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

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.