PolyOCP.jl -- A Julia Package for Stochastic OCPs and MPC

TL;DR

PolyOCP.jl is a Julia package that efficiently solves stochastic optimal control problems with additive disturbances using Polynomial Chaos Expansions, filling a gap in open-source tools for such problems.

Contribution

The paper introduces PolyOCP.jl, an open-source Julia toolbox for solving stochastic OCPs with additive disturbances, based on PCE methods, which was previously unavailable.

Findings

PolyOCP.jl enables efficient solution of stochastic OCPs for linear systems.

The toolbox supports a large class of disturbance distributions.

Two examples demonstrate the toolbox's functionalities.

Abstract

The consideration of stochastic uncertainty in optimal and predictive control is a well-explored topic. Recently Polynomial Chaos Expansions (PCE) have received considerable attention for problems involving stochastically uncertain system parameters and also for problems with additive stochastic i.i.d. disturbances. While there exist a number of open-source PCE toolboxes, tailored open-source codes for the solution of OCPs involving additive stochastic i.i.d. disturbances in julia are not available. Hence, this paper introduces the toolbox PolyOCP$.$jl which enables to efficiently solve stochastic OCPs for linear systems subject to a large class of disturbance distributions. We explain the main mathematical concepts between the PCE transcription of stochastic OCPs and how they are provided in the toolbox. We draw upon two examples to illustrate the functionalities of PolyOCP$.$jl.