AN ANALYTICAL SOLUTION TO MULTIVARIABLE NONLINEAR MPC FOR SECOND-ORDER LAGUERRE SYSTEMS

An analytical solution to the multivariable (two-input, two-output) nonlinear model predictive control (NMPC) problem was derived for systems represented by (Volterra-)Laguerre models. The standard two-norm squared NMPC objective function was employed, and the minimization was carried out with m = 1 and over the prediction horizon, p. The polynomial structure of the system model yielded a polynomial objective function for the NMPC problem. Differentiation of this scalar objective function with respect to the manipulated input variables provided the first-order necessary conditions for optimality: a set of nu (equal to the number of inputs) coupled polynomials. Via Gröbner basis transformation, this set of polynomials was converted to a structured set of higher-order polynomials solvable via roots calculations and back-substitution. The algorithm was tested using a two-input two-output polymerization case study.