined-slip scenarios.