Fast, Convexified Stochastic Optimal Open-Loop Control For Linear Systems Using Empirical Characteristic Functions
Optimization and Control
2020-12-16 v3
Abstract
We consider the problem of stochastic optimal control in the presence of an unknown disturbance. We characterize the disturbance via empirical characteristic functions, and employ a chance constrained approach. By exploiting properties of characteristic functions and underapproximating cumulative distribution functions, we can reformulate a nonconvex problem by a conic, convex under-approximation. This results in extremely fast solutions that are assured to maintain probabilistic constraints. We construct algorithms for optimal open-loop control using piecewise linear approximations of the empirical characteristic function, and demonstrate our approach on two examples.
Cite
@article{arxiv.2003.04861,
title = {Fast, Convexified Stochastic Optimal Open-Loop Control For Linear Systems Using Empirical Characteristic Functions},
author = {Vignesh Sivaramakrishnan and Meeko M. K. Oishi},
journal= {arXiv preprint arXiv:2003.04861},
year = {2020}
}