Adaptive Horizon Multistage Nonlinear Model Predictive Control

In this paper, we present a computationally efficient multistage nonlinear model predictive controller (NMPC) with a prediction horizon update using nonlinear programming (NLP) sensitivities. Computational delay is minimized by updating the prediction horizon to a sufficient length at every time step. For a set-point tracking multistage NMPC, we first determine a terminal region around an optimal equilibrium point for each uncertainty realization in offline mode. Then using NLP-sensitivity we estimate a sufficient horizon length for the next time step such that all scenarios will be driven into their respective terminal regions. This adaptive horizon multistage NMPC (AH-msNMPC) is recursively feasible and input-to-state practically stable. In a simulation study, the AH-msNMPC was used to control a benchmark cooled CSTR process under parametric uncertainty. The AH-msNMPC computations take 1.4% and 29.5% of the sampling interval duration for robust horizon of 1 and 2, respectively. With a robust horizon length of 1 the controller is 15 times faster than ideal-multistage NMPC with a long enough prediction horizon. The computational delay is halved with robust horizon length of 2. The performance of the two controllers was found to be similar. The improved efficiency is vital in practice for improved control performance and closed-loop stability. It is desired for real-time optimal decision making, and also under limited computing resources such as in embedded systems.