Implications of discretization on dissipativity and economic model predictive control. (January 2017)

• Record Type: Journal Article
• Authors: Olanrewaju, Olumuyiwa I.; Maciejowski, Jan M.
• Is Part Of: Journal of process control. Volume 49(2017:Jan.)
• Page Start: 1
• Page End: 8
• Publication Date: 2017-01
• Subjects: Economic model predictive control -- Dissipativity -- Stability -- Discretization -- Direct collocation; Process control -- Periodicals; Fabrication -- Contrôle -- Périodiques; Process control; Periodicals; Electronic journals; 660.281
• DOI: 10.1016/j.jprocont.2016.11.002
• Languages: English
• ISSNs: 0959-1524

Abstract

Abstract : Highlights: Loss of dissipativity of continuous-time optimal control problems when discretized. Output of optimizer not necessarily true solution when cost function is non-convex. Wrong conclusions can be reached about system's behaviour when using economic MPC. Abstract: Economic model predictive control, where a generic cost is employed as the objective function to be minimized, has recently gained much attention in model predictive control literature. Stability proof of the resulting closed-loop system is often based on strict dissipativity of the system with respect to the objective function. In this paper, starting with a continuous-time setup, we consider the ' discretize then optimize ' approach to solving continuous-time optimal control problems and investigate the effect of the discretization process on the closed-loop system. We show that while the continuous-time system may be strictly dissipative with respect to the objective function, it is possible that the resulting closed-loop system is unstable if the discrete-approximation of the continuous-time optimal control problem is not properly set up. We use a popular example from the economic MPC literature to illustrate our results.