Explicit nonlinear predictive control algorithms with neural approximation

•Two nonlinear control algorithms with neural approximation are described.•They mimic control algorithms with on-line model and trajectory linearisation.•The control signal is calculated directly from an explicit control law.•The coefficients of the control law are determined on-line by a neural approximator.•Algorithms’ advantages are demonstrated in the control system of a distillation column.

This paper describes two nonlinear Model Predictive Control (MPC) algorithms with neural approximation. The first algorithm mimics the MPC algorithm in which a linear approximation of the model is successively calculated on-line at each sampling instant and used for prediction. The second algorithm mimics the MPC strategy in which a linear approximation of the predicted output trajectory is successively calculated on-line. The presented MPC algorithms with neural approximation are very computationally efficient because the control signal is calculated directly from an explicit control law, without any optimisation. The coefficients of the control law are determined on-line by a neural network (an approximator) which is trained off-line. Thanks to using neural approximation, successive on-line linearisation and calculations typical of the classical MPC algorithms are not necessary. Development of the described MPC algorithms and their advantages (good control accuracy and computational efficiency) are demonstrated in the control system of a high-purity high-pressure ethylene-ethane distillation column. In particular, the algorithms are compared with the classical MPC algorithms with on-line linearisation.