Implications of discretization on dissipativity and economic model predictive control. (January 2017) - Olanrewaju, Olumuyiwa I.; Maciejowski, Jan M.
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.