General Control Horizon Extension Method for Nonlinear Model Predictive Control

In the nonlinear model predictive control (NMPC) field, it is well-known that the multistep control approach is superior to the single-step approach when examining high-order nonlinear systems. In the multistep control approach, however, the online minimization of a 2-norm square objective function over a control horizon of length M always requires solving a set of complex polynomial equations, for which no definite solution exists so far. Moreover, the complex nature of the receding horizon optimization also causes additional problems to its closed-loop stability analysis. With these two serious challenges in mind, using a Volterra-Laguerre model-based NMPC for discussion, we propose a general technique to extend the control horizon with the assistance of Groebner basis, which transforms the set of complex polynomial equations to a much simpler form. We prove the closed-loop stability of the algorithm in the sense that the input and output series are both mean-square-bounded. Finally, the efficiency of this improved algorithm is examined on an industrial constant-pressure water supply system. Compared to the conventional NMPC schemes, the proposed method with the control horizon extension has shown a great potential to control a wide range of nonlinear dynamic systems.