Robust nonlinear MPC based on Volterra series and polynomial chaos expansions

Abstract

A robust nonlinear model predictive controller (NMPC) based on a Volterra series is proposed. Polynomial chaos expansions (PCE) are used to represent the uncertainty in the Volterra series coefficients and this uncertainty is then propagated onto the output predictions. The key advantage of the PCE is that it provides an analytical expression to compute the L2-norm of the output prediction error resulting in computational savings, compared to previously proposed techniques, which are essential for real time implementation. Terminal and input constraints based on Structured Singular Value based-norms are used to ensure convergence to a set-point and compliance with constraints in manipulated variables. The algorithm is applied to a multivariable pH neutralization system. A comparative study shows superior closed loop performance and computational efficiency of the proposed technique as compared to previously proposed algorithms.