线性伪谱模型预测能量最优姿态机动控制方法

针对大气层外飞行器大角度姿态机动控制问题，提出了一种能量最优的线性伪谱模型预测大角度姿态机动控制方法。首先，通过离线弹道规划获得满足初始、终端约束且能量最优的姿态机动控制轨迹；然后，以离线弹道为基准对姿态动力学方程进行小扰动线性化处理，获得以状态偏差为自变量的线性误差传播方程；最后，以能量最优作为性能指标，通过高斯伪谱法对原问题进行离散，推导获得满足终端偏差修正的控制解析表达式。数值计算和蒙特卡罗仿真表明，该方法不仅计算精度高、求解速度快，满足实时计算要求，而且具有较强的鲁棒性，能够实时消除各种干扰。此外，在同等控制精度条件下，该方法相对传统线性二次型调节器（LQR）跟踪方法，能量消耗减小10%。

Fuel-optimal attitude maneuver using linear pseudo-spectral model predictive control method

In order to perform large angle attitude maneuvers of spacecraft outside the atmosphere, we propose a fuel-optimal large angle attitude maneuver strategy using modified linear pseudo-spectral model predictive control method. First, a fuel-optimal attitude maneuver trajectory satisfying initial and terminal constrains is planned offline. Then, the nonlinear equation of motion is linearized under the condition of little perturbation based on the planned trajectory, and thus the linear perturbation propagation equations are obtained. Finally, the analytical solution of fuel-optimal control correction to the planned trajectory has been derivated through the discretization of state variables and control variables using Gauss pseudo-spectral method. Numerical calculation and Monte Carlo simulations were performed to validate the feasibility and effectiveness of the proposed strategy, which can provide real-time control with terminal state satisfied in high accuracy and save almost 10% fuel cost under the same control precision compared with traditional linear quadratic regulator (LQR) tracking method.