Stochastic Variational Integrators for System Propagation and Linearization
G. De La Torre and E. A. Theodorou
https://doi.org/10.19124/ima.2015.001.17
Abstract
In this paper we present a stochastic variational integrator and its linearization. In order to motivate the use of the proposed variational integrator the Stochastic Differential Dynamical Programming (S-DDP) algorithm is considered as a benchmark for comparison. Specifically, we are interested in investigating if it is advantageous to utilize the variational integrator to propagate system trajectories and linearize system dynamics. Through numerical experiments we show that the Stochastic Differential Dynamical Programming algorithm becomes less dependent on the discretization time step and more predictable when it utilizes the proposed integrator. Furthermore, we show that a significant reduction in computational time can be achieved without sacrificing algorithm performance. Therefore, the proposed variational integrator can be used to enable real-time implementation of nonlinear optimal control algorithms.