Trigonometric Regularization and Continuation Method Based Time-Optimal Control of Hypersonic Vehicles

基于三角正则化和延拓法的高超声速飞行器时间最优控制

Aiming at the time-optimal control problem of hypersonic vehicles(HSV)in ascending stage,a trigonometric regularization method(TRM)is introduced based on the indirect method of optimal control.This method avoids analyzing the switching function and distinguishing between singular control and bang-bang control,where the singular control problem is more complicated.While in bang-bang control,the costate variables are unsmooth due to the control jumping,resulting in difficulty in solving the two-point boundary value problem(TPBVP)induced by the indirect method.Aiming at the easy divergence when solving the TPBVP,the continuation method is introduced.This method uses the solution of the simplified problem as the initial value of the iteration.Then through solving a series of TPBVP,it approximates to the solution of the original complex problem.The calculation results show that through the above two methods,the time-optimal control problem of HSV in ascending stage under the complex model can be solved conveniently.

针对高超声速飞行器(Hypersonic vehicles,HSV)上升段的最优控制问题,基于间接法引入了三角正则化方法(Trigonometric regularization method,TRM)。相较于传统间接法,该方法免于分析开关函数,从而区分bang-bang控制或难以求解的奇异最优控制。bang-bang控制情况会使协态变量在控制跃变处不平滑,从而引起由间接法转化的两点边值问题(Two-point boundary value problem,TPBVP),导致求解困难。为了TPBVP求解更易收敛,引入了延拓法。该方法由简化问题的解作为延拓初值,通过求解一系列TPBVP,逼近至原复杂问题的解。计算结果表明,以上方法能够方便有效地求解高超声速飞行器上升段时间最优控制问题。