Stochastic Optimal Trajectory Generation via Multivariate Polynomial Chaos

Abstract: This thesis presents a framework that has been developed in order to compute stochastic optimal trajectories. This is achieved by transforming the initial set of stochastic ordinary differential 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 using pseudospectral methods. The resultant trajectory is therefore less sensitive to the uncertainties included in the analysis, e.g., those present in system parameters, initial conditions or path constraints. The accurate, yet computationally efficient manner in which solutions are obtained is presented and a comparison with deterministic results show the benefits of the proposed approach for a variety of numerical examples.