This paper presents a framework that has been developed to compute stochastic optimaludtrajectories. This is done by transforming the initial set of stochastic ordinary di�erentialudequations into their deterministic equivalent by application of Multivariate PolynomialudChaos. Via Galerkin projection, it is possible to include stochastic information in theudoptimal-trajectory generation process, and to solve the corresponding Optimal ControludProblem via pseudospectral methods. The resultant trajectory is less sensitive to theuduncertainties included in the analysis, e.g., those present in system parameters or initialudconditions. The accurate, yet computationally e�cient manner in which solutions areudobtained is demonstrated; a comparison with deterministic results show the bene�ts of theudproposed approach for a linear and a non-linear problem.
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机译：本文提出了一个已开发的用于计算随机最优超轨的框架。这是通过应用多元多项式 udChaos将初始随机常微分不等式集转换为确定性等价来完成的。通过Galerkin投影，可以将随机信息包括在 uoptoptical轨迹生成过程中，并可以通过伪光谱方法解决相应的Optimal Control udProblem问题。结果轨迹对分析中包括的不确定性不敏感，例如系统参数或初始条件中存在的不确定性。证明了获得解决方案的准确但计算有效的方式；与确定性结果的比较表明，对于线性和非线性问题，建议的方法的好处。
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