Flight strategy optimization for high-altitude long-endurance solar-powered aircraft based on Gauss pseudo-spectral method

Solar-powered aircraft have attracted great attention owing to their potential for longendurance flight and wide application prospects.Due to the particularity of energy system,flight strategy optimization is a significant way to enhance the flight performance for solar-powered aircraft.In this study,a flight strategy optimization model for high-altitude long-endurance solar-powered aircraft was proposed.This model consists of three-dimensional kinematic model,aerodynamic model,energy collection model,energy store model and energy loss model.To solve the nonlinear optimal control problem with process constraints and terminal constraints,Gauss pseudo-spectral method was employed to discretize the state equations and constraint equations.Then a typical mission flying from given initial point to given final point within a time interval was considered.Results indicate that proper changes of the attitude angle contribute to increasing the energy gained by photovoltaic cells.Utilization of gravitational potential energy can partly take the role of battery pack.Integrating these two measures,the optimized flight strategy can improve the final state of charge compared with current constant-altitude constant-velocity strategy.The optimized strategy brings more profits on condition of lower sunlight intensity and shorter daytime.

分段对称反向高斯-约当消元法及其应用

求解变系数方程的高斯消元法与高斯-约当消元法计算原理类似、问题相近,但前者计算速度高于后者。提出分段对称反向高斯-约当消元法,其中包括根据系数矩阵结构特点构成特殊增广阵,以展示和应用元素的变化规律,并分段对上下三角元素消元以大大提高计算效率。对矩阵下三角元素正向消元及对称计算可简化所有下三角元素计算,而对上三角元素反向消元可再省略所有上三角元素计算,而取倒后的对角元素作为规格化因子可大大减少除法计算。根据单位矩阵结构特点,对其规格化或对系数矩阵上下三角元素消元时均仅计算部分对角元素和下三角元素可进一步提高计算效率。所有元素均用四角规则计算而无需计算公式以简化计算和编程。新方法大大减少了高斯-约当消元法中元素的计算,且原理简单、易于编程,可快速求解各种变系数方程,还可利用元素对称性求解常系数的节点阻抗矩阵。与高斯消元法和高斯-约当消元法相比,新方法计算速度大大提高。

基于分段高斯伪谱法的平行自主泊车路径规划

本文中提出一种在不同泊车空间采用分段高斯伪谱法的自主泊车路径规划方法。首先,通过建立车辆运动学模型,结合动力学约束、端点约束和路径避障约束,将自主泊车路径规划问题转换为最优控制问题,而在不同泊车区域内采用分段高斯伪谱法将最优控制问题离散化为非线性问题。接着,以最短泊车完成时间为优化目标函数,采用内点法对非线性问题进行优化求解得到最优泊车路径。然后,在Matlab/Simulink中搭建仿真模型,并设定了5种不同泊车位长度的平行自主泊车工况,其泊车位长度分别为车长的1.1~1.8倍。仿真结果表明,所提出的方法可统一有效对自主泊车路径规划问题进行求解,且与传统伪谱法相比仿真收敛速度更快,泊车时间更短。最后,通过实车试验进一步验证采用所提出方法的有效性。

一种火箭动力助飞高超声速飞行器轨迹优化设计方法

为提升高超声速飞行器的射程和飞行性能,提出一种基于气动力与火箭发动机推力混合控制的轨迹优化设计方法。针对高超声速飞行器再入阶段的混合控制轨迹优化问题,提出求解多段不同特征轨迹的分段高斯伪谱法,将多段最优控制问题转化为非线性规划问题。采用SQP算法对其进行求解,获取以最大射程为性能指标的飞行器轨迹优化方法,并以此研究火箭发动机在有限燃料、适当启动条件下单次和多次启动对飞行轨迹的影响。数值仿真结果表明,分段高斯伪谱法可较快速求解出火箭动力助飞高超声速飞行器最优轨迹,发动机单次启动和多次启动方案能够在不同方面改善飞行器性能。