基于Legendre伪谱法的卫星轨道转移燃料最优控制

Fuel-optimal control of satellite relative orbit transfer based on legendre pseudospectral method

以真近点角为自变量,介绍了形式简单的卫星相对运动动力学模型,给出了和真近点角相匹配的性能指标.利用伪谱法将最优控制问题转化为参数优化问题,以状态转移矩阵为基础给出了仅以初末状态为约束的最优控制律,然后针对线性化模型,给出了以状态方程为约束的最优控制律.设计的控制律均为解析形式,不需要利用NPL算法进行计算.仿真结果表明设计的控制律是有效的.

This paper addresses the fuel-optimal control problem of satellite relative orbit transfer on an arbitrary elliptical orbit based on Legendre pseudospectral method. Firstly, the relative motion equations are formulated with the true anomaly as the independent variable, which are much simple. To ensure the consistency with the dynamic equations, a special cost function is proposed. Next, the optimal control problem is transformed to a parameter optimization problem using Legendre pseudospectral method. Based on the state translation matrix, a control law is obtained under the constraint of the start and final state. Then, to the linear model, another control law based on the whole state equation is presented. Unlike the methods in the literature, the above control laws are both analytical, and no computer soft is needed. Finally, the numerical results show that the control laws work well for the fuel-optimal relative orbit transfer.