飞机轨迹优化问题通常涉及奇异弧类型控制、Bang-bang类型控制、主动约束类型控制等复杂情况,控制量存在突变,现有求解方法在处理含突变控制量的问题时,精度和数值稳定性之间难以达到平衡。本文分析了飞机轨迹优化问题中的控制奇异性以及主动约束对控制律突变的影响,并构建了自动解算方法。本文方法不需要人为推导控制结构的先验知识,而是在Radau伪谱法求解的基础上,添加了控制突变时刻的自动估计方法,据此将整个控制过程划分为多个阶段,然后识别各阶段的控制类型并有针对性地构建求解策略,在优化迭代中逐次逼近问题的最优解。以空客A320飞机为对象,分别采用本文方法和最优控制软件GPOPS-Ⅱ求解了含奇异性和主动约束的轨迹优化问题。数值实验表明,面对含控制突变的飞机轨迹优化问题,本文方法在数值稳定性、收敛精度等方面呈现较好的优势。
The aircraft trajectory optimization problem usually involves complex situations such as singular arc type control, Bang-bang type control and active constraint type control, and the control variable is switched. The existing solution methods are difficult to achieve a balance between accuracy and numerical stability when dealing with the problem containing switch control. In this paper, the control singularity and the influence of active constraints on the switch of control law in the aircraft trajectory optimization problem are analyzed, and an automatic solution method is constructed. The proposed method does not require the manual derivation of the prior knowledge of the control structure. Instead, based on the solution by the Radau pseudo-spectral method, an automatic estimation method for the control switch moment is added. According to this, the entire control process is divided into multiple stages. Then, the control types of each stage are identified and the solution strategies are constructed in a targeted manner to gradually approximate the optimal solution of the problem in the optimization iteration. Taking Airbus A320 aircraft as an example, the trajectory optimization problem with singularity and active constraints is solved by using the proposed method and the optimal control software GPOPS-Ⅱ respectively. Numerical experiments show that the proposed method has better advantages in numerical stability and convergence accuracy for the aircraft trajectory optimization problem with control switching.