Stability-guaranteed model predictive control for UAVs: A survey of the Lyapunov-based framework

Unmanned Aerial Vehicles (UAVs) are increasingly deployed in safety–critical missions that demand advanced control strategies capable of addressing nonlinear dynamics, stringent constraints, and uncertain environments. Model Predictive Control (MPC) has emerged as a powerful framework for these challenges, yet its finite-horizon nature requires additional stabilizing mechanisms to ensure reliable closed-loop performance. Among the existing stabilizing strategies, Lyapunov-based MPC has attracted significant attention for embedding explicit stability conditions into the optimization problem, providing a flexible and computationally efficient alternative to terminal-ingredient formulations. This paper provides a comprehensive survey of Lyapunov-based MPC for UAVs, examining its stabilizing mechanism and tracing its evolution from a theoretical tool to a practical framework. The survey classifies existing contributions according to control tasks, modeling fidelity, system architectures, stability assurance mechanisms, and validation strategies. Beyond a descriptive review, the survey critically analyzes fundamental limitations and deployment bottlenecks related to conservatism, assumptions, and real-time implementation. Finally, key research directions are outlined, focusing on reducing conservatism, improving scalability, enhancing robustness, and strengthening implementation-aware validation. These findings position Lyapunov-based MPC as a promising framework for next-generation UAV autonomy.