Economic model predictive control based on a periodicity constraint. (August 2018)

• Record Type: Journal Article
• Authors: Wang, Ye; Salvador, José Ramón; Muñoz de la Peña, David; Puig, Vicenç; Cembrano, Gabriela
• Is Part Of: Journal of process control. Volume 68(2018)
• Page Start: 226
• Page End: 239
• Publication Date: 2018-08
• Subjects: Economic model predictive control -- Periodicity constraint -- Recursive feasibility -- Convergence analysis -- Water distribution networks; Process control -- Periodicals; Fabrication -- Contrôle -- Périodiques; Process control; Periodicals; Electronic journals; 660.281
• DOI: 10.1016/j.jprocont.2018.06.008
• Languages: English
• ISSNs: 0959-1524

Abstract

Highlights: A novel economic model predictive control formulation based on a periodicity constraint for achieving an optimal periodic operation. At each time step, the economic cost function is optimized with a periodicity constraint over all the periodic trajectories that include the current state. Convergence of the closed-loop system to a periodic trajectory is guaranteed. An optimality certificate of this trajectory is provided based on the Karush–Kuhn–Tucker conditions. An application to a well-known water distribution network benchmark is presented to demonstrate the proposed economic MPC controller. Abstract: This paper addresses a novel economic model predictive control (MPC) formulation based on a periodicity constraint to achieve an optimal periodic operation for discrete-time linear systems. The proposed control strategy does not rely on forcing the terminal state by means of a terminal equality constraint and hence it does not require a priori knowledge of a periodic steady trajectory. Instead, at each sampling time step the economic cost function is optimized based on a periodicity constraint over all the periodic trajectories that include the current state. The recursive feasibility and the closed-loop convergence to a periodic steady trajectory are discussed. Moreover, an optimality certificate of this steady trajectory is provided based on the Karush–Kuhn–Tucker (KKT) optimality conditions. Finally, an application to a well-known water distribution network benchmark is presented to demonstrate the proposed economic MPC in which the closed-loop simulation results obtained with a linear model and a virtual–reality simulator are both provided.