Learning affine predictors for MPC of nonlinear systems via artificial neural networks

Nonlinear model predictive control (MPC) problems can be well approximated by linear time-varying (LTV) MPC formulations in which, at each sampling step, a quadratic programming (QP) problem based on linear predictions is constructed and solved at runtime. To reduce the associated computation burden, in this paper we explore and compare two methodologies for learning the entire output prediction over the MPC horizon as a nonlinear function of the current state but affine with respect to the sequence of future control moves to be optimized. Such a learning process is based on input/output data collected from the process to be controlled. The approach is assessed in a simulation example and compared to other similar techniques proposed in the literature, showing that it provides accurate predictions of the future evolution of the process and good closed-loop performance of the resulting MPC controller. Guidelines for tuning the proposed method to achieve a desired memory occupancy / quality of fit tradeoff are also given.