Economic model predictive control based on a periodicity constraint. (August 2018) - Wang, Ye; Salvador, José Ramón; Muñoz de la Peña, David; Puig, Vicenç; Cembrano, Gabriela
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.