# Design of a Morphing Aircraft Based on Model Predictive Control
## 1 Introduction  
With the rapid advancement of aerospace technology, the performance requirements for aircraft have significantly increased. Traditional fixed-configuration aircraft are no longer capable of meeting the complex and diverse mission demands in both military and civilian applications [1]. In contrast, morphing aircraft, which enhance flight efficiency by dynamically adjusting their shape, have emerged as a promising solution. For instance, simulation experiments [2] have demonstrated that telescopic-wing aircraft can achieve greater roll angular velocity, maintain a larger control margin for control surfaces, and significantly improve maneuverability. This adaptability allows morphing aircraft to operate effectively across various environments and mission modes, such as cruise and maneuvering. However, the shape changes introduce significant nonlinear variations in the aircraft's dynamic characteristics, transforming it into a nonlinear system dependent on geometric parameters. This property poses new challenges for flight control system design and has become a focal point of research [3, 4, 5, 6, 7]. To address the control challenges of morphing aircraft, various solutions have been proposed. Traditional approaches, such as gain scheduling or linear parameter-varying(LPV)-based robust control methods, combine multiple simple linear controllers to handle nonlinearity, thereby reducing system design complexity while meeting the requirements of large-envelope flight [8]. For example, the study in [9] analyzes the aerodynamic parameters and morphing relationships of variable-span aircraft, establishing a LPV model and designing a global controller using robust gain scheduling. Similarly, ref. [10] proposes a two-layer polyhedral LPV multi-objective control approach, where the first layer manages scheduling parameters and designs a gain-scheduled controller on vertex-uncertain systems, while the second layer ensures robustness in the closed-loop system. Additionally, ref. [11] introduces a class of finite-time convergent adaptive sliding mode controllers (ASMC) based on a linear time-varying parameter model to enhance system adaptability and control performance. In the domain of nonlinear control, ref. [12] explores strategies for tailless aircraft in vertical flight, analyzing the following three controllers: an existing literature-based strategy, nonlinear dynamic inversion (NDI), and its incremental version (INDI). These controllers were implemented and tuned in simulations, validated through hardware-in-the-loop (HITL) tests, and applied in flight experiments. Furthermore, ref. [13] introduces a robust gain scheduling control strategy based on a sliding mode disturbance observer, improving closed-loop system robustness through disturbance compensation. Model predictive control (MPC) has also gained significant attention due to its excellent real-time optimization and constraint-handling capabilities, making it well-suited for controlling dynamically morphing aircraft [14; 15]. For instance, ref. [16] designs a multi-model switching MPC controller for the longitudinal motion equilibrium transition of morphing aircraft, optimally coordinating morphing mechanisms, engine thrust, and elevator deflections to enhance flight performance, while ensuring state variables remain within predefined limits. Similarly, ref. [17] proposes a LPV-based MPC method for the transient deformation process of a bio-inspired folding-wing UAV, reformulating the online optimization problem into a quadratic programming (QP) problem for efficient real-time solutions. However, this study primarily focuses on pitch angle and airspeed tracking, without fully considering flight stability. To further enhance robustness, ref. [18] proposes an enhanced robust nonlinear MPC method that employs an incremental Lyapunov function to compensate for disturbance effects, and it efficiently handles constraints through online optimization.