An Grid Refinement Parameterization Of Control Vector Method For Reentry Trajectroy Optimization Of Hypersonic Vehicle

Hypersonci Vehicle(HV),with its fast and long-range strike capability,has attracted more and more attention from all countries,especially in the military field,and has become one of the important ways for countries to construct strategic threats and compete for space resources.Since HV does not rely on its own power in the reentry phase,it has a very high flight speed and a wide range of maneuvering capabilities,as well as strong nonlinear,which brings great difficulties to the reentry trajectory optimization.Taking HV as the research object,this thesis studies the trajectory optimization problem(TOP)of reentry phase.The aerodynamic model of HV and the constraint conditions of trajectory optimization are established.The TOP is transformed into a general optimal control problem(OCP),and the general handling method is given when the terminal time is free.Taking the maximum downrange as the objective function,the Control vector parameterization(CVP)method is used to numerically solve the HV reentry TOP under given model and aerodynamic parameters.In order to solve the problem of insufficient precision caused by the low grid discretization level of HV in the process of reentry trajectory optimization,a CVP method based on Gauss time grid parameterization is proposed.Firstly,the time scale transformation formula is used to transform the original time domain into a new time domain.Then,the LG points of Legendre polynomial in the new time domain are obtained by solving the H matrix.Then,the time scale transformation formula is used to reverse the LG points into the original time domain,and the Gauss time grid in the original time domain is obtained.Finally,numerical simulation are carried out for free terminal time and fixed terminal time,and the maximum downrange of objective function and the satisfaction of terminal constraint are analyzed.The simulation results show that the proposed CVP-G method can improve the downrange of HV reentry TOP and the satisfaction of terminal constraints under the conditions of free terminal time and fixed terminal time,respectively.Considering that CVP-G could not control the curve change adaptive during the HV reentry trajectory optimization,which led to the inaccuracy of the solution,an AC-CVP method based on time grid refinement is proposed.Firstly,the angle of attack(AOA)parameters are fitted by polynomial interpolation formula,and the expression of AOA control curve by using polynomial interpolation formula based on the Gauss time grid is obtained.Then,the arc length of the control curve is obtained by length integration.The arc length of the equidistant AOA curve and corresponding time nodes can be computed.Finally,the CVP method is carried out on the refined time grid and numerical simulation are carried out on the HV reentry TOP under the terminal time free condition.The analysis results show that the proposed AC-CVP method can further improve the downrange of HV in the reentry phase.