A multi-objective optimal control trajectory optimization method for aircraft under wind influence

The constraints of the 4D trajectory optimization problem under wind influence are complex, and the multi-objective 4D trajectory optimization model is difficult to solve. To this end, the modeling and solution of the multi-objective optimization problem of the vertical profile of the trajectory under a fixed horizontal flight path considering wind influence were studied based on the optimal control method. Firstly, the optimal trajectory control model was established with the objectives of minimizing flight time and flight fuel consumption. Then, a model solution method combining trapezoidal points with $\varepsilon \text{-} {\mathrm{constraint}} $ was designed, and a two-stage solution method was proposed especially for trajectory optimization under the flight scenario by altitude layer. Then, a 4D trajectory simulation model was established to verify the effect of trajectory optimization. Finally, the actual flight plan data of the long flight route was used as an example to analyze the performance of the algorithm, and two scenarios of flight at free altitude and flight by altitude layer were used to verify the effect of trajectory optimization. The experimental results show that the proposed model and algorithm can obtain better Pareto frontier solutions than the other two commonly used algorithms, and the two-stage solution method can obtain better frontier solutions in the flight scenario by altitude layer. In the frontier solutions obtained in the scenarios of flight at free altitude and flight by altitude layer, the lowest flight fuel consumption trajectories are reduced by 6.33% and 5.94%, respectively, compared with those of the flight plan simulation trajectories. The shortest flight time trajectory is 10.16% and 10.01% lower than that of the flight plan simulation trajectory.