动力下降制导问题的两阶段序列凸化方法  

A two-stage successive convexification method for the powered descent guidance problem

作　　者：杨沐明 攸国攸 Muming Yang;Guo-You You

机构地区：[1]中国科学院数学与系统科学研究院,北京100190 [2]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学：数学》2020年第9期1361-1374,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11631013,11991020,11991021和11971372);北京智源人工智能研究院资助项目。

摘　　要：可重复使用火箭技术是近五年来航天工程领域的焦点话题.以三自由度燃料最优控制问题为具体模型,本文研究火箭回收中的关键问题—动力下降制导问题的求解.由于此模型中包含非凸动力学约束(带空气阻力项)、非凸推力大小和方向控制约束等,直接求解方法难以满足工程上实时性的需求.为了消除非凸性带来的困难,本文通过无损凸化、时间离散化和线性化技术将问题转化为一类凸规化问题,即二阶锥规划问题进行求解.此外,为了避免传统的序列凸化策略在求解本文模型时的数值不稳定现象,本文提出一个新的两阶段序列凸化方法.数值结果表明所提方法仅需求解少量的凸规化问题,且拥有比单阶段方法更稳定和高效的数值表现.In recent five years, the reusable rocket technology is a focus topic in the aerospace engineeringfield. Aiming at the three-degree-of-freedom fuel-optimal control problem, this paper studies the key problem in the rocket recovery technology: the solution of the powered descent guidance problem. Direct methods on the optimal control problem can hardly meet the real-time requirement since the model contains nonconvex dynamics,including the aerodynamic drag term, and nonconvex thrust magnitudes and direction control constraints. To eliminate the difficulty coming from the nonconvexity, we transform the model to a kind of convex programming problem, i.e., a second order cone programming problem to solve by lossless convexification, time discretization,and linearization. In addition, this paper introduces a new two-stage successive convexification method to avoid the numerical unstable phenomenon. The numerical results show that the proposed method only needs to solve several convex optimization problems and is more stable and efficient than the traditional single stage method.

关 键 词：火箭 动力下降制导 最优控制 凸化 两阶段 

分 类 号：O224[理学—运筹学与控制论] V52[理学—数学]