Sequential Convex Programming For Non-Linear Stochastic Optimal Control

TL;DR

This paper develops a sequential convex programming method for solving non-linear stochastic optimal control problems with Wiener process uncertainties, providing theoretical guarantees and a practical numerical approach.

Contribution

It introduces a new framework for stochastic optimal control, proving convergence properties and designing a deterministic numerical method based on the convex programming approach.

Findings

Proves that accumulation points are candidate locally-optimal solutions.

Provides sufficient conditions for the existence of accumulation points.

Designs a practical numerical method for stochastic control problems.

Abstract

This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the sequence of iterates generated by sequential convex programming is a candidate locally-optimal solution for the original problem in the sense of the stochastic Pontryagin Maximum Principle. Moreover, we provide sufficient conditions for the existence of at least one such accumulation point. We then leverage these properties to design a practical numerical method for solving non-linear stochastic optimal control problems based on a deterministic transcription of stochastic sequential convex programming.