Stochastic Optimal Trajectory Generation via Multivariate Polynomial Chaos

Abstract

This paper presents a framework that has been developed to compute stochastic optimal trajectories. This is done by transforming the initial set of stochastic ordinary di�erential equations into their deterministic equivalent by application of Multivariate Polynomial Chaos. Via Galerkin projection, it is possible to include stochastic information in the optimal-trajectory generation process, and to solve the corresponding Optimal Control Problem via pseudospectral methods. The resultant trajectory is less sensitive to the uncertainties included in the analysis, e.g., those present in system parameters or initial conditions. The accurate, yet computationally e�cient manner in which solutions are obtained is demonstrated; a comparison with deterministic results show the bene�ts of the proposed approach for a linear and a non-linear problem.