Constrained NMPC Using Polynomial Chaos Theory

Establishing an accurate model of a multivariable nonlinear process with uncertain parameters can be difficult. Application of control methods based on nonlinear optimization may result in sub-optimal performance due to changes in the parameters. This paper presents a new control method to handle parametric uncertainty through incorporation of a Polynomial Chaos Theory (PCT) model used in a constrained Nonlinear Model Predictive Control (NMPC) formulation. Uncertain parameters are treated as random variables with a uniform distribution. PCT expresses the entire uncertain process by a complete and orthogonal Legendre polynomial basis in terms of random variables where expanded process outputs are determined by applying Galerkin projection onto the polynomial basis. NMPC formulation has the ability to apply hard input and soft output constraints to maintain the process within specified bounds. It is shown that the proposed formulation can be applied with an adequate tuning to minimize the effect of parametric uncertainty on the process outputs.