基于混沌多项式的指令鲁棒优化及在飞行控制中的应用

Robust optimization of commands based on polynomial chaos and application in flight control

中文关键词  随机系统  不确定性分析  混沌多项式  动力学预测  鲁棒优化

英文关键词  stochastic systems  uncertainty analysis  polynomial chaos  dynamic prediction  robust optimization

中文摘要

      本文提出一种新的方法对随机系统进行运动预测和控制指令设计, 该方法可以充分利用已知信息设计控 制指令以提高闭环随机系统的鲁棒性. 首先采用混沌多项式对随机信息进行数学表述, 并利用Galerkin投影法将随 机变量的混沌多项式引入常微分方程中. 然后, 将随机变量的均值和方差考虑至优化问题的成本函数中, 并利用伪 谱法对控制指令进行鲁棒优化. 最后, 将该方法应用于飞行器的动力学预测以及控制指令设计. 仿真结果表明, 该 方法能够预测飞行器飞行过程中不确定性的演化, 其精度与蒙特卡罗方法相当, 并且计算效率更高. 此外, 获得的 控制指令对存在不确定参数或初始条件的随机系统具有强鲁棒性.

英文摘要

      In this paper, a novel method is proposed for a stochastic system to motion prediction and control command design. The proposed method can make full use of known information to design control commands to improve the robustness of the closed-loop stochastic system. First, the stochastic information is represented mathematically via polynomial chaos, and the polynomial chaos of stochastic variables are introduced into the ordinary differential equations via the Galerkin projection method. Then, the mean and variance of stochastic variables are considered into the cost function of the optimization problem, and the control command is optimized robustly via the pseudospectral method. Finally, the method is applied to dynamic prediction and control command design of aircraft. The simulation results show that the method can predict the evolution of uncertainty, in aircraft flight, with the same order of accuracy as the Monte-Carlo methods and with higher computational efficiency. Furthermore, the resultant control command has strong robustness to the stochastic system with uncertain parameters or initial conditions.