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.