Accurate and stable trajectory tracking is a key challenge for autonomous vehicles due to their highly nonlinear dynamics and multiple physical constraints. Conventional control methods often struggle to ensure closed-loop stability while satisfying these constraints in real time. To address this, this paper proposes a novel Control Lyapunov Function constrained Model Predictive Control (MPC-CLF) framework for robust nonlinear trajectory tracking. By embedding a Lyapunov stability condition as an explicit constraint within the MPC optimization, the proposed method unifies the advantages of MPC and Lyapunov theory-ensuring closed-loop stability while optimizing tracking performance under actuator limits. The controller is developed based on a nonlinear vehicle model and a quadratic Lyapunov function defined over the tracking error states. Simulation results demonstrate that the proposed MPC-CLF achieves high-accuracy trajectory tracking, satisfies input constraints, and maintains robust stability under disturbances and initial state deviations. The controller is implemented as a sparse QP solved by warm-started OSQP with a 50 ms sampling time, enabling real-time feasibility.
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