Optimization and Analysis on Trajectory with Multiple Constraints for Hypersonic Air-vehicle

Abstract

The trajectory optimization technology is one of the key technologies for hypersonic air-vehicle. There are multiple constraints in the process of hypersonic flight, such as uncertainty of flight environment, thermal current, dynamic pressure and overload. The trajectory optimization of hypersonic air-vehicle is facing with a great challenge. This article studies the direct shooting method, the Gauss pseudo spectral method and sequential gradient-restoration algorithm, among which the direct shooting method simply makes the control variables discrete in the time domain, and obtains the status value by explicit numerical integration; Gauss pseudo spectral method makes the status variable and control variable discrete in a series of Gauss points, and constructs multinomial to approximate to the status and control variable by taking the discrete points as the nodes; sequential gradient-restoration algorithm uses iteration to meet the constraints and minimize the increment of initial value of control and status variable in order to constantly approximate to the optimal solution on condition that the constraints meet first order approximation. Finally this article conducts a numerical simulation by taking the diving segment of hypersonic air-vehicle as an example for comparative analysis on those three algorithms respectively from, such as, the initial value selection, constraint handling, convergence speed and calculation accuracy. The simulation result indicates Gauss pseudo spectral method is a method with fairly good comprehensive performance.

Keywords

• hypersonic air-vehicle
• direct shooting method
• Gauss pseudo spectral method
• sequential gradient-restoration algorithm