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High Order Optimal Control of Space Trajectories with Uncertain Boundary Conditions

机译:具有不确定边界条件的空间轨迹的高阶最优控制

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摘要

A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth-Mars transfer.
机译:在这项工作中,基于微分代数技术的使用,提出了一种高阶最优控制策略。在轨道力学的框架中,微分代数允许通过高阶泰勒多项式表示航天器状态对初始条件和环境参数的依赖性。可以对所得多项式进行处理,以获得两点边值问题解的高阶展开。由于可以将最优控制问题简化为两点边值问题,因此使用微分代数来计算最优控制问题关于参考轨迹的解的高阶展开。只要在标称条件下发生扰动,就可以通过仅对多项式求值来获得扰动的初始状态和最终状态的新的最佳控制律。该方法的性能在登月,交会演习和低推力地-火星转移时进行评估。

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