A novel model-based predictive control (MPC) method is developed with the aim of applying it to periodic process control problems. By borrowing concepts From repetitive control (RC), we endow the MPC method with the ability to make continuous period-to-period improvements. The method uses a linear time-varying system description of a periodic process and can handle constraints on inputs and outputs. Some numerical examples are shown to illustrate performance improvements that can be achieved by the new method over the conventional MPC and RC methods. (C) 2001 Published by Elsevier Science Ltd. All rights reserved.