Nonlinear model predictive control of a continuous bioreactor using approximate data-driven models

An analytical solution to the nonlinear model predictive control (NMPC) problem is developed for a class of nonlinear systems. Process input-output behavior is captured using Volterra and Volterra-Laguerre nonlinear polynomial models. By employing the traditional 2-norm squared NMPC objective function, the prediction equations, and hence the objective function, are explicitly constructed for an arbitrary prediction horizon of length p. Minimization of this objective function is equivalent to solving the set of polynomial equations resulting from differentiation of the objective with respect to the future manipulated variable moves over a horizon of length m. A reduced Grobner basis is constructed for the resulting polynomials, and roots of the basis polynomials represent candidate sets of solutions for the manipulated variable profile. Results from a continuous-flow bioreactor case study demonstrate the superior performance of this algorithm versus previous analytical solution methods that were limited to single-input single-output problems with a move horizon of unity.