基于Radau伪谱法的临近空间飞行器助推-滑翔段轨迹优化仿真

Boost-glide Trajectory Optimization for Near Space Vehicle using Radau Pseudospectral Method

利用Radau伪谱法求解临近空间飞行器的助推-滑翔段轨迹优化问题。该方法在一组Legendre-GaussRadau点上构造全局Lagrange插值多项式对状态变量和控制变量进行逼近,在动力学方程中状态变量对时间的导数可由插值多项式的导数来近似,故可将动力学方程约束转化为在Legendre-Gauss-Radau点上的代数微分方程约束。因此,可将连续时间的最优控制问题转化为有限维的非线性规划(NLP)问题,之后通过稀疏NLP求解器SNOPT即可对其进行求解。最后利用GPOPS软件对一种多级火箭助推-无动力滑翔的临近空间飞行器进行了上升-滑翔段的轨迹优化仿真研究和规律性总结。

Radau pseudospectral method（ RPM） is employed in solving the optimal boost-glide trajectory problem for near-space vehicle. In this method,a finite base of global Lagrange interpolating polynomials is used to approximate the states and control at a set of Legendre-Gauss-Radau points. The time derivative of the state in the dynamic equations is approximated by the derivative of the interpolating polynomial,which can be converted to the differential-algebraic equations at the Legendre-Gauss-Radau points. Consequently,the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming（ NLP） problem. Then,the resulting NLP problem is solved by a sparse nonlinear programming solver named SNOPT. GPOPS is used to solve the optimal boost-glide trajectory problem for the near-space vehicle,and the simulation results are analyzed.