Robust nonlinear MPC based on Volterra series and polynomial chaos expansions

• New robust control algorithm is proposed using Volterra series model where PCE is used for representing parametric uncertainty.
• The orthogonal polynomials in PCE allows for quick calculation of output variability with an analytical expression.
• Resulting controller is computationally fast and has superior closed-loop performance when compared to SSV-based robust controller.
• Proposed controller shows superior performance compared to non-robust predictive controller based on first principles model of the process.

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.