A Distributed Optimization Algorithm for Stochastic Optimal Control

Abstract

This paper presents a distributed non-convex optimization algorithm for solving stochastic optimal control problems to local optimality. Here, our focus is on a class of methods that approximates the probability distribution of the states of a stochastic optimal control problem with uncertain parameters by using a sigma point approach. This leads to a large but structured optimal control problem comprising a number of carefully selected uncertainty scenarios in order to enforce chance constraints. The approach achieves accuracies that are equivalent to a third order moment expansion. However, as the resulting large but structured optimal control problem is challenging to solve with existing numerical tools, this paper proposes a tailored distributed algorithm that exploits the particular structure that arises when applying the sigma point approach. The method is based on a tailored variant of the recently proposed augmented Lagrangian based alternating direction inexact Newton (ALADIN) algorithm. The approach is illustrated by the application to a benchmark case study involving a predator-prey-fishing model.