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Stochastic Optimal Control using polynomial chaos variational integrators

In this paper a novel method towards solving the Stochastic Optimal Control problem is proposed, which is based on the combination of the generalized Polynomial Chaos theory and the Differential Dynamic Programming framework. Utilizing the Polynomial Chaos theory allows us to handle a wide range of uncertainties, without having to rely on limiting assumptions regarding the form of stochasticity. In addition, the Differential Dynamic Programming framework provides an iterative algorithm for finding optimal controls, which attains scalability and, under mild assumptions, fast convergence. Last but not least, towards increasing the numerical stability of our algorithm, the concept of Variational Integrators is incorporated. Numerical examples validate the applicability of the proposed approach.