(61c) Stability and Performance of Economic Model Predictive Control with Discrete Actuators
By incorporating discrete actuators, economic MPC can be applied to a much wider variety of systems, for example switched systems whose dynamics can change based on the current operating mode, as well as scheduling environments in which discrete assignments must be made between units and specific tasks. Due to the geometry of the input set, steady-state operation is often not sufficient to achieve low economic cost while still satisfying all of the necessary constraints, and thus we show how a periodic reference trajectory can be used to bound closed-loop performance. In addition, we demonstrate how cost structures like demand charges, which penalize the peak value of a state rather than a time-varying sum, can be incorporated into the economic MPC framework. Finally, by means of of simulation, we will examine the gap between realized closed-loop cost and the optimal infinite-horizon cost. The end goal is to provide a means to utilize the ongoing advances in math programming methods to implement real-time dynamic optimization within a rigorous mathematical framework. By incorporating feedback at each timestep, these controllers can quickly respond to unexpected disturbances to ensure that the process continues to operate as close to optimally as possible. With the addition of discrete actuators, economic MPC can be used to make higher-level decisions that have previously been outside the realm of feedback control, leading to improved economic performance.
Rawlings, J.B., Risbeck, M.J., 2017. Model predictive control with discrete actuators: Theory and application. Automatica 78, 258-265.
Angeli, D., Amrit, R., Rawlings, J.B., 2012. On average performance and stability of economic model predictive control. IEEE Trans. Auto. Cont. 57, 1615-1626.
Allan, D.A., Risbeck, M.J., Rawlings, J.B., 2016. Stability and robustness of model predictive control with discrete actuators. Proceedings of the American Control Conference, 32-37.