Stochastic Model Predictive Control (MPC)

Polynomial Chaos Expansions are used to track uncertainties in model parameters to enable stochastic model predictive control.

Stochastic Model Predictive Control formulations, based on quadratic dynamic matrix control. Polynomial chaos expansions are used to quantify the effect of uncertainties in model parameters on the predicted model output. The resulting MPC allows for fast setpoint tracking of systems with high state dimension and uncertain parameters.

This is the entire code for the paper von Andrian, M. and Braatz, R. D. (2019) "Offset-free Input-Output Formulations of Stochastic Model Predictive Control based on Polynomial Chaos Theory", Proceedings of the American Control Conference, 2019, 360-365, available at: https://doi.org/10.23919/ACC.2019.8814366

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, independent of the number of states. An explanation and mathematical proof, using the z-transform, is provided for why the structure of some SMPC formulations have zero steady-state error whereas other seemingly reasonable formulations do not.