Robust model predictive control (MPC) with integral action is designed for the shell-and-tube heat exchangers that are a part of an industrial heat-exchanger network. The advanced control strategy is used for optimizing the control performance as fouling influences operation of the heat exchangers and causes changes of the heat exchangers' parameters. The time-varying parameters of the heat exchangers are considered as parametric uncertainties and robust MPC is used as it is able to handle processes with uncertainties. Integral action is implemented in the robust MPC to assure offset-free control responses. The extensive simulation case study of the robust MPC and proportional-integral-derivative (PID) control of the shell-and-tube heat exchangers confirms significantly improved control performance and energy savings when the newly designed robust MPC with integral action is used. (C) 2018 Elsevier Ltd. All rights reserved.