The Optimization of the Design of Ascent Trajectory of a Vehicle
Bailing Tian · Control Engineering of China · 2012
A new method based on orthogonal collocation is proposed to deal with the difficulty of solving the ascent trajectory optimization problem.Lagrange polynomial is employed to approximate the state and control variables which are discrete values from the zeros of the second Chebyshev polynomial.The constraints of the dynamic differential equations can be transformed into algebraic equation constraints by deriving the polynomial.As a result,the infinite dimensional optimal control problem is converted to a finite dimensional nonlinear programming(NLP) problem.Following that,the transformed problem can be solved by the sequential quadratic programming(SQP) method to obtain the optimal trajectory of a vehicle.Finally,simulation results verify the effectiveness of the proposed method.The results of this study can provide feasible flight trajectory for the guidance and control of a vehicle.Besides that,the application of this method to engineering is also valuable.