Convergence and stability analysis of the Extended Infinite Horizon Model Predictive Control

Model Predictive Control (MPC) is a popular technology to operate industrial systems. It refers to a class of control algorithms that use an explicit model of the system to obtain the control action by minimizing a cost function. At each time step, MPC solves an optimization problem that minimizes the future deviation of the outputs which are calculated from the model. The solution of the optimization problem is a sequence of control inputs, the first of which is actually applied to the system. The optimization process is then repeated at subsequent time steps. In the context of MPC, convergence and stability are fundamental issues. This paper presents a mathematical analysis for convergence and stability of two important controllers: the Extended Infinite Horizon MPC developed by Odloak [Odloak D. Extended robust model predictive control. AIChE J. 2004;50(8): 1824–1836] and the Extended Infinite Horizon MPC with zone control [González AH, Odloak D. A stable MPC with zone control. J Process Control. 2009;19: 110–122]. Our analysis provides tuning strategies that can be implemented in practice, and the mathematical tools we use are intended to serve as a rigorous background for future studies and developments of related MPC approaches.