Offset-free Input-Output Formulations of Stochastic Model Predictive Control Based on Polynomial Chaos Theory

Abstract

Stochastic model predictive control (SMPC) formulations are proposed that have both low on-line computational cost and zero steady-state offset for constrained dynamical systems of high state dimension. The effects of probabilistic parameter uncertainties on the process outputs are quantified using polynomial chaos theory, and the scalability with state dimension is obtained by using an input-output formulation. An explanation is provided for why the structure of some SMPC formulations provide zero steady-state error whereas other seemingly reasonable formulations do not. The article also describes how to incorporate chance constraints on the states and outputs into the SMPC formulations, while retaining an online optimization whose cost has a weak dependency on the number of states and outputs.