Application Research Of Nonlinear Programming Problem Solving Method In Pseudospectral Method

Pseudospectral method has unique advantages in solving the optimal control problem of aircraft trajectory,and it can parameterize the optimal control problem of aircraft trajectory into a nonlinear programming problem.The transformed trajectory nonlinear programming problems are generally highly nonlinear,strongly constrained,and large-scale.The sequential quadratic programming algorithm has fast convergence speed and high calculation accuracy,and is often used to solve the nonlinear programming problem obtained from the pseudospectral method transformation.However,when using the sequential quadratic programming algorithm to solve a large-scale complex trajectory non-linear programming problem,it will fall into a local extreme value due to insufficient initial value dependence and small convergence radius.As a result,no optimal solution or even a feasible solution can be found.This paper studies the method of solving the nonlinear programming problem in the optimal trajectory of an aircraft based on the pseudospectral method.First,taking the gliding horizontal distance of X-51A-like aircraft as the optimization target,the flight height,speed,track angle,angle of attack,and flight time as decision variables were used to construct the Bolza-type three-degree-of-freedom glide section trajectory optimization problem.Based on the aircraft longitudinal aerodynamic model theory,based on the baseline data set and the rudder effect data set,the incremental aerodynamic model of the aircraft was constructed by using the incremental method and look-up table interpolation to obtain the longitudinal aerodynamic model in the cold flow state.It provides data support for flight trajectory simulation.Secondly,the parameterization process of optimal trajectory control of aircraft based on pseudospectral method is studied,and the constructed optimal trajectory control problem is parameterized into nonlinear programming problem using Legendre pseudospectral method.Then,for the sequential quadratic programming algorithm to solve the initial value sensitivity of this type of nonlinear programming problems,two methods of multilevel iterative optimization strategy and homotopy-sequential quadratic programming are proposed.The solution provided a reliable initial value.Through simulation comparison,it is proved that both methods can effectively improve the computational efficiency and accuracy of the trajectory non-linear programming problem.Among them,the multilevel iterative optimization strategy has the most significant effect on the improvement of computing efficiency,but the accuracy of the optimal solution obtained by the homotopy-sequence quadratic programming algorithm is higher than that of the multilevel iterative optimization strategy.Finally,the improved method is applied to practice,and an online ballistic planning based on pseudospectral method is developed,which proves that the research in this paper has good practical application value.