Optimal control method for distributed morphing aircraft based on Karhunen-Loève expansion

To solve the calculation difficulty in morphing rule optimization of the distributed morphing aircraft, an effective method is proposed. The morphing control parameters in the optimization have infinite dimensions in time and space, and the calculation difficulties are shown as follows: the present method cannot obtain the parameters for infinite dimension control; as morphing control parameters are added to the model, the aerodynamic calculation cost grows fastly to restrict the optimization process. To overcome the two difficulties, the Karhunen-Loève expansion is used to discrete the morphing area and reduce dimensions. The original optimization problem is then transformed into finite dimension optimal control problem based on parameters and geometry modalities of finite dimension morphing control. The surrogate model of aerodynamics relating to morphing control parameters is developed by Latin Hypercube Sampling (LHS) and Kriging method, reducing dramatically the high cost of computation based on CFD. The discrete finite dimension optimal control model and the surrogate model of aerodynamics are combined to build the optimization process of the morphing rule based on the hp-adaptive pseudospectral method. The optimization of the airfoil morphing progress and control parameters such as angle of attack and fuel mass flow rate in the whole trajectory is achieved in a given flight, obtaining the optimal fuel consumption morphing flight plan and demonstrating the effectiveness of the method proposed. The method can be expanded to more complex morphing objects such as airframe, and provides a support for future morphing flight technology.