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针对飞行器上升段轨迹优化求解困难的问题,提出一种基于正交配点的优化求解方法。该方法以第二类切比雪夫正交多项式的零点作为系统控制变量和状态变量的离散点,利用拉格朗日插值多项式对状态和控制变量进行拟合。通过对多项式的求导将动力学微分方程约束转化为代数约束,从而把无限维的最优控制问题转化为一个有限维的非线性规划(Nonlinear Programming,NLP)问题。随后,利用序列二次规划(Sequential Quadratic Program-ming,SQP)方法求解转化后的NLP问题,获得最优的飞行轨迹。最后,飞行器上的仿真结果验证了所提方法的有效性。研究成果可为飞行器的制导控制提供可行的飞行轨迹,有一定的工程应用价值。
In order to solve the problem of the ascending section trajectory optimization difficultly, an optimization method based on orthogonal collocation is proposed. In this method, the zeros of the second Chebyshev orthogonal polynomials are used as the discrete points of the system control variables and state variables. The Lagrange interpolation polynomials are used to fit the state and control variables. Through the derivation of polynomials, the constraint of dynamic differential equations is transformed into algebraic constraints, so that the problem of the optimal control of infinite dimension is transformed into a finite-dimensional Nonlinear Programming (NLP) problem. Subsequently, the Sequential Quadratic Program-ming (SQP) method is used to solve the transformed NLP problem to obtain the optimal flight path. Finally, the simulation results on the aircraft verify the effectiveness of the proposed method. The research results can provide feasible flight path for the guidance and control of the aircraft, and have certain engineering application value.